# Full List of INPUT Keywords

## System variables

These variables are used to control general system parameters.

### suffix

**Type**: String**Description**: In each run, ABACUS will generate a subdirectory in the working directory. This subdirectory contains all the information of the run. The subdirectory name has the format: OUT.suffix, where the`suffix`

is the name you can pick up for your convenience.**Default**: ABACUS

### ntype

**Type**: Integer**Description**: Number of different atom species in this calculation. If this value is not equal to the atom species in the STRU file, ABACUS will stop and quit. If not set or set to 0, ABACUS will automatically set it to the atom species in the STRU file.**Default**: 0

### calculation

**Type**: String**Description**: Specify the type of calculation.scf: do self-consistent electronic structure calculation

relax: do structure relaxation calculation, one can use

`relax_nmax`

to decide how many ionic relaxations you wantcell-relax: do variable-cell relaxation calculation

nscf: do the non self-consistent electronic structure calculations. For this option, you need a charge density file. For nscf calculations with planewave basis set, pw_diag_thr should be <= 1e-3

get_pchg: For LCAO basis. Please see the explanation for variable

`nbands_istate`

get_wf: Envelope function for LCAO basis. Please see the explanation for variable

`nbands_istate`

md: molecular dynamics

test_memory : checks memory required for the calculation. The number is not quite reliable, please use it with care

test_neighbour : only performs neighbouring atom search, please specify a positive search_radius manually.

gen_bessel : generates projectors (a series of Bessel functions) for DeePKS; see also keywords bessel_descriptor_lmax, bessel_descriptor_rcut and bessel_descriptor_tolerence. A file named

`jle.orb`

will be generated which contains the projectors. An example is provided in examples/H2O-deepks-pwget_S : only works for multi-k calculation with LCAO basis. Generates and writes the overlap matrix to a file named

`SR.csr`

in the working directory. The format of the file will be the same as that generated by out_mat_hs2

**Default**: scf

### esolver_type

**Type**: String**Description**: choose the energy solver.ksdft: Kohn-Sham density functional theory

ofdft: orbital-free density functional theory

tddft: real-time time-dependent density functional theory (TDDFT)

lj: Leonard Jones potential

dp: DeeP potential, see details in md.md

**Default**: ksdft

### symmetry

**Type**: Integer**Description**: takes value 1, 0 or -1.-1: No symmetry will be considered.

0: Only time reversal symmetry would be considered in symmetry operations, which implied k point and -k point would be treated as a single k point with twice the weight.

1: Symmetry analysis will be performed to determine the type of Bravais lattice and associated symmetry operations. (point groups, space groups, primitive cells, and irreducible k-points)

**Default**:-1: if (

*dft_fuctional==hse/hf/pbe0/scan0/opt_orb*or*rpa==True*) and*calculation!=nscf*. Currently symmetry is not supported in EXX (exact exchange) calculation.0: if

*calculation==md/nscf/get_pchg/get_wf/get_S*or*[gamma_only]==True*1: else

### symmetry_prec

**Type**: Real**Description**: The accuracy for symmetry judgment. Usually the default value is good enough, but if the lattice parameters or atom positions in STRU file is not accurate enough, this value should be enlarged.Note: if

*calculation==cell_relax*, this value can be dynamically changed corresponding to the variation of accuracy of the lattice parameters and atom positions during the relaxation. The new value will be printed in`OUT.${suffix}/running_cell-relax.log`

in that case.**Default**: 1.0e-6**Unit**: Bohr

### symmetry_autoclose

**Type**: Boolean**Availability**:*symmetry==1***Description**: Control how to deal with error in symmetry analysis due to inaccurate lattice parameters or atom positions in STRU file, especially useful when*calculation==cell-relax*False: quit with an error message

True: automatically set symmetry to 0 and continue running without symmetry analysis

**Default**: True

### kpar

**Type**: Integer**Description**: divide all processors into kpar groups, and k points will be distributed among each group. The value taken should be less than or equal to the number of k points as well as the number of MPI processes.**Default**: 1

### bndpar

**Type**: Integer**Description**: divide all processors into bndpar groups, and bands (only stochastic orbitals now) will be distributed among each group. It should be larger than 0.**Default**: 1

### latname

**Type**: String**Description**: Specifies the type of Bravias lattice. When set to`none`

, the three lattice vectors are supplied explicitly in STRU file. When set to a certain Bravais lattice type, there is no need to provide lattice vector, but a few lattice parameters might be required. For more information regarding this parameter, consult the page on STRU file.Available options are (correspondence with ibrav in QE(Quantum Espresso) is given in parenthesis):

none: free structure

sc: simple cubic (1)

fcc: face-centered cubic (2)

bcc: body-centered cubic (3)

hexagonal: hexagonal (4)

trigonal: trigonal (5)

st: simple tetragonal (6)

bct: body-centered tetragonal (7)

so: orthorhombic (8)

baco: base-centered orthorhombic (9)

fco: face-centered orthorhombic (10)

bco: body-centered orthorhombic (11)

sm: simple monoclinic (12)

bacm: base-centered monoclinic (13)

triclinic: triclinic (14)

**Default**: none

### psi_initializer

**Type**: Integer**Description**: enable the experimental feature psi_initializer, to support use numerical atomic orbitals initialize wavefunction (`basis_type pw`

case).NOTE: this feature is not well-implemented for

`nspin 4`

case (closed presently), and cannot use with`calculation nscf`

/`esolver_type sdft`

cases. Available options are:0: disable psi_initializer

1: enable psi_initializer

**Default**: 0

### init_wfc

**Type**: String**Description**: Only useful for plane wave basis only now. It is the name of the starting wave functions. In the future. we should also make this variable available for localized orbitals set.Available options are:

atomic: from atomic pseudo wave functions. If they are not enough, other wave functions are initialized with random numbers.

atomic+random: add small random numbers on atomic pseudo-wavefunctions

file: from binary files

`WAVEFUNC*.dat`

, which are output by setting out_wfc_pw to`2`

.random: random numbers

with

`psi_initializer 1`

, two more options are supported:nao: from numerical atomic orbitals. If they are not enough, other wave functions are initialized with random numbers.

nao+random: add small random numbers on numerical atomic orbitals

**Default**: atomic

### init_chg

**Type**: String**Description**: This variable is used for both plane wave set and localized orbitals set. It indicates the type of starting density.atomic: the density is starting from the summation of the atomic density of single atoms.

file: the density will be read in from a binary file

`charge-density.dat`

first. If it does not exist, the charge density will be read in from cube files. Besides, when you do`nspin=1`

calculation, you only need the density file SPIN1_CHG.cube. However, if you do`nspin=2`

calculation, you also need the density file SPIN2_CHG.cube. The density file should be output with these names if you set out_chg = 1 in INPUT file.

**Default**: atomic

### init_vel

**Type**: Boolean**Description**:True: read the atom velocity (atomic unit : 1 a.u. = 21.877 Angstrom/fs) from the atom file (

`STRU`

) and determine the initial temperature md_tfirst. If md_tfirst is unset or less than zero,`init_vel`

is autoset to be`true`

.False: assign value to atom velocity using Gaussian distributed random numbers.

**Default**: False

### nelec

**Type**: Real**Description**:0.0: the total number of electrons will be calculated by the sum of valence electrons (i.e. assuming neutral system).

`>0.0`

: this denotes the total number of electrons in the system. Must be less than 2*nbands.

**Default**: 0.0

### nupdown

**Type**: Real**Description**:0.0: no constrain apply to system.

`>0.0`

: this denotes the difference number of electrons between spin-up and spin-down in the system. The range of value must in [-nelec ~ nelec]. It is one method of constraint DFT, the fermi energy level will separate to E_Fermi_up and E_Fermi_down.

**Default**: 0.0

### dft_functional

**Type**: String**Description**: In our package, the XC functional can either be set explicitly using the`dft_functional`

keyword in`INPUT`

file. If`dft_functional`

is not specified, ABACUS will use the xc functional indicated in the pseudopotential file. On the other hand, if dft_functional is specified, it will overwrite the functional from pseudopotentials and performs calculation with whichever functional the user prefers. We further offer two ways of supplying exchange-correlation functional. The first is using ‘short-hand’ names such as ‘LDA’, ‘PBE’, ‘SCAN’. A complete list of ‘short-hand’ expressions can be found in the source code. The other way is only available when, and it allows for supplying exchange-correlation functionals as combinations of LIBXC keywords for functional components, joined by a plus sign, for example, ‘dft_functional=‘LDA_X_1D_EXPONENTIAL+LDA_C_1D_CSC’. The list of LIBXC keywords can be found on its website. In this way,**compiling with LIBXC****we support all the LDA,GGA and mGGA functionals provided by LIBXC**.Furthermore, the old INPUT parameter exx_hybrid_type for hybrid functionals has been absorbed into dft_functional. Options are

`hf`

(pure Hartree-Fock),`pbe0`

(PBE0),`hse`

(Note: in order to use HSE functional, LIBXC is required). Note also that HSE has been tested while PBE0 has NOT been fully tested yet, and the maximum CPU cores for running exx in parallel is \(N(N+1)/2\), with N being the number of atoms. And forces for hybrid functionals are not supported yet.If set to

`opt_orb`

, the program will not perform hybrid functional calculation. Instead, it is going to generate opt-ABFs as discussed in this article.**Default**: same as UPF file.

### xc_temperature

**Type**: Real**Description**: specifies temperature when using temperature-dependent XC functionals (KSDT and so on).**Default**: 0.0**Unit**: Ry

### pseudo_rcut

**Type**: Real**Description**: Cut-off of radial integration for pseudopotentials**Default**: 15**Unit**: Bohr

### pseudo_mesh

**Type**: Integer**Description**:0: use our own mesh for radial integration of pseudopotentials

1: use the mesh that is consistent with quantum espresso

**Default**: 0

### mem_saver

**Type**: Boolean**Description**: Used only for nscf calculations.0: no memory saving techniques are used.

1: a memory saving technique will be used for many k point calculations.

**Default**: 0

### diago_proc

**Type**: Integer**Availability**: pw base**Description**:0: it will be set to the number of MPI processes. Normally, it is fine just leave it to the default value.

`>0`

: it specifies the number of processes used for carrying out diagonalization. Must be less than or equal to total number of MPI processes. Also, when cg diagonalization is used, diago_proc must be the same as the total number of MPI processes.

**Default**: 0

### nbspline

**Type**: Integer**Description**: If set to a natural number, a Cardinal B-spline interpolation will be used to calculate Structure Factor.`nbspline`

represents the order of B-spline basis and a larger one can get more accurate results but cost more. It is turned off by default.**Default**: -1

### kspacing

**Type**: Real**Description**: Set the smallest allowed spacing between k points, unit in 1/bohr. It should be larger than 0.0, and suggest smaller than 0.25. When you have set this value > 0.0, then the KPT file is unnecessary, and the number of K points nk_i = max(1, int(|b_i|/KSPACING_i)+1), where b_i is the reciprocal lattice vector. The default value 0.0 means that ABACUS will read the applied KPT file. If only one value is set (such as`kspacing 0.5`

), then kspacing values of a/b/c direction are all set to it; and one can also set 3 values to set the kspacing value for a/b/c direction separately (such as:`kspacing 0.5 0.6 0.7`

).Note: if gamma_only is set to be true, kspacing is invalid.

**Default**: 0.0

### min_dist_coef

**Type**: Real**Description**: a factor related to the allowed minimum distance between two atoms. At the beginning, ABACUS will check the structure, and if the distance of two atoms is shorter than min_dist_coef*(standard covalent bond length), we think this structure is unreasonable. If you want to calculate some structures in extreme conditions like high pressure, you should set this parameter as a smaller value or even 0.**Default**: 0.2

### device

**Type**: String**Description**: Specifies the computing device for ABACUS.Available options are:

cpu: for CPUs via Intel, AMD, or Other supported CPU devices

gpu: for GPUs via CUDA or ROCm.

Known limitations:

pw basis: required by the

`gpu`

acceleration optionscg/bpcg/dav ks_solver: required by the

`gpu`

acceleration options

**Default**: cpu

### precision

**Type**: String**Description**: Specifies the precision of the PW_SCF calculation.Available options are:

single: single precision

double: double precision

Known limitations:

pw basis: required by the

`single`

precision optionscg/bpcg/dav ks_solver: required by the

`single`

precision options

**Default**: double

## Electronic structure

These variables are used to control the electronic structure and geometry relaxation calculations.

### basis_type

**Type**: String**Description**: Choose the basis set.**pw**: Using plane-wave basis set only.**lcao**: Using localized atomic orbital sets.**lcao_in_pw**: Expand the localized atomic set in plane-wave basis, non-self-consistent field calculation not tested.

**Default**: pw

### ks_solver

**Type**: String**Description**: Choose the diagonalization methods for the Hamiltonian matrix expanded in a certain basis set.For plane-wave basis,

**cg**: cg method.**bpcg**: bpcg method, which is a block-parallel Conjugate Gradient (CG) method, typically exhibits higher acceleration in a GPU environment.**dav**: the Davidson algorithm.

For atomic orbitals basis,

**genelpa**: This method should be used if you choose localized orbitals.**scalapack_gvx**: Scalapack can also be used for localized orbitals.**cusolver**: (Unavailable currently, it will be fixed in future versions) This method needs building with the cusolver component for lcao and at least one gpu is available.

If you set ks_solver=

`genelpa`

for basis_type=`pw`

, the program will be stopped with an error message:genelpa can not be used with plane wave basis.

Then the user has to correct the input file and restart the calculation.

**Default**: cg (plane-wave basis), or genelpa (localized atomic orbital basis, if compiling option`USE_ELPA`

has been set), scalapack_gvx, (localized atomic orbital basis, if compiling option`USE_ELPA`

has not been set)

### nbands

**Type**: Integer**Description**: The number of Kohn-Sham orbitals to calculate. It is recommended to setup this value, especially when smearing techniques are utilized, more bands should be included.**Default**:nspin=1: max(1.2*occupied_bands, occupied_bands + 10)

nspin=2: max(1.2*nelec_spin, nelec_spin + 10), in which nelec_spin = max(nelec_spin_up, nelec_spin_down)

nspin=4: max(1.2*nelec, nelec + 20)

### nbands_istate

**Type**: Integer**Availability**: Only used when`calculation = get_wf`

or`calculation = get_pchg`

.**Description**: The number of bands around the Fermi level you would like to calculate.`get_wf`

means to calculate the envelope functions of wave functions \(\Psi_{i}=\Sigma_{\mu}C_{i\mu}\Phi_{\mu}\), where \(\Psi_{i}\) is the ith wave function with the band index \(i\) and \(\Phi_{\mu}\) is the localized atomic orbital set.`get_pchg`

means to calculate the density of each wave function \(|\Psi_{i}|^{2}\). Specifically, suppose we have highest occupied bands at 100th wave functions. And if you set this variable to 5, it will print five wave functions from 96th to 105th. But before all this can be carried out, the wave functions coefficients should be first calculated and written into a file by setting the flag`out_wfc_lcao = 1`

.**Default**: 5

### nspin

**Type**: Integer**Description**: The number of spin components of wave functions.**1**: Spin degeneracy**2**: Collinear spin polarized.**4**: For the case of noncollinear polarized, nspin will be automatically set to 4 without being specified by the user.

**Default**: 1

### smearing_method

**Type**: String**Description**: It indicates which occupation and smearing method is used in the calculation.**fixed**: fixed occupations (available for non-coductors only)**gauss**or**gaussian**: Gaussian smearing method.**mp**: methfessel-paxton smearing method; recommended for metals.**mp2**: 2-nd methfessel-paxton smearing method; recommended for metals.**mv**or**cold**: marzari-vanderbilt smearing method.**fd**: Fermi-Dirac smearing method: \(f=1/\{1+\exp[(E-\mu)/kT]\}\) and smearing_sigma below is the temperature \(T\) (in Ry).

**Default**: gauss

### smearing_sigma

**Type**: Real**Description**: Energy range for smearing.**Default**: 0.015**Unit**: Ry

### smearing_sigma_temp

**Type**: Real**Description**: Energy range for smearing,`smearing_sigma`

= 1/2 * kB *`smearing_sigma_temp`

.**Default**: 2 *`smearing_sigma`

/ kB.**Unit**: K

### mixing_type

**Type**: String**Description**: Charge mixing methods.**plain**: Just simple mixing.**pulay**: Standard Pulay method. P. Pulay Chemical Physics Letters, (1980)**broyden**: Simplified modified Broyden method. D.D. Johnson Physical Review B (1988)

In general, the convergence of the Broyden method is slightly faster than that of the Pulay method.

**Default**: broyden

### mixing_beta

**Type**: Real**Description**: In general, the formula of charge mixing can be written as \(\rho_{new} = \rho_{old} + \beta * \rho_{update}\), where \(\rho_{new}\) represents the new charge density after charge mixing, \(\rho_{old}\) represents the charge density in previous step, \(\rho_{update}\) is obtained through various mixing methods, and \(\beta\) is set by the parameter`mixing_beta`

. A lower value of ‘mixing_beta’ results in less influence of \(\rho_{update}\) on \(\rho_{new}\), making the self-consistent field (SCF) calculation more stable. However, it may require more steps to achieve convergence. We recommend the following options:**0.8**:`nspin=1`

**0.4**:`nspin=2`

and`nspin=4`

**0**: keep charge density unchanged, usually used for restarting with`init_chg=file`

or testing.**0.1 or less**: if convergence of SCF calculation is difficult to reach, please try`0 < mixing_beta < 0.1`

.

Note: For low-dimensional large systems, the setup of

`mixing_beta=0.1`

,`mixing_ndim=20`

, and`mixing_gg0=1.0`

usually works well.**Default**: 0.8 for`nspin=1`

, 0.4 for`nspin=2`

and`nspin=4`

.

### mixing_beta_mag

**Type**: Real**Description**: Mixing parameter of magnetic density.**Default**:`4*mixing_beta`

, but the maximum value is 1.6.

### mixing_ndim

**Type**: Integer**Description**: It indicates the mixing dimensions in Pulay or Broyden. Pulay and Broyden method use the density from previous mixing_ndim steps and do a charge mixing based on this density.For systems that are difficult to converge, one could try increasing the value of ‘mixing_ndim’ to enhance the stability of the self-consistent field (SCF) calculation.

**Default**: 8

### mixing_restart

**Type**: Integer**Description**: At`mixing_restart`

-th iteration, SCF will restart by using output charge density from perivos iteration as input charge density directly, and start a new mixing.`mixing_restart=0|1`

means SCF starts from scratch.**Default**: 0

### mixing_dmr

**Type**: bool**Availability**: Only for`mixing_restart>=2`

**Description**: At`mixing_restart`

-th iteration, SCF will start a mixing for real-space density matrix by using the same coefficiences as the mixing of charge density.**Default**: false

### mixing_gg0

**Type**: Real**Description**: Whether to perfom Kerker scaling for charge density.**>0**: The high frequency wave vectors will be suppressed by multiplying a scaling factor \(\frac{k^2}{k^2+gg0^2}\). Setting`mixing_gg0 = 1.0`

is normally a good starting point. Kerker preconditioner will be automatically turned off if`mixing_beta <= 0.1`

.**0**: No Kerker scaling is performed.

For systems that are difficult to converge, particularly metallic systems, enabling Kerker scaling may aid in achieving convergence.

**Default**: 1.0

### mixing_gg0_mag

**Type**: Real**Description**: Whether to perfom Kerker preconditioner of magnetic density. Note: we do not recommand to open Kerker preconditioner of magnetic density unless the system is too hard to converge.**Default**: 0.0

### mixing_gg0_min

**Type**: Real**Description**: the minimum kerker coefficient**Default**: 0.1

### mixing_angle

**Type**: Real**Availability**: Only relevant for non-colinear calculations`nspin=4`

.**Description**: Normal broyden mixing can give the converged result for a given magnetic configuration. If one is not interested in the energies of a given magnetic configuration but wants to determine the ground state by relaxing the magnetic moments’ directions, one cannot rely on the standard Broyden mixing algorithm. To enhance the ability to find correct magnetic configuration for non-colinear calculations, ABACUS implements a promising mixing method proposed by J. Phys. Soc. Jpn. 82 (2013) 114706. Here,`mixing_angle`

is the angle mixing parameter. In fact, only`mixing_angle=1.0`

is implemented currently.**<=0**: Normal broyden mixing for \(m_{x}, m_{y}, m_{z}\)**>0**: Angle mixing for the modulus \(|m|\) with`mixing_angle=1.0`

**Default**: -10.0

Note: In new angle mixing, you should set `mixing_beta_mag >> mixing_beta`

. The setup of `mixing_beta=0.2`

, `mixing_beta_mag=1.0`

usually works well.

### mixing_tau

**Type**: Boolean**Availability**: Only relevant for meta-GGA calculations.**Description**: Whether to mix the kinetic energy density.**True**: The kinetic energy density will also be mixed. It seems for general cases, SCF converges fine even without this mixing. However, if there is difficulty in converging SCF for meta-GGA, it might be helpful to turn this on.**False**: The kinetic energy density will not be mixed.

**Default**: False

### mixing_dftu

**Type**: Boolean**Availability**: Only relevant for DFT+U calculations.**Description**: Whether to mix the occupation matrices.**True**: The occupation matrices will also be mixed by plain mixing. From experience this is not very helpful if the +U calculation does not converge.**False**: The occupation matrices will not be mixed.

**Default**: False

### gamma_only

**Type**: Integer**Availability**: Only used in localized orbitals set**Description**: Whether to use gamma_only algorithm.**0**: more than one k-point is used and the ABACUS is slower compared to the gamma only algorithm.**1**: ABACUS uses gamma only, the algorithm is faster and you don’t need to specify the k-points file.

Note: If gamma_only is set to 1, the KPT file will be overwritten. So make sure to turn off gamma_only for multi-k calculations.

**Default**: 0

### printe

**Type**: Integer**Description**: Print out energy for each band for every printe step**Default**: 100

### scf_nmax

**Type**: Integer**Description**: This variable indicates the maximal iteration number for electronic iterations.**Default**: 100

### scf_thr

**Type**: Real**Description**: It’s the threshold for electronic iteration. It represents the charge density error between two sequential densities from electronic iterations. Usually for local orbitals, usually 1e-6 may be accurate enough.**Default**: 1.0e-9 (plane-wave basis), or 1.0e-7 (localized atomic orbital basis).

### scf_thr_type

**Type**: Integer**Description**: Choose the calculation method of convergence criterion.**1**: the criterion is defined as \(\Delta\rho_G = \frac{1}{2}\iint{\frac{\Delta\rho(r)\Delta\rho(r')}{|r-r'|}d^3r d^3r'}\).**2**: the criterion is defined as \(\Delta\rho_R = \int{|\Delta\rho(r)|d^3r}\).

Note: This parameter is still under testing and the default setting is usually sufficient.

**Default**: 1 (plane-wave basis), or 2 (localized atomic orbital basis).

### chg_extrap

**Type**: String**Description**: Methods to do extrapolation of density when ABACUS is doing geometry relaxations or molecular dynamics.**atomic**: atomic extrapolation.**first-order**: first-order extrapolation.**second-order**: second-order extrapolation.

**Default**: first-order (geometry relaxations), second-order (molecular dynamics), else atomic

### lspinorb

**Type**: Boolean**Description**: Whether to consider spin-orbital coupling effect in the calculation.**True**: Consider spin-orbital coupling effect, and`nspin`

is also automatically set to 4.**False**: Do not consider spin-orbital coupling effect.

**Default**: False

### noncolin

**Type**: Boolean**Description**: Whether to allow non-collinear polarization, in which case the coupling between spin up and spin down will be taken into account.**True**: Allow non-collinear polarization, and`nspin`

is also automatically set to 4.**False**: Do not allow non-collinear polarization.

**Default**: False

### soc_lambda

**Type**: Real**Availability**: Relevant for soc calculations.**Description**: Sometimes, for some real materials, both scalar-relativistic and full-relativistic can not describe the exact spin-orbit coupling. Artificial modulation may help in such cases.`soc_lambda`

, which has value range [0.0, 1.0] , is used for modulate SOC effect.In particular,

`soc_lambda 0.0`

refers to scalar-relativistic case and`soc_lambda 1.0`

refers to full-relativistic case.**Default**: 1.0

## Electronic structure (SDFT)

These variables are used to control the parameters of stochastic DFT (SDFT), mix stochastic-deterministic DFT (MDFT), or complete-basis Chebyshev method (CT). In the following text, stochastic DFT is used to refer to these three methods. We suggest using SDFT to calculate high-temperature systems and we only support smearing_method “fd”. Both “scf” and “nscf” calculation are supported.

### method_sto

**Type**: Integer**Availability**: esolver_type =`sdft`

**Description**: Different methods to do stochastic DFT1: Calculate \(T_n(\hat{h})\ket{\chi}\) twice, where \(T_n(x)\) is the n-th order Chebyshev polynomial and \(\hat{h}=\frac{\hat{H}-\bar{E}}{\Delta E}\) owning eigenvalues \(\in(-1,1)\). This method cost less memory but is slower.

2: Calculate \(T_n(\hat{h})\ket{\chi}\) once but needs much more memory. This method is much faster. Besides, it calculates \(N_e\) with \(\bra{\chi}\sqrt{\hat f}\sqrt{\hat f}\ket{\chi}\), which needs a smaller nche_sto. However, when the memory is not enough, only method 1 can be used.

other: use 2

**Default**: 2

### nbands_sto

**Type**: Integer or string**Availability**: esolver_type =`sdft`

**Description**: The number of stochastic orbitals> 0: Perform stochastic DFT. Increasing the number of bands improves accuracy and reduces stochastic errors, which scale as \(1/\sqrt{N_{\chi}}\); To perform mixed stochastic-deterministic DFT, you should set nbands, which represents the number of KS orbitals.

0: Perform Kohn-Sham DFT.

all: All complete basis sets are used to replace stochastic orbitals with the Chebyshev method (CT), resulting in the same results as KSDFT without stochastic errors.

**Default**: 256

### nche_sto

**Type**: Integer**Availability**: esolver_type =`sdft`

**Description**: Chebyshev expansion orders for stochastic DFT.**Default**: 100

### emin_sto

**Type**: Real**Availability**: esolver_type =`sdft`

**Description**: Trial energy to guess the lower bound of eigen energies of the Hamiltonian Operator \(\hat{H}\).**Default**: 0.0**Unit**: Ry

### emax_sto

**Type**: Real**Availability**: esolver_type =`sdft`

**Description**: Trial energy to guess the upper bound of eigen energies of the Hamiltonian Operator \(\hat{H}\).**Default**: 0.0**Unit**: Ry

### seed_sto

**Type**: Integer**Availability**: esolver_type =`sdft`

**Description**: The random seed to generate stochastic orbitals.>= 0: Stochastic orbitals have the form of \(\exp(i2\pi\theta(G))\), where \(\theta\) is a uniform distribution in \((0,1)\).

0: the seed is decided by time(NULL).

<= -1: Stochastic orbitals have the form of \(\pm1\) with equal probability.

-1: the seed is decided by time(NULL).

**Default**: 0

### initsto_ecut

**Type**: Real**Availability**: esolver_type =`sdft`

**Description**: Stochastic wave functions are initialized in a large box generated by “4*`initsto_ecut`

”.`initsto_ecut`

should be larger than ecutwfc. In this method, SDFT results are the same when using different cores. Besides, coefficients of the same G are the same when ecutwfc is rising to initsto_ecut. If it is smaller than ecutwfc, it will be turned off.**Default**: 0.0**Unit**: Ry

### initsto_freq

**Type**: Integer**Availability**: esolver_type =`sdft`

**Description**: Frequency (once each initsto_freq steps) to generate new stochastic orbitals when running md.positive integer: Update stochastic orbitals

0: Never change stochastic orbitals.

**Default**: 0

### npart_sto

**Type**: Integer**Availability**: method_sto =`2`

and out_dos =`True`

or cal_cond =`True`

**Description**: Make memory cost to 1/npart_sto times of the previous one when running the post process of SDFT like DOS or conductivities.**Default**: 1

## Geometry relaxation

These variables are used to control the geometry relaxation.

### relax_method

**Type**: String**Description**: The methods to do geometry optimization.cg: using the conjugate gradient (CG) algorithm. Note that there are two implementations of the conjugate gradient (CG) method, see relax_new.

bfgs: using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.

cg_bfgs: using the CG method for the initial steps, and switching to BFGS method when the force convergence is smaller than relax_cg_thr.

sd: using the steepest descent (SD) algorithm.

fire: the Fast Inertial Relaxation Engine method (FIRE), a kind of molecular-dynamics-based relaxation algorithm, is implemented in the molecular dynamics (MD) module. The algorithm can be used by setting calculation to

`md`

and md_type to`fire`

. Also ionic velocities should be set in this case. See fire for more details.

**Default**: cg

### relax_new

**Type**: Boolean**Description**: At around the end of 2022 we made a new implementation of the Conjugate Gradient (CG) method for`relax`

and`cell-relax`

calculations. But the old implementation was also kept.True: use the new implementation of CG method for

`relax`

and`cell-relax`

calculations.False: use the old implementation of CG method for

`relax`

and`cell-relax`

calculations.

**Default**: True

### relax_scale_force

**Type**: Real**Availability**: only used when`relax_new`

set to`True`

**Description**: The paramether controls the size of the first conjugate gradient step. A smaller value means the first step along a new CG direction is smaller. This might be helpful for large systems, where it is safer to take a smaller initial step to prevent the collapse of the whole configuration.**Default**: 0.5

### relax_nmax

**Type**: Integer**Description**: The maximal number of ionic iteration steps, the minimum value is 1.**Default**: 1

### relax_cg_thr

**Type**: Real**Description**: When move-method is set to`cg_bfgs`

, a mixed algorithm of conjugate gradient (CG) method and Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is used. The ions first move according to CG method, then switched to BFGS method when the maximum of force on atoms is reduced below the CG force threshold, which is set by this parameter.**Default**: 0.5**Unit**: eV/Angstrom

### cal_force

**Type**: Boolean**Description**:**True**calculate the force at the end of the electronic iteration**False**no force calculation at the end of the electronic iteration

**Default**: False if`calculation`

is set to`scf`

, True if`calculation`

is set to`cell-relax`

,`relax`

, or`md`

.

### force_thr

**Type**: Real**Description**: Threshold of the force convergence in Ry/Bohr. The threshold is compared with the largest force among all of the atoms. The recommended value for using atomic orbitals is 0.04 eV/Angstrom (0.0016 Ry/Bohr). The parameter is equivalent to force_thr_ev except for the unit. You may choose either you like.**Default**: 0.001**Unit**: Ry/Bohr (25.7112 eV/Angstrom)

### force_thr_ev

**Type**: Real**Description**: Threshold of the force convergence in eV/Angstrom. The threshold is compared with the largest force among all of the atoms. The recommended value for using atomic orbitals is 0.04 eV/Angstrom (0.0016 Ry/Bohr). The parameter is equivalent to force_thr except for the unit. You may choose either you like.**Default**: 0.0257112**Unit**: eV/Angstrom (0.03889 Ry/Bohr)

### force_thr_ev2

**Type**: Real**Description**: The calculated force will be set to 0 when it is smaller than the parameter`force_thr_ev2`

.**Default**: 0.0**Unit**: eV/Angstrom

### relax_bfgs_w1

**Type**: Real**Description**: This variable controls the Wolfe condition for Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm used in geometry relaxation. You can look into the paper Phys.Chem.Chem.Phys.,2000,2,2177 for more information.**Default**: 0.01

### relax_bfgs_w2

**Type**: Real**Description**: This variable controls the Wolfe condition for Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm used in geometry relaxation. You can look into the paper Phys.Chem.Chem.Phys.,2000,2,2177 for more information.**Default**: 0.5

### relax_bfgs_rmax

**Type**: Real**Description**: This variable is for geometry optimization. It stands for the maximal movement of all the atoms. The sum of the movements from all atoms can be increased during the optimization steps. However, it can not be larger than`relax_bfgs_rmax`

**Unit**: Bohr**Default**: 0.8

### relax_bfgs_rmin

**Type**: Real**Description**: This variable is for geometry optimization. It indicates the minimal movement of all the atoms. When the movement of all the atoms is smaller than relax_bfgs_rmin Bohr, and the force convergence is still not achieved, the calculation will break down.**Default**: 1e-5**Unit**: Bohr

### relax_bfgs_init

**Type**: Real**Description**: This variable is for geometry optimization. It stands for the sum of initial movements of all of the atoms.**Default**: 0.5**Unit**: Bohr

### cal_stress

**Type**: Boolean**Description**:**True**: calculate the stress at the end of the electronic iteration**False**: no calculation of the stress at the end of the electronic iteration

**Default**: True if`calculation`

is`cell-relax`

, False otherwise.

### stress_thr

**Type**: Real**Description**: The threshold of the stress convergence. The threshold is compared with the largest component of the stress tensor.**Default**: 0.5**Unit**: kbar

### press1, press2, press3

**Type**: Real**Description**: The external pressures along three axes. Positive input value is taken as compressive stress.**Default**: 0**Unit**: kbar

### fixed_axes

**Type**: String**Availability**: only used when`calculation`

set to`cell-relax`

**Description**: Axes that are fixed during cell relaxation. Possible choices are:**None**: default; all of the axes can relax**volume**: relaxation with fixed volume**shape**: fix shape but change volume (i.e. only lattice constant changes)**a**: fix a axis during relaxation**b**: fix b axis during relaxation**c**: fix c axis during relaxation**ab**: fix both a and b axes during relaxation**ac**: fix both a and c axes during relaxation**bc**: fix both b and c axes during relaxation

Note : fixed_axes = “shape” and “volume” are only available for relax_new = True

**Default**: None

### fixed_ibrav

**Type**: Boolean**Availability**: Must be used along with relax_new set to True, and a specific latname must be provided**Description**:**True**: the lattice type will be preserved during relaxation**False**: No restrictions are exerted during relaxation in terms of lattice type

Note: it is possible to use

`fixed_ibrav`

with`fixed_axes`

, but please make sure you know what you are doing. For example, if we are doing relaxation of a simple cubic lattice (`latname`

= “sc”), and we use`fixed_ibrav`

along with`fixed_axes`

= “volume”, then the cell is never allowed to move and as a result, the relaxation never converges.

**Default**: False

### fixed_atoms

**Type**: Boolean**Description**:**True**: The direct coordinates of atoms will be preserved during variable-cell relaxation.**False**: No restrictions are exerted on positions of all atoms. However, users can still fix certain components of certain atoms by using the`m`

keyword in`STRU`

file. For the latter option, check the end of this instruction.

**Default**: False

### cell_factor

**Type**: Real**Description**: Used in the construction of the pseudopotential tables. It should exceed the maximum linear contraction of the cell during a simulation.**Default**: 1.2

## Density of states

These variables are used to control the calculation of DOS. Detailed introduction

### dos_edelta_ev

**Type**: Real**Description**: the step size in writing Density of States (DOS)**Default**: 0.01**Unit**: eV

### dos_sigma

**Type**: Real**Description**: the width of the Gaussian factor when obtaining smeared Density of States (DOS)**Default**: 0.07**Unit**: eV

### dos_scale

**Type**: Real**Description**: Defines the energy range of DOS output as (emax-emin)*(1+dos_scale), centered at (emax+emin)/2. This parameter will be used when dos_emin and dos_emax are not set.**Default**: 0.01**Unit**: eV

### dos_emin_ev

**Type**: Real**Description**: the minimal range for Density of States (DOS)If set, “dos_scale” will be ignored.

**Default**: Minimal eigenenergy of \(\hat{H}\)**Unit**: eV

### dos_emax_ev

**Type**: Real**Description**: the maximal range for Density of States (DOS)If set, “dos_scale” will be ignored.

**Default**: Maximal eigenenergy of \(\hat{H}\)**Unit**: eV

### dos_nche

**Type**: Integer The order of Chebyshev expansions when using Stochastic Density Functional Theory (SDFT) to calculate DOS.**Default**: 100

## NAOs

These variables are used to control the generation of numerical atomic orbitals (NAOs), whose radial parts are linear combinations of spherical Bessel functions with a node (i.e., evaluate to zero) at the cutoff radius. In plane-wave-based calculations, necessary information will be printed into `OUT.${suffix}/orb_matrix.${i}.dat`

, which serves as an input file for the generation of NAOs. Please check SIAB package for more information.

### bessel_nao_ecut

**Type**: Real**Description**: “Energy cutoff” (in Ry) of spherical Bessel functions. The number of spherical Bessel functions that constitute the radial parts of NAOs is determined by sqrt(`bessel_nao_ecut`

)\(\times\)`bessel_nao_rcut`

/\(\pi\).**Default**:`ecutwfc`

### bessel_nao_tolerence

**Type**: Real**Description**: tolerance when searching for the zeros of spherical Bessel functions.**Default**: 1.0e-12

### bessel_nao_rcut

**Type**: Real**Description**: Cutoff radius (in Bohr) and the common node of spherical Bessel functions used to construct the NAOs.**Default**: 6.0

### bessel_nao_smooth

**Type**: Boolean**Description**: if True, NAOs will be smoothed near the cutoff radius by \(1-\exp\left(-\frac{(r-r_{cut})^2}{2\sigma^2}\right)\). See`bessel_nao_rcut`

for \(r_{cut}\) and`bessel_nao_sigma`

for \(\sigma\).**Default**: True

### bessel_nao_sigma

**Type**: Real**Description**: Smoothing range (in Bohr). See also`bessel_nao_smooth`

.**Default**: 0.1

## DeePKS

These variables are used to control the usage of DeePKS method (a comprehensive data-driven approach to improve the accuracy of DFT). Warning: this function is not robust enough for the current version. Please try the following variables at your own risk:

### deepks_out_labels

**Type**: Boolean**Availability**: numerical atomic orbital basis**Description**: print energy and force labels and descriptors for DeePKS training**Note**: In`LCAO`

calculation, the path of a numerical descriptor (an`orb`

file) is needed to be specified under the`NUMERICAL_DESCRIPTOR`

tag in the`STRU`

file. For example:NUMERICAL_ORBITAL H_gga_8au_60Ry_2s1p.orb O_gga_7au_60Ry_2s2p1d.orb NUMERICAL_DESCRIPTOR jle.orb

**Default**: False

### deepks_scf

**Type**: Boolean**Availability**: numerical atomic orbital basis**Description**: perform self-consistent field iteration in DeePKS method**Note**: A trained, traced model file is needed.**Default**: False

### deepks_model

**Type**: String**Availability**: numerical atomic orbital basis and`deepks_scf`

is true**Description**: the path of the trained, traced neural network model file generated by deepks-kit**Default**: None

### bessel_descriptor_lmax

**Type**: Integer**Availability**:`gen_bessel`

calculation**Description**: the maximum angular momentum of the Bessel functions generated as the projectors in DeePKS**NOte**: To generate such projectors, set calculation type to`gen_bessel`

in ABACUS. See also calculation.**Default**: 2

### bessel_descriptor_ecut

**Type**: Real**Availability**:`gen_bessel`

calculation**Description**: energy cutoff of Bessel functions**Default**: same as ecutwfc**Unit**: Ry

### bessel_descriptor_tolerence

**Type**: Real**Availability**:`gen_bessel`

calculation**Description**: tolerance for searching the zeros of Bessel functions**Default**: 1.0e-12

### bessel_descriptor_rcut

**Type**: Real**Availability**:`gen_bessel`

calculation**Description**: cutoff radius of Bessel functions**Default**: 6.0**Unit**: Bohr

### bessel_descriptor_smooth

**Type**: Boolean**Availability**:`gen_bessel`

calculation**Description**: smooth the Bessel functions at radius cutoff**Default**: False

### bessel_descriptor_sigma

**Type**: Real**Availability**:`gen_bessel`

calculation**Description**: smooth parameter at the cutoff radius of projectors**Default**: 0.1**Unit**: Bohr

### deepks_bandgap

**Type**: Boolean**Availability**: numerical atomic orbital basis and`deepks_scf`

is true**Description**: include bandgap label for DeePKS training**Default**: False

### deepks_out_unittest

**Type**: Boolean**Description**: generate files for constructing DeePKS unit test**Note**: Not relevant when running actual calculations. When set to 1, ABACUS needs to be run with only 1 process.**Default**: False

## OFDFT: orbital free density functional theory

### of_kinetic

**Type**: String**Availability**: OFDFT**Description**: The type of KEDF (kinetic energy density functional).**wt**: Wang-Teter.**tf**: Thomas-Fermi.**vw**: von Weizsäcker.**tf+**: TF\(\rm{\lambda}\)vW, the parameter \(\rm{\lambda}\) can be set by`of_vw_weight`

.**lkt**: Luo-Karasiev-Trickey.

**Default**: wt

### of_method

**Type**: String**Availability**: OFDFT**Description**: The optimization method used in OFDFT.**cg1**: Polak-Ribiere. Standard CG algorithm.**cg2**: Hager-Zhang (generally faster than cg1).**tn**: Truncated Newton algorithm.

**Default**:tn

### of_conv

**Type**: String**Availability**: OFDFT**Description**: Criterion used to check the convergence of OFDFT.**energy**: Ttotal energy changes less than`of_tole`

.**potential**: The norm of potential is less than`of_tolp`

.**both**: Both energy and potential must satisfy the convergence criterion.

**Default**: energy

### of_tole

**Type**: Real**Availability**: OFDFT**Description**: Tolerance of the energy change for determining the convergence.**Default**: 2e-6**Unit**: Ry

### of_tolp

**Type**: Real**Availability**: OFDFT**Description**: Tolerance of potential for determining the convergence.**Default**: 1e-5**Unit**: Ry

### of_tf_weight

**Type**: Real**Availability**: OFDFT with`of_kinetic=tf, tf+, wt`

**Description**: Weight of TF KEDF (kinetic energy density functional).**Default**: 1.0

### of_vw_weight

**Type**: Real**Availability**: OFDFT with`of_kinetic=vw, tf+, wt, lkt`

**Description**: Weight of vW KEDF (kinetic energy density functional).**Default**: 1.0

### of_wt_alpha

**Type**: Real**Availability**: OFDFT with`of_kinetic=wt`

**Description**: Parameter alpha of WT KEDF (kinetic energy density functional).**Default**: \(5/6\)

### of_wt_beta

**Type**: Real**Availability**: OFDFT with`of_kinetic=wt`

**Description**: Parameter beta of WT KEDF (kinetic energy density functional).**Default**: \(5/6\)

### of_wt_rho0

**Type**: Real**Availability**: OFDFT with`of_kinetic=wt`

**Description**: The average density of system.**Default**: 0.0**Unit**: Bohr^-3

### of_hold_rho0

**Type**: Boolean**Availability**: OFDFT with`of_kinetic=wt`

**Description**: Whether to fix the average density rho0.**True**: rho0 will be fixed even if the volume of system has changed, it will be set to True automatically if`of_wt_rho0`

is not zero.**False**: rho0 will change if volume of system has changed.

**Default**: False

### of_lkt_a

**Type**: Real**Availability**: OFDFT with`of_kinetic=lkt`

**Description**: Parameter a of LKT KEDF (kinetic energy density functional).**Default**: 1.3

### of_read_kernel

**Type**: Boolean**Availability**: OFDFT with`of_kinetic=wt`

**Description**: Whether to read in the kernel file.**True**: The kernel of WT KEDF (kinetic energy density functional) will be filled from the file specified by`of_kernel_file`

.**False**: The kernel of WT KEDF (kinetic energy density functional) will be filled from formula.

**Default**: False

### of_kernel_file

**Type**: String**Availability**: OFDFT with`of_read_kernel=True`

**Description**: The name of WT kernel file.**Default**: WTkernel.txt

### of_full_pw

**Type**: Boolean**Availability**: OFDFT**Description**: Whether to use full planewaves.**True**: Ecut will be ignored while collecting planewaves, so that all planewaves will be used in FFT.**False**: Only use the planewaves inside ecut, the same as KSDFT.

**Default**: True

### of_full_pw_dim

**Type**: Integer**Availability**: OFDFT with`of_full_pw = True`

**Description**: Specify the parity of FFT dimensions.**0**: either odd or even.**1**: odd only.**2**: even only.

Note: Even dimensions may cause slight errors in FFT. It should be ignorable in ofdft calculation, but it may make Cardinal B-spline interpolation unstable, so please set

`of_full_pw_dim = 1`

if`nbspline != -1`

.**Default**: 0

## Electric field and dipole correction

These variables are relevant to electric field and dipole correction

### efield_flag

**Type**: Boolean**Description**: added the electric field.True: A saw-like potential simulating an electric field is added to the bare ionic potential.

False: Not added the electric field.

**Default**: False

### dip_cor_flag

**Type**: Boolean**Availability**: with dip_cor_flag = True and efield_flag = True.**Description**: Added a dipole correction to the bare ionic potential.True：A dipole correction is also added to the bare ionic potential.

False: A dipole correction is not added to the bare ionic potential.

Note: If you want no electric field, parameter efield_amp should be zero. Must be used ONLY in a slab geometry for surface alculations, with the discontinuity FALLING IN THE EMPTY SPACE.

**Default**: False

### efield_dir

**Type**: Integer**Availability**: with efield_flag = True.**Description**: The direction of the electric field or dipole correction is parallel to the reciprocal lattice vector, so the potential is constant in planes defined by FFT grid points, efield_dir can set to 0, 1 or 2.0: parallel to \(b_1=\frac{2\pi(a_2\times a_3)}{a_1\cdot(a_2\times a_3)}\)

1: parallel to \(b_2=\frac{2\pi(a_3\times a_1)}{a_1\cdot(a_2\times a_3)}\)

2: parallel to \(b_3=\frac{2\pi(a_1\times a_2)}{a_1\cdot(a_2\times a_3)}\)

**Default**: 2

### efield_pos_max

**Type**: Real**Availability**: with efield_flag = True.**Description**: Position of the maximum of the saw-like potential along crystal axis efield_dir, within the unit cell, 0 <= efield_pos_max < 1.**Default**: Autoset to`center of vacuum - width of vacuum / 20`

### efield_pos_dec

**Type**: Real**Availability**: with efield_flag = True.**Description**: Zone in the unit cell where the saw-like potential decreases, 0 < efield_pos_dec < 1.**Default**: Autoset to`width of vacuum / 10`

### efield_amp

**Type**: Real**Availability**: with efield_flag = True.**Description**: Amplitude of the electric field. The saw-like potential increases with slope efield_amp in the region from efield_pos_max+efield_pos_dec-1) to (efield_pos_max), then decreases until (efield_pos_max+efield_pos_dec), in units of the crystal vector efield_dir.

Note: The change of slope of this potential must be located in the empty region, or else unphysical forces will result.

**Default**: 0.0**Unit**: a.u., 1 a.u. = 51.4220632*10^10 V/m.

## Gate field (compensating charge)

These variables are relevant to gate field (compensating charge) Detailed introduction

### gate_flag

**Type**: Boolean**Description**: Controls the addition of compensating charge by a charged plate for charged cells.true: A charged plate is placed at the

**zgate**position to add compensating charge. The direction is determined by**efield_dir**.false: No compensating charge is added.

**Default**: false

### zgate

**Type**: Real**Description**: position of the charged plate in the unit cell**Unit**: Unit cell size**Default**: 0.5**Constraints**: 0 <=**zgate**< 1

### block

**Type**: Boolean**Description**: Controls the addition of a potential barrier to prevent electron spillover.true: A potential barrier is added from

**block_down**to**block_up**with a height of**block_height**. If**dip_cor_flag**is set to true,**efield_pos_dec**is used to smoothly increase and decrease the potential barrier.false: No potential barrier is added.

**Default**: false

### block_down

**Type**: Real**Description**: lower beginning of the potential barrier**Unit**: Unit cell size**Default**: 0.45**Constraints**: 0 <=**block_down**<**block_up**< 1

### block_up

**Type**: Real**Description**: upper beginning of the potential barrier**Unit**: Unit cell size**Default**: 0.55**Constraints**: 0 <=**block_down**<**block_up**< 1

### block_height

**Type**: Real**Description**: height of the potential barrier**Unit**: Rydberg**Default**: 0.1

## Exact Exchange

These variables are relevant when using hybrid functionals.

**Availablity**: *dft_functional==hse/hf/pbe0/scan0/opt_orb* or *rpa==True*, and *basis_type==lcao/lcao_in_pw*

### exx_hybrid_alpha

**Type**: Real**Description**: fraction of Fock exchange in hybrid functionals, so that \(E_{X}=\alpha E_{X}+(1-\alpha)E_{X,\text{LDA/GGA}}\)**Default**:1: if

*dft_functional==hf*0.25: else

### exx_hse_omega

**Type**: Real**Description**: range-separation parameter in HSE functional, such that \(1/r=\text{erfc}(\omega r)/r+\text{erf}(\omega r)/r\)**Default**: 0.11

### exx_separate_loop

**Type**: Boolean**Description**: There are two types of iterative approaches provided by ABACUS to evaluate Fock exchange.False: Start with a GGA-Loop, and then Hybrid-Loop, in which EXX Hamiltonian \(H_{exx}\) is updated with electronic iterations.

True: A two-step method is employed, i.e. in the inner iterations, density matrix is updated, while in the outer iterations, \(H_{exx}\) is calculated based on density matrix that converges in the inner iteration.

**Default**: True

### exx_hybrid_step

**Type**: Integer**Availability**:*exx_separate_loop==1***Description**: the maximal iteration number of the outer-loop, where the Fock exchange is calculated**Default**: 100

### exx_mixing_beta

**Type**: Real**Availability**:*exx_separate_loop==1***Description**: mixing_beta for densty matrix in each iteration of the outer-loop**Default**: 1.0

### exx_lambda

**Type**: Real**Availability**:*basis_type==lcao_in_pw***Description**: It is used to compensate for divergence points at G=0 in the evaluation of Fock exchange using*lcao_in_pw*method.**Default**: 0.3

### exx_pca_threshold

**Type**: Real**Description**: To accelerate the evaluation of four-center integrals (\(ik|jl\)), the product of atomic orbitals are expanded in the basis of auxiliary basis functions (ABF): \(\Phi_{i}\Phi_{j}\sim C^{k}_{ij}P_{k}\). The size of the ABF (i.e. number of \(P_{k}\)) is reduced using principal component analysis. When a large PCA threshold is used, the number of ABF will be reduced, hence the calculation becomes faster. However, this comes at the cost of computational accuracy. A relatively safe choice of the value is 1e-4.**Default**: 1E-4

### exx_c_threshold

**Type**: Real**Description**: See also the entry exx_pca_threshold. Smaller components (less than exx_c_threshold) of the \(C^{k}_{ij}\) matrix are neglected to accelerate calculation. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-4.**Default**: 1E-4

### exx_v_threshold

**Type**: Real**Description**: See also the entry exx_pca_threshold. With the approximation \(\Phi_{i}\Phi_{j}\sim C^{k}_{ij}P_{k}\), the four-center integral in Fock exchange is expressed as \((ik|jl)=\Sigma_{a,b}C^{a}_{ij}V_{ab}C^{b}_{kl}\), where \(V_{ab}=(P_{a}|P_{b})\) is a double-center integral. Smaller values of the V matrix can be truncated to accelerate calculation. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 0, i.e. no truncation.**Default**: 1E-1

### exx_dm_threshold

**Type**: Real**Description**: The Fock exchange can be expressed as \(\Sigma_{k,l}(ik|jl)D_{kl}\) where D is the density matrix. Smaller values of the density matrix can be truncated to accelerate calculation. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-4.**Default**: 1E-4

### exx_c_grad_threshold

**Type**: Real**Description**: See also the entry exx_pca_threshold. \(\nabla C^{k}_{ij}\) is used in force and stress. Smaller components (less than exx_c_grad_threshold) of the \(\nabla C^{k}_{ij}\) matrix are neglected to accelerate calculation. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-4.**Default**: 1E-4

### exx_v_grad_threshold

**Type**: Real**Description**: See also the entry exx_pca_threshold. With the approximation \(\Phi_{i}\Phi_{j}\sim C^{k}_{ij}P_{k}\), the four-center integral in Fock exchange is expressed as \((ik|jl)=\Sigma_{a,b}C^{a}_{ij}V_{ab}C^{b}_{kl}\), where \(V_{ab}=(P_{a}|P_{b})\) is a double-center integral. \(\nabla V_{ab}\) is used in force and stress. Smaller values of the V matrix can be truncated to accelerate calculation. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 0, i.e. no truncation.**Default**: 1E-1

### exx_schwarz_threshold

**Type**: Real**Description**: In practice the four-center integrals are sparse, and using Cauchy-Schwartz inequality, we can find an upper bound of each integral before carrying out explicit evaluations. Those that are smaller than exx_schwarz_threshold will be truncated. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-5. (Currently not used)**Default**: 0

### exx_cauchy_threshold

**Type**: Real**Description**: In practice the Fock exchange matrix is sparse, and using Cauchy-Schwartz inequality, we can find an upper bound of each matrix element before carrying out explicit evaluations. Those that are smaller than exx_cauchy_threshold will be truncated. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-7.**Default**: 1E-7

### exx_cauchy_force_threshold

**Type**: Real**Description**: In practice the Fock exchange matrix in force is sparse, and using Cauchy-Schwartz inequality, we can find an upper bound of each matrix element before carrying out explicit evaluations. Those that are smaller than exx_cauchy_force_threshold will be truncated. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-7.**Default**: 1E-7

### exx_cauchy_stress_threshold

**Type**: Real**Description**: In practice the Fock exchange matrix in stress is sparse, and using Cauchy-Schwartz inequality, we can find an upper bound of each matrix element before carrying out explicit evaluations. Those that are smaller than exx_cauchy_stress_threshold will be truncated. The larger the threshold is, the faster the calculation and the lower the accuracy. A relatively safe choice of the value is 1e-7.**Default**: 1E-7

### exx_ccp_threshold

**Type**: Real**Description**: It is related to the cutoff of on-site Coulomb potentials. (Currently not used)**Default**: 1e-8

### exx_ccp_rmesh_times

**Type**: Real**Description**: This parameter determines how many times larger the radial mesh required for calculating Columb potential is to that of atomic orbitals. For HSE, setting it to 1 is enough. But for PBE0, a much larger number must be used.**Default**:1.5: if

*dft_functional==hse*5: else

### exx_distribute_type

**Type**: String**Description**: When running in parallel, the evaluation of Fock exchange is done by distributing atom pairs on different processes, then gather the results. exx_distribute_type governs the mechanism of distribution. Available options are`htime`

,`order`

,`kmean1`

and`kmeans2`

.`order`

: Atom pairs are simply distributed by their orders.`htime`

: The balance in time is achieved on each processor, hence if the memory is sufficient, this is the recommended method.`kmeans1`

,`kmeans2`

: Two methods where the k-means clustering method is used to reduce memory requirement. They might be necessary for very large systems. (Currently not used)

**Default**:`htime`

### exx_opt_orb_lmax

**Type**: Integer**Availability**:*dft_functional==opt_orb***Description**: The maximum l of the spherical Bessel functions, when the radial part of opt-ABFs are generated as linear combinations of spherical Bessel functions. A reasonable choice is 2.**Default**: 0

### exx_opt_orb_ecut

**Type**: Real**Availability**:*dft_functional==opt_orb***Description**: The cut-off of plane wave expansion, when the plane wave basis is used to optimize the radial ABFs. A reasonable choice is 60.**Default**: 0**Unit**: Ry

### exx_opt_orb_tolerence

**Type**: Real**Availability**:*dft_functional==opt_orb***Description**: The threshold when solving for the zeros of spherical Bessel functions. A reasonable choice is 1e-12.**Default**: 0

### exx_real_number

**Type**: Boolean**Description**:True: Enforce LibRI to use

`double`

data type.False: Enforce LibRI to use

`complex`

data type.

**Default**: depends on the gamma_only optionTrue: if gamma_only

False: else

## Molecular dynamics

These variables are used to control molecular dynamics calculations. For more information, please refer to md.md in detail.

### md_type

**Type**: String**Description**: Control the algorithm to integrate the equation of motion for molecular dynamics (MD), see md.md in detail.fire: a MD-based relaxation algorithm, named fast inertial relaxation engine.

nve: NVE ensemble with velocity Verlet algorithm.

nvt: NVT ensemble, see md_thermostat in detail.

npt: Nose-Hoover style NPT ensemble, see md_pmode in detail.

langevin: NVT ensemble with Langevin thermostat, see md_damp in detail.

msst: MSST method, see msst_direction, msst_vel, msst_qmass, msst_vis, msst_tscale in detail.

**Default**: nvt

### md_nstep

**Type**: Integer**Description**: The total number of molecular dynamics steps.**Default**: 10

### md_dt

**Type**: Real**Description**: The time step used in molecular dynamics calculations.**Default**: 1.0**Unit**: fs

### md_thermostat

**Type**: String**Description**: Specify the temperature control method used in NVT ensemble.nhc: Nose-Hoover chain, see md_tfreq and md_tchain in detail.

anderson: Anderson thermostat, see md_nraise in detail.

berendsen: Berendsen thermostat, see md_nraise in detail.

rescaling: velocity Rescaling method 1, see md_tolerance in detail.

rescale_v: velocity Rescaling method 2, see md_nraise in detail.

**Default**: nhc

### md_tfirst, md_tlast

**Type**: Real**Description**: The temperature used in molecular dynamics calculations.If

`md_tfirst`

is unset or less than zero, init_vel is autoset to be`true`

. If init_vel is`true`

, the initial temperature will be determined by the velocities read from`STRU`

. In this case, if velocities are unspecified in`STRU`

, the initial temperature is set to zero.If

`md_tfirst`

is set to a positive value and init_vel is`true`

simultaneously, please make sure they are consistent, otherwise abacus will exit immediately.Note that

`md_tlast`

is only used in NVT/NPT simulations. If`md_tlast`

is unset or less than zero,`md_tlast`

is set to`md_tfirst`

. If`md_tlast`

is set to be different from`md_tfirst`

, ABACUS will automatically change the temperature from`md_tfirst`

to`md_tlast`

.**Default**: No default**Unit**: K

### md_restart

**Type**: Boolean**Description**: Control whether to restart molecular dynamics calculations and time-dependent density functional theory calculations.True: ABACUS will read in

`${read_file_dir}/Restart_md.dat`

to determine the current step`${md_step}`

, then read in the corresponding`STRU_MD_${md_step}`

in the folder`OUT.$suffix/STRU/`

automatically. For tddft, ABACUS will also read in`LOWF_K_${kpoint}`

of the last step (You need to set out_wfc_lcao=1 and out_app_flag=0 to obtain this file).False: ABACUS will start molecular dynamics calculations normally from the first step.

**Default**: False

### md_restartfreq

**Type**: Integer**Description**: The output frequency of`OUT.${suffix}/Restart_md.dat`

and structural files in the directory`OUT.${suffix}/STRIU/`

, which are used to restart molecular dynamics calculations, see md_restart in detail.**Default**: 5

### md_dumpfreq

**Type**: Integer**Description**: The output frequency of`OUT.${suffix}/MD_dump`

in molecular dynamics calculations, which including the information of lattices and atoms.**Default**: 1

### dump_force

**Type**: Boolean**Description**: Whether to output atomic forces into the file`OUT.${suffix}/MD_dump`

.**Default**: True

### dump_vel

**Type**: Boolean**Description**: Whether to output atomic velocities into the file`OUT.${suffix}/MD_dump`

.**Default**: True

### dump_virial

**Type**: Boolean**Description**: Whether to output lattice virials into the file`OUT.${suffix}/MD_dump`

.**Default**: True

### md_seed

**Type**: Integer**Description**: The random seed to initialize random numbers used in molecular dynamics calculations.< 0: No srand() function is called.

>= 0: The function srand(md_seed) is called.

**Default**: -1

### md_tfreq

**Type**: Real**Description**: Control the frequency of temperature oscillations during the simulation. If it is too large, the temperature will fluctuate violently; if it is too small, the temperature will take a very long time to equilibrate with the atomic system.Note: It is a system-dependent empirical parameter, ranging from 1/(40*md_dt) to 1/(100*md_dt). An improper choice might lead to the failure of jobs.

**Default**: 1/40/md_dt**Unit**: \(\mathrm{fs^{-1}}\)

### md_tchain

**Type**: Integer**Description**: Number of thermostats coupled with the particles in the NVT/NPT ensemble based on the Nose-Hoover style non-Hamiltonian equations of motion.**Default**: 1

### md_pmode

**Type**: String**Description**: Specify the cell fluctuation mode in NPT ensemble based on the Nose-Hoover style non-Hamiltonian equations of motion.iso: The three diagonal elements of the lattice are fluctuated isotropically.

aniso: The three diagonal elements of the lattice are fluctuated anisotropically.

tri: The lattice must be a lower-triangular matrix, and all six freedoms are fluctuated.

**Default**: iso**Relavent**: md_tfreq, md_tchain, md_pcouple, md_pfreq, and md_pchain.

### md_prec_level

**Type**: Integer**Description**: Determine the precision level of variable-cell molecular dynamics calculations.0: FFT grids do not change, only G vectors and K vectors are changed due to the change of lattice vector. This level is suitable for cases where the variation of the volume and shape is not large, and the efficiency is relatively higher.

2: FFT grids change per step. This level is suitable for cases where the variation of the volume and shape is large, such as the MSST method. However, accuracy comes at the cost of efficiency.

**Default**: 0

### ref_cell_factor

**Type**: Real**Description**: Construct a reference cell bigger than the initial cell. The reference cell has to be large enough so that the lattice vectors of the fluctuating cell do not exceed the reference lattice vectors during MD. Typically, 1.02 ~ 1.10 is sufficient. However, the cell fluctuations depend on the specific system and thermodynamic conditions. So users must test for a proper choice. This parameters should be used in conjunction with erf_ecut, erf_height, and erf_sigma.**Default**: 1.0

### md_pcouple

**Type**: String**Description**: The coupled lattice vectors will scale proportionally in NPT ensemble based on the Nose-Hoover style non-Hamiltonian equations of motion.none: Three lattice vectors scale independently.

xyz: Lattice vectors x, y, and z scale proportionally.

xy: Lattice vectors x and y scale proportionally.

xz: Lattice vectors x and z scale proportionally.

yz: Lattice vectors y and z scale proportionally.

**Default**: none

### md_pfirst, md_plast

**Type**: Real**Description**: The target pressure used in NPT ensemble simulations, the default value of`md_plast`

is`md_pfirst`

. If`md_plast`

is set to be different from`md_pfirst`

, ABACUS will automatically change the target pressure from`md_pfirst`

to`md_plast`

.**Default**: -1.0**Unit**: kbar

### md_pfreq

**Type**: Real**Description**: The frequency of pressure oscillations during the NPT ensemble simulation. If it is too large, the pressure will fluctuate violently; if it is too small, the pressure will take a very long time to equilibrate with the atomic system.Note: It is a system-dependent empirical parameter. An improper choice might lead to the failure of jobs.

**Default**: 1/400/md_dt**Unit**: \(\mathrm{kbar^{-1}}\)

### md_pchain

**Type**: Integer**Description**: The number of thermostats coupled with the barostat in the NPT ensemble based on the Nose-Hoover style non-Hamiltonian equations of motion.**Default**: 1

### lj_rcut

**Type**: Real**Description**: Cut-off radius for Leonard Jones potential.**Default**: 8.5 (for He)**Unit**: Angstrom

### lj_epsilon

**Type**: Real**Description**: The value of epsilon for Leonard Jones potential.**Default**: 0.01032 (for He)**Unit**: eV

### lj_sigma

**Type**: Real**Description**: The value of sigma for Leonard Jones potential.**Default**: 3.405 (for He)**Unit**: Angstrom

### pot_file

**Type**: String**Description**: The filename of DP potential files, see md.md in detail.**Default**: graph.pb

### msst_direction

**Type**: Integer**Description**: The direction of the shock wave in the MSST method.0: x direction

1: y direction

2: z direction

**Default**: 2

### msst_vel

**Type**: Real**Description**: The velocity of the shock wave in the MSST method.**Default**: 0.0**Unit**: Angstrom/fs

### msst_vis

**Type**: Real**Description**: Artificial viscosity in the MSST method.**Default**: 0.0**Unit**: g/(mol*Angstrom*fs)

### msst_tscale

**Type**: Real**Description**: The reduction percentage of the initial temperature used to compress volume in the MSST method.**Default**: 0.01

### msst_qmass

**Type**: Real**Description**: Inertia of the extended system variable. You should set a number larger than 0.**Default**: No default**Unit**: \(\mathrm{g^{2}/(mol^{2}*Angstrom^{4})}\)

### md_damp

**Type**: Real**Description**: The damping parameter used to add fictitious force in the Langevin method.**Default**: 1.0**Unit**: fs

### md_tolerance

**Type**: Real**Description**: Thr temperature tolerance for velocity rescaling. Velocities are rescaled if the current and target temperature differ more than`md_tolerance`

.**Default**: 100.0**Unit**: K

### md_nraise

**Type**: Integer**Description**:Anderson: The “collision frequency” parameter is given as 1/

`md_nraise`

.Berendsen: The “rise time” parameter is given in units of the time step: tau =

`md_nraise`

*`md_dt`

, so`md_dt`

/tau = 1/`md_nraise`

.Rescale_v: Every

`md_nraise`

steps the current temperature is rescaled to the target temperature.

**Default**: 1

### cal_syns

**Type**: Boolean**Description**: Whether the asynchronous overlap matrix is calculated for Hefei-NAMD.**Default**: False

### dmax

**Type**: Real**Description**: The maximum displacement of all atoms in one step. This parameter is useful when cal_syns = True.**Default**: 0.01**Unit**: bohr

## DFT+*U* correction

These variables are used to control DFT+U correlated parameters

### dft_plus_u

**Type**: Boolean**Description**: Determines whether to calculate the plus U correction, which is especially important for correlated electrons.True: Calculate plus U correction.

False: Do not calculate plus U correction.

**Default**: False

### orbital_corr

**Type**: Integer**Description**: Specifies which orbits need plus U correction for each atom type (\(l_1,l_2,l_3,\ldots\) for atom type 1, 2, 3, respectively).-1: The plus U correction will not be calculated for this atom.

1: For p-electron orbits, the plus U correction is needed.

2: For d-electron orbits, the plus U correction is needed.

3: For f-electron orbits, the plus U correction is needed.

**Default**: None

### hubbard_u

**Type**: Real**Description**: Specifies the Hubbard Coulomb interaction parameter U (eV) in plus U correction, which should be specified for each atom unless the Yukawa potential is used.

Note: Since only the simplified scheme by Duradev is implemented, the ‘U’ here is actually U-effective, which is given by Hubbard U minus Hund J.

**Default**: 0.0

### yukawa_potential

**Type**: Boolean**Description**: Determines whether to use the local screen Coulomb potential method to calculate the values of U and J.True:

`hubbard_u`

does not need to be specified.False:

`hubbard_u`

does need to be specified.

**Default**: False

### yukawa_lambda

**Type**: Real**Availability**: DFT+U with`yukawa_potential`

= True.**Description**: The screen length of Yukawa potential. If left to default, the screen length will be calculated as an average of the entire system. It’s better to stick to the default setting unless there is a very good reason.**Default**: Calculated on the fly.

### omc

**Type**: Integer**Description**: The parameter controls the form of occupation matrix control used.0: No occupation matrix control is performed, and the onsite density matrix will be calculated from wavefunctions in each SCF step.

1: The first SCF step will use an initial density matrix read from a file named

`[initial_onsite.dm](http://initial_onsite.dm/)`

, but for later steps, the onsite density matrix will be updated.2: The same onsite density matrix from

`initial_onsite.dm`

will be used throughout the entire calculation.

Note : The easiest way to create

`initial_onsite.dm`

is to run a DFT+U calculation, look for a file named`onsite.dm`

in the OUT.prefix directory, and make replacements there. The format of the file is rather straight-forward.

**Default**: 0

## vdW correction

These variables are used to control vdW-corrected related parameters.

### vdw_method

**Type**: String**Description**: Specifies the method used for Van der Waals (VdW) correction. Available options are:`d2`

: Grimme’s D2 dispersion correction method`d3_0`

: Grimme’s DFT-D3(0) dispersion correction method`d3_bj`

: Grimme’s DFTD3(BJ) dispersion correction method`none`

: no vdW correction

**Default**: none

### vdw_s6

**Type**: Real**Availability**:`vdw_method`

is set to`d2`

,`d3_0`

, or`d3_bj`

**Description**: This scale factor is used to optimize the interaction energy deviations in van der Waals (vdW) corrected calculations. The recommended values of this parameter are dependent on the chosen vdW correction method and the DFT functional being used. For DFT-D2, the recommended values are 0.75 (PBE), 1.2 (BLYP), 1.05 (B-P86), 1.0 (TPSS), and 1.05 (B3LYP). For DFT-D3, recommended values with different DFT functionals can be found on the here. The default value of this parameter in ABACUS is set to be the recommended value for PBE.**Default**:0.75: if

`vdw_method`

is set to`d2`

1.0: if

`vdw_method`

is set to`d3_0`

or`d3_bj`

### vdw_s8

**Type**: Real**Availability**:`vdw_method`

is set to`d3_0`

or`d3_bj`

**Description**: This scale factor is relevant for D3(0) and D3(BJ) van der Waals (vdW) correction methods. The recommended values of this parameter with different DFT functionals can be found on the webpage. The default value of this parameter in ABACUS is set to be the recommended value for PBE.**Default**:0.722: if

`vdw_method`

is set to`d3_0`

0.7875: if

`vdw_method`

is set to`d3_bj`

### vdw_a1

**Type**: Real**Availability**:`vdw_method`

is set to`d3_0`

or`d3_bj`

**Description**: This damping function parameter is relevant for D3(0) and D3(BJ) van der Waals (vdW) correction methods. The recommended values of this parameter with different DFT functionals can be found on the webpage. The default value of this parameter in ABACUS is set to be the recommended value for PBE.**Default**:1.217: if

`vdw_method`

is set to`d3_0`

0.4289: if

`vdw_method`

is set to`d3_bj`

### vdw_a2

**Type**: Real**Availability**:`vdw_method`

is set to`d3_0`

or`d3_bj`

**Description**: This damping function parameter is only relevant for D3(0) and D3(BJ) van der Waals (vdW) correction methods. The recommended values of this parameter with different DFT functionals can be found on the webpage. The default value of this parameter in ABACUS is set to be the recommended value for PBE.**Default**:1.0: if

`vdw_method`

is set to`d3_0`

4.4407: if

`vdw_method`

is set to`d3_bj`

### vdw_d

**Type**: Real**Availability**:`vdw_method`

is set to`d2`

**Description**: Controls the damping rate of the damping function in the DFT-D2 method.**Default**: 20

### vdw_abc

**Type**: Integer**Availability**:`vdw_method`

is set to`d3_0`

or`d3_bj`

**Description**: Determines whether three-body terms are calculated for DFT-D3 methods.True: ABACUS will calculate the three-body term.

False: The three-body term is not included.

**Default**: False

### vdw_C6_file

**Type**: String**Availability**:`vdw_method`

is set to`d2`

**Description**: Specifies the name of the file containing \(C_6\) parameters for each element when using the D2 method. If not set, ABACUS uses the default \(C_6\) parameters (Jnm6/mol) stored in the program. To manually set the \(C_6\) parameters, provide a file containing the parameters. An example is given by:H 0.1 Si 9.0

Namely, each line contains the element name and the corresponding \(C_6\) parameter.

**Default**: default

### vdw_C6_unit

**Type**: String**Availability**:`vdw_C6_file`

is not default**Description**: Specifies the unit of the provided \(C_6\) parameters in the D2 method. Available options are:`Jnm6/mol`

(J·nm^6/mol)`eVA`

(eV·Angstrom)

**Default**: Jnm6/mol

### vdw_R0_file

**Type**: String**Availability**:`vdw_method`

is set to`d2`

**Description**: Specifies the name of the file containing \(R_0\) parameters for each element when using the D2 method. If not set, ABACUS uses the default \(R_0\) parameters (Angstrom) stored in the program. To manually set the \(R_0\) parameters, provide a file containing the parameters. An example is given by:Li 1.0 Cl 2.0

Namely, each line contains the element name and the corresponding \(R_0\) parameter.

**Default**: default

### vdw_R0_unit

**Type**: String**Availability**:`vdw_R0_file`

is not default**Description**: Specifies the unit for the \(R_0\) parameters in the D2 method when manually set by the user. Available options are:`A`

(Angstrom)`Bohr`

**Default**: A

### vdw_cutoff_type

**Type**: String**Description**: Determines the method used for specifying the cutoff radius in periodic systems when applying Van der Waals correction. Available options are:`radius`

: The supercell is selected within a sphere centered at the origin with a radius defined by`vdw_cutoff_radius`

.`period`

: The extent of the supercell is explicitly specified using the`vdw_cutoff_period`

keyword.

**Default**: radius

### vdw_cutoff_radius

**Type**: Real**Availability**:`vdw_cutoff_type`

is set to`radius`

**Description**: Defines the radius of the cutoff sphere when`vdw_cutoff_type`

is set to`radius`

. The default values depend on the chosen`vdw_method`

.**Default**:56.6918 if

`vdw_method`

is set to`d2`

95 if

`vdw_method`

is set to`d3_0`

or`d3_bj`

**Unit**: defined by`vdw_radius_unit`

(default`Bohr`

)

### vdw_radius_unit

**Type**: String**Availability**:`vdw_cutoff_type`

is set to`radius`

**Description**: specify the unit of`vdw_cutoff_radius`

. Available options are:`A`

(Angstrom)`Bohr`

**Default**: Bohr

### vdw_cutoff_period

**Type**: Integer Integer Integer**Availability**:`vdw_cutoff_type`

is set to`period`

**Description**: The three integers supplied here explicitly specify the extent of the supercell in the directions of the three basis lattice vectors.**Default**: 3 3 3

### vdw_cn_thr

**Type**: Real**Availability**:`vdw_method`

is set to`d3_0`

or`d3_bj`

**Description**: The cutoff radius when calculating coordination numbers.**Default**: 40**Unit**: defined by`vdw_cn_thr_unit`

(default:`Bohr`

)

### vdw_cn_thr_unit

**Type**: String**Description**: Unit of the coordination number cutoff (`vdw_cn_thr`

). Available options are:`A`

(Angstrom)`Bohr`

**Default**: Bohr

## Berry phase and wannier90 interface

These variables are used to control berry phase and wannier90 interface parameters. Detail introduce

### berry_phase

**Type**: Boolean**Description**: controls the calculation of Berry phasetrue: Calculate Berry phase.

false: Do not calculate Berry phase.

**Default**: false

### gdir

**Type**: Integer**Description**: the direction of the polarization in the lattice vector for Berry phase calculation1: Calculate the polarization in the direction of the lattice vector a_1 defined in the STRU file.

2: Calculate the polarization in the direction of the lattice vector a_2 defined in the STRU file.

3: Calculate the polarization in the direction of the lattice vector a_3 defined in the STRU file.

**Default**: 3

### towannier90

**Type**: Integer**Description**: Controls the generation of files for the Wannier90 code.1: Generate files for the Wannier90 code.

0: Do not generate files for the Wannier90 code.

**Default**: 0

### nnkpfile

**Type**: String**Description**: the file name generated when running “wannier90 -pp …” command**Default**: seedname.nnkp

### wannier_method

**Type**: Integer**Description**: Only available on LCAO basis, using different methods to generate “*.mmn” file and “*.amn” file.1: Calculated using the

`lcao_in_pw`

method, the calculation accuracy can be improved by increasing`ecutwfc`

to maintain consistency with the pw basis set results.2: The overlap between atomic orbitals is calculated using grid integration. The radial grid points are generated using the Gauss-Legendre method, while the spherical grid points are generated using the Lebedev-Laikov method.

**Default**: 1

### wannier_spin

**Type**: String**Description**: the spin direction for the Wannier function calculation when nspin is set to 2`up`

: Calculate spin up for the Wannier function.`down`

: Calculate spin down for the Wannier function.

**Default**:`up`

### out_wannier_mmn

**Type**: Bool**Description**: write the “*.mmn” file or not.0: don’t write the “*.mmn” file.

1: write the “*.mmn” file.

**Default**: 1

### out_wannier_amn

**Type**: Bool**Description**: write the “*.amn” file or not.0: don’t write the “*.amn” file.

1: write the “*.amn” file.

**Default**: 1

### out_wannier_eig

**Type**: Bool**Description**: write the “*.eig” file or not.0: don’t write the “*.eig” file.

1: write the “*.eig” file.

**Default**: 1

### out_wannier_unk

**Type**: Bool**Description**: write the “UNK.*” file or not.0: don’t write the “UNK.*” file.

1: write the “UNK.*” file.

**Default**: 0

### out_wannier_wvfn_formatted

**Type**: Bool**Description**: write the “UNK.*” file in ASCII format or binary format.0: write the “UNK.*” file in binary format.

1: write the “UNK.*” file in ASCII format (text file format).

**Default**: 1

## TDDFT: time dependent density functional theory

### td_edm

**Type**: Integer**Description**: the method to calculate the energy density matrix0: new method (use the original formula).

1: old method (use the formula for ground state).

**Default**: 0

### td_print_eij

**Type**: Real**Description**:<0: don’t print \(E_{ij}\).

>=0: print the \(E_{ij}\ (<\psi_i|H|\psi_j>\)) elements which are larger than td_print_eij.

**Default**: -1

### td_propagator

**Type**: Integer**Description**: method of propagator0: Crank-Nicolson.

1: 4th Taylor expansions of exponential.

2: enforced time-reversal symmetry (ETRS).

**Default**: 0

### td_vext

**Type**: Boolean**Description**:True: add a laser material interaction (extern laser field).

False: no extern laser field.

**Default**: False

### td_vext_dire

**Type**: String**Description**: If`td_vext`

is True, the td_vext_dire is a string to set the number of electric fields, like`td_vext_dire 1 2`

representing external electric field is added to the x and y axis at the same time. Parameters of electric field can also be written as a string, like`td_gauss_phase 0 1.5707963267948966`

representing the Gauss field in the x and y directions has a phase delay of Pi/2. See below for more parameters of electric field.1: the direction of external light field is along x axis.

2: the direction of external light field is along y axis.

3: the direction of external light field is along z axis.

**Default**: 1

### td_stype

**Type**: Integer**Description**: type of electric field in space domain0: length gauge.

1: velocity gauge.

**Default**: 0

### td_ttype

**Type**: Integer**Description**: type of electric field in time domain0: Gaussian type function.

1: Trapezoid function.

2: Trigonometric function.

3: Heaviside function.

4: HHG function.

**Default**: 0

### td_tstart

**Type**: Integer**Description**: number of steps where electric field starts**Default**: 1

### td_tend

**Type**: Integer**Description**: number of steps where electric field ends**Default**: 100

### td_lcut1

**Type**: Real**Description**: cut1 of interval in length gauge

E = E0 , cut1<x<cut2

E = -E0/(cut1+1-cut2) , x<cut1 or cut2<x<1**Default**: 0.05

### td_lcut2

**Type**: Real**Description**: cut2 of interval in length gauge

E = E0 , cut1<x<cut2

E = -E0/(cut1+1-cut2) , x<cut1 or cut2<x<1**Default**: 0.05

### td_gauss_freq

**Type**: Real**Description**: frequency (freq) of Gauss type electric field (fs^-1)

amp*cos(2pi*freq(t-t0)+phase)exp(-(t-t0)^2/2sigma^2)**Default**: 22.13

### td_gauss_phase

**Type**: Real**Description**: phase of Gauss type electric field

amp*(2pi*freq(t-t0)+phase)exp(-(t-t0)^2/2sigma^2)**Default**: 0.0

### td_gauss_sigma

**Type**: Real**Description**: sigma of Gauss type electric field (fs)

amp*cos(2pi*freq(t-t0)+phase)exp(-(t-t0)^2/2sigma^2)**Default**: 30.0

### td_gauss_t0

**Type**: Real**Description**: step number of time center (t0) of Gauss type electric field

amp*cos(2pi*freq(t-t0)+phase)exp(-(t-t0)^2/2sigma^2)**Default**: 100

### td_gauss_amp

**Type**: Real**Description**: amplitude (amp) of Gauss type electric field (V/Angstrom)

amp*cos(2pi*freq(t-t0)+phase)exp(-(t-t0)^2/2sigma^2)**Default**: 0.25

### td_trape_freq

**Type**: Real**Description**: frequency (freq) of Trapezoid type electric field (fs^-1)

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 1.60

### td_trape_phase

**Type**: Real**Description**: phase of Trapezoid type electric field

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 0.0

### td_trape_t1

**Type**: Real**Description**: step number of time interval 1 (t1) of Trapezoid type electric field

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 1875

### td_trape_t2

**Type**: Real**Description**: step number of time interval 2 (t2) of Trapezoid type electric field

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 5625

### td_trape_t3

**Type**: Real**Description**: step number of time interval 3 (t3) of Trapezoid type electric field

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 7500

### td_trape_amp

**Type**: Real**Description**: amplitude (amp) of Trapezoid type electric field (V/Angstrom)

E = amp*cos(2pi*freq*t+phase) t/t1 , t<t1

E = amp*cos(2pi*freq*t+phase) , t1<t<t2

E = amp*cos(2pi*freq*t+phase) (1-(t-t2)/(t3-t2)) , t2<t<t3

E = 0 , t>t3**Default**: 2.74

### td_trigo_freq1

**Type**: Real**Description**: frequency 1 (freq1) of Trigonometric type electric field (fs^-1)

amp*cos(2*pi*freq1*t+phase1)*sin(2*pi*freq2*t+phase2)^2**Default**: 1.164656

### td_trigo_freq2

**Type**: Real**Description**: frequency 2 (freq2) of Trigonometric type electric field (fs^-1)

amp*cos(2*pi*freq1*t+phase1)*sin(2*pi*freq2*t+phase2)^2**Default**: 0.029116

### td_trigo_phase1

**Type**:Real**Description**: phase 1 (phase1) of Trigonometric type electric field

amp*cos(2*pi*freq1*t+phase1)*sin(2*pi*freq2*t+phase2)^2**Default**: 0.0

### td_trigo_phase2

**Type**: Real**Description**: phase 2 (phase2) of Trigonometric type electric field

amp*cos(2*pi*freq1*t+phase1)*sin(2*pi*freq2*t+phase2)^2**Default**: 0.0

### td_trigo_amp

**Type**: Real**Description**: amplitude (amp) of Trigonometric type electric field (V/Angstrom)

amp*cos(2*pi*freq1*t+phase1)*sin(2*pi*freq2*t+phase2)^2**Default**: 2.74

### td_heavi_t0

**Type**: Real**Description**: step number of switch time (t0) of Heaviside type electric field

E = amp , t<t0

E = 0.0 , t>t0**Default**: 100

### td_heavi_amp

**Type**: Real**Description**: amplitude (amp) of Heaviside type electric field (V/Angstrom)

E = amp , t<t0

E = 0.0 , t>t0**Default**: 2.74

### td_out_dipole

**Type**: Boolean**Description**:True: output dipole.

False: do not output dipole.

**Default**: False

### td_out_efield

**Type**: Boolean**Description**: The unit of output file is atomic unit (1 a.u. = 1 Ry/(bohr \(\cdot\) e) = 51.422 V/Angstrom).True: output efield.

False: do not output efield.

**Default**: False

### ocp

**Type**: Boolean**Availability**:For PW and LCAO codes. if set to 1, occupations of bands will be setting of “ocp_set”.

For TDDFT in LCAO codes. if set to 1, occupations will be constrained since second ionic step.

For OFDFT, this feature can’t be used.

**Description**:True: fix the occupations of bands.

False: do not fix the occupations of bands.

**Default**: False

### ocp_set

**Type**: String**Description**: If ocp is True, the ocp_set is a string to set the number of occupancy, like ‘1 10 * 1 0 1’ representing the 13 band occupancy, 12th band occupancy 0 and the rest 1, the code is parsing this string into an array through a regular expression.**Default**: none

## Variables useful for debugging

### t_in_h

**Type**: Boolean**Description**: Specify whether to include kinetic term in obtaining the Hamiltonian matrix.0: No.

1: Yes.

**Default**: 1

### vl_in_h

**Type**: Boolean**Description**: Specify whether to include local pseudopotential term in obtaining the Hamiltonian matrix.0: No.

1: Yes.

**Default**: 1

### vnl_in_h

**Type**: Boolean**Description**: Specify whether to include non-local pseudopotential term in obtaining the Hamiltonian matrix.0: No.

1: Yes.

**Default**: 1

### vh_in_h

**Type**: Boolean**Description**: Specify whether to include Hartree potential term in obtaining the Hamiltonian matrix.0: No.

1: Yes.

**Default**: 1

### vion_in_h

**Type**: Boolean**Description**: Specify whether to include local ionic potential term in obtaining the Hamiltonian matrix.0: No.

1: Yes.

**Default**: 1

### test_force

**Type**: Boolean**Description**: Specify whether to output the detailed components in forces.0: No.

1: Yes.

**Default**: 0

### test_stress

**Type**: Boolean**Description**: Specify whether to output the detailed components in stress.0: No.

1: Yes.

**Default**: 0

### colour

**Type**: Boolean**Description**: Specify whether to set the colorful output in terminal.0: No.

1: Yes.

**Default**: 0

### test_skip_ewald

**Type**: Boolean**Description**: Specify whether to skip the calculation of the ewald energy.0: No.

1: Yes.

**Default**: 0

## Electronic conductivities

Frequency-dependent electronic conductivities can be calculated with Kubo-Greenwood formula [Phys. Rev. B 83, 235120 (2011)].

Onsager coefficients:

\(L_{mn}(\omega)=(-1)^{m+n}\frac{2\pi e^2\hbar^2}{3m_e^2\omega\Omega}\)

\(\times\sum_{ij\alpha\mathbf{k}}W(\mathbf{k})\left(\frac{\epsilon_{i\mathbf{k}}+\epsilon_{j\mathbf{k}}}{2}-\mu\right)^{m+n-2} \times |\langle\Psi_{i\mathbf{k}}|\nabla_\alpha|\Psi_{j\mathbf{k}}\rangle|^2\)

\(\times[f(\epsilon_{i\mathbf{k}})-f(\epsilon_{j\mathbf{k}})]\delta(\epsilon_{j\mathbf{k}}-\epsilon_{i\mathbf{k}}-\hbar\omega).\)

They can also be computed by \(j\)-\(j\) correlation function.

\(L_{mn}=\frac{2e^{m+n-2}}{3\Omega\hbar\omega}\Im[\tilde{C}_{mn}(\omega)]\) Guassian smearing: \(\tilde{C}_{mn}=\int_0^\infty C_{mn}(t)e^{-i\omega t}e^{-\frac{1}{2}s^2t^2}dt\) Lorentzian smearing: \(\tilde{C}_{mn}=\int_0^\infty C_{mn}(t)e^{-i\omega t}e^{-\gamma t}dt\)

\(C_{mn}(t)=-2\theta(t)\Im\left\{Tr\left[\sqrt{\hat f}\hat{j}_m(1-\hat{f})e^{i\frac{\hat{H}}{\hbar}t}\hat{j}_ne^{-i\frac{\hat{H}}{\hbar}t}\sqrt{\hat f}\right]\right\}\),

where \(j_1\) is electric flux and \(j_2\) is thermal flux.

Frequency-dependent electric conductivities: \(\sigma(\omega)=L_{11}(\omega)\).

Frequency-dependent thermal conductivities: \(\kappa(\omega)=\frac{1}{e^2T}\left(L_{22}-\frac{L_{12}^2}{L_{11}}\right)\).

DC electric conductivities: \(\sigma = \lim_{\omega\to 0}\sigma(\omega)\).

Thermal conductivities: \(\kappa = \lim_{\omega\to 0}\kappa(\omega)\).

### cal_cond

**Type**: Boolean**Availability**: basis_type =`pw`

**Description**: Whether to calculate electronic conductivities.**Default**: False

### cond_che_thr

**Type**: Real**Availability**: esolver_type =`sdft`

**Description**: Control the error of Chebyshev expansions for conductivities.**Default**: 1e-8

### cond_dw

**Type**: Real**Availability**: basis_type =`pw`

**Description**: Frequency interval (\(\mathrm{d}\omega\)) for frequency-dependent conductivities.**Default**: 0.1**Unit**: eV

### cond_wcut

**Type**: Real**Availability**: basis_type =`pw`

**Description**: Cutoff frequency for frequency-dependent conductivities.**Default**: 10.0**Unit**: eV

### cond_dt

**Type**: Real**Availability**: basis_type =`pw`

**Description**: Time interval (\(\mathrm{d}t\)) to integrate Onsager coefficients.**Default**: 0.02**Unit**: a.u.

### cond_dtbatch

**Type**: Integer**Availability**: esolver_type =`sdft`

**Description**: exp(iH*dt*cond_dtbatch) is expanded with Chebyshev expansion to calculate conductivities. It is faster but costs more memory.If

`cond_dtbatch = 0`

: Autoset this parameter to make expansion orders larger than 100.

**Default**: 0

### cond_smear

**Type**: Integer**Description**: Smearing method for conductivities1: Gaussian smearing

2: Lorentzian smearing

**Default**: 1

### cond_fwhm

**Type**: Real**Availability**: basis_type =`pw`

**Description**: FWHM for conductivities. For Gaussian smearing, \(\mathrm{FWHM}=2\sqrt{2\ln2}s\); for Lorentzian smearing, \(\mathrm{FWHM}=2\gamma\).**Default**: 0.4**Unit**: eV

### cond_nonlocal

**Type**: Boolean**Availability**: basis_type =`pw`

**Description**: Whether to consider nonlocal potential correction when calculating velocity matrix \(\bra{\psi_i}\hat{v}\ket{\psi_j}\).True: \(m\hat{v}=\hat{p}+\frac{im}{\hbar}[\hat{V}_{NL},\hat{r}]\).

False: \(m\hat{v}\approx\hat{p}\).

**Default**: True

## Implicit solvation model

These variables are used to control the usage of implicit solvation model. This approach treats the solvent as a continuous medium instead of individual “explicit” solvent molecules, which means that the solute is embedded in an implicit solvent and the average over the solvent degrees of freedom becomes implicit in the properties of the solvent bath.

### imp_sol

**Type**: Boolean**Description**: calculate implicit solvation correction**Default**: False

### eb_k

**Type**: Real**Availability**:`imp_sol`

is true.**Description**: the relative permittivity of the bulk solvent, 80 for water**Default**: 80

### tau

**Type**: Real**Description**: The effective surface tension parameter that describes the cavitation, the dispersion, and the repulsion interaction between the solute and the solvent which are not captured by the electrostatic terms**Default**: 1.0798e-05**Unit**: \(Ry/Bohr^{2}\)

### sigma_k

**Type**: Real**Description**: the width of the diffuse cavity that is implicitly determined by the electronic structure of the solute**Default**: 0.6

### nc_k

**Type**: Real**Description**: the value of the electron density at which the dielectric cavity forms**Default**: 0.00037**Unit**: \(Bohr^{-3}\)

## Deltaspin

These variables are used to control the usage of deltaspin functionality.

### sc_mag_switch

**Type**: boolean**Description**: the switch of deltaspin functionality0: no deltaspin

1: use the deltaspin method to constrain atomic magnetic moments

**Default**: 0

### decay_grad_switch

**Type**: boolean**Description**: the switch of decay gradient method0: no decay gradient method

1: use the decay gradient method and set ScDecayGrad in the file specified by

`sc_file`

. ScDecayGrad is an element dependent parameter, which is used to control the decay rate of the gradient of the magnetic moment.

**Default**: 0

### sc_thr

**Type**: Real**Description**: the threshold of the spin constraint atomic magnetic moment**Default**: 1e-6**Unit**: Bohr Mag (\muB)

### nsc

**Type**: Integer**Description**: the maximum number of steps in the inner lambda loop**Default**: 100

### nsc_min

**Type**: Integer**Description**: the minimum number of steps in the inner lambda loop**Default**: 2

### sc_scf_nmin

**Type**: Integer**Description**: the minimum number of outer scf loop before initializing lambda loop**Default**: 2

### alpha_trial

**Type**: Real**Description**: initial trial step size for lambda in eV/uB^2**Default**: 0.01**Unit**: eV/uB^2

### sccut

**Type**: Real**Description**: restriction of step size in eV/uB**Default**: 3**Unit**: eV/uB

### sc_file

**Type**: String**Description**: the file in json format to specify atomic constraining parameters. An example of the sc_file json file is shown below for the`nspin 4`

case:

```
[
{
"element": "Fe",
"itype": 0,
"ScDecayGrad": 0.9,
"ScAtomData": [
{
"index": 0,
"lambda": [0, 0, 0],
"target_mag": [2.0, 0.0, 0.0],
"constrain": [1,1,1]
},
{
"index": 1,
"lambda": [0, 0, 0],
"target_mag_val": 2.0,
"target_mag_angle1": 80.0,
"target_mag_angle2": 0.0,
"constrain": [1,1,1]
}
]
}
]
```

and

```
[
{
"element": "Fe",
"itype": 0,
"ScDecayGrad": 0.9,
"ScAtomData": [
{
"index": 0,
"lambda": 0.0,
"target_mag": 2.0,
"constrain": 1
},
{
"index": 1,
"lambda": 0,
"target_mag": 2.0,
"constrain": 1
}
]
}
]
```

for `nspin 2`

case. The difference is that `lambda`

, `target_mag`

, and `constrain`

are scalars in `nspin 2`

case, and are vectors in `nspin 4`

case.

**Default**: none

## Quasiatomic Orbital (QO) analysis

These variables are used to control the usage of QO analysis. Please note present implementation of QO always yield numerically instable results, use with much care.

### qo_switch

**Type**: Boolean**Description**: whether to let ABACUS output QO analysis required files**Default**: 0

### qo_basis

**Type**: String**Description**: specify the type of atomic basis`pswfc`

: use the pseudowavefunction in pseudopotential files as atomic basis. To use this option, please make sure in pseudopotential file there is pswfc in it.`hydrogen`

: generate hydrogen-like atomic basis.

*warning: to use*`pswfc`

*, please use norm-conserving pseudopotentials with pseudowavefunctions, SG15 pseudopotentials cannot support this option.***Default**:`hydrogen`

### qo_strategy

**Type**: String [String…](optional)**Description**: specify the strategy to generate radial orbitals for each atom type. If one parameter is given, will apply to all atom types. If more than one parameters are given but fewer than number of atom type, those unspecified atom type will use default value.For

`qo_basis hydrogen`

`minimal-nodeless`

: according to principle quantum number of the highest occupied state, generate only nodeless orbitals, for example Cu, only generate 1s, 2p, 3d and 4f orbitals (for Cu, 4s is occupied, thus \(n_{max} = 4\))`minimal-valence`

: according to principle quantum number of the highest occupied state, generate only orbitals with highest principle quantum number, for example Cu, only generate 4s, 4p, 4d and 4f orbitals.`full`

: similarly according to the maximal principle quantum number, generate all possible orbitals, therefore for Cu, for example, will generate 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f.`energy`

: will generate hydrogen-like orbitals according to Aufbau principle. For example the Cu (1s2 2s2 2p6 3s2 3p6 3d10 4s1), will generate these orbitals.

For

`qo_basis pswfc`

`all`

: use all possible pseudowavefunctions in pseudopotential file.`s`

/`p`

/`d`

/…: only use s/p/d/f/…-orbital(s).`spd`

: use s, p and d orbital(s). Any unordered combination is acceptable.

*warning: for*`qo_basis hydrogen`

*to use*`full`

,*generation strategy may cause the space spanned larger than the one spanned by numerical atomic orbitals, in this case, must filter out orbitals in some way***Default**:`minimal-valence`

### qo_screening_coeff

**Type**: Real [Real…](optional)**Availability**: for`qo_basis pswfc`

only.**Description**: for each atom type, screening factor \(e^{-\eta|\mathbf{r}|}\) is multiplied to the pswfc to mimic the behavior of some kind of electron. \(\eta\) is the screening coefficient. If only one value is given, then will apply to each atom type. If not enough values are given, will apply default value to rest of atom types. This parameter plays important role in controlling the spread of QO orbitals together with`qo_thr`

.**Default**: 0.1**Unit**: Bohr^-1

### qo_thr

**Type**: Real**Description**: the convergence threshold determining the cutoff of generated orbital. Lower threshold will yield orbital with larger cutoff radius.**Default**: 1.0e-6