# Qbox variables¶

- alpha_PBE0 - coefficient of Hartree-Fock exchange in PBE0 DFT
- alpha_RSH - parameter of the RSH hybrid density functional
- atoms_dyn - atom dynamics control variable
- beta_RSH parameter of the RSH hybrid density functional
- blHF bisection levels in Hartree-Fock exchange
- btHF bisection threshold in Hartree-Fock exchange
- cell dimensions of the unit cell
- cell_dyn unit cell dynamics control variable
- cell_lock control of allowed unit cell motions
- cell_mass fictitious mass of the unit cell
- charge_mix_coeff mixing coefficient for charge density updates
- charge_mix_ndim Anderson dimension for charge density updates
- charge_mix_rcut Kerker screening length for charge density updates
- debug debug parameters (not for normal use)
- delta_spin number of spin excitations
- dt time step (a.u.)
- ecut plane wave energy cutoff (Ry)
- ecutprec energy cutoff of the preconditioner (Ry)
- ecuts energy cutoff of the confinement potential for variable cell calculations
- e_field total electric field
- emass fictitious electronic mass (for Car-Parrinello dynamics)
- ext_stress externally applied stress (GPa)
- fermi_temp Fermi temperature (K)
- iter_cmd script executed every iter_cmd_period steps
- iter_cmd period number of steps between iter_cmd executions
- mu_RSH parameter of the RSH hybrid density functional
- nempty number of empty states
- net_charge net charge of the system
- nrowmax maximum size of process grid columns
- nspin number of spin degrees of freedom
- polarization algorithm used to compute dipole and quadrupole moments
- ref_cell dimensions of the reference unit cell for variable cell calculations
- scf_tol tolerance criterion for convergence of SCF iterations
- stress stress control variable
- thermostat thermostat control variable
- th_temp thermostat temperature (K)
- th_time thermostat time constant (a.u.)
- th_width thermostat width (K)
- vext external potential file name
- wf_diag wave function diagonalization control variable
- wf_dyn wave function dynamics control variable
- xc exchange-correlation functional control variable

## alpha_PBE0¶

- NAME
**alpha_PBE0**– coefficient of Hartree-Fock exchange in PBE0 DFT- DESCRIPTION
- The
**alpha_PBE0**variable defines the coefficient multiplying the Hartree-Fock exchange energy in the PBE0 exchange-correlation functional. The default value is 0.25. - ALLOWED VALUES
- non-negative real numbers
- RELATED INFORMATION
- xc

## alpha_RSH¶

## atoms_dyn¶

- NAME
**atoms_dyn**– atom dynamics control variable- DESCRIPTION
The

**atoms_dyn**variable determines the algorithm used to update atomic positions during a simulation. The following values are allowed:LOCKED: Ionic forces are not computed and atomic positions are not updated. This is the default.

SD: Steepest Descent. Ionic forces are computed and atomic positions are updated using the steepest descent algorithm

\[R(t+dt) = R(t) + \frac{dt^2}{m} F(t)\]where \(F\) is the force, \(m\) is the ionic mass and \(dt\) is the time step (see variable dt ).

SDA: Steepest Descent with Acceleration. A line minimization algorithm is used to find a minimum satisfying the Wolfe conditions before changing the descent direction. Using this algorithm requires a full calculation of the electronic ground state at each ionic step, i.e. nitscf > 1 in the run command.

CG: Conjugate Gradient. A line minimization algorithm is used to find a minimum satisfying the Wolfe conditions before changing the descent direction. The Polak-Ribiere formula is used to update descent directions. Using this algorithm requires a full calculation of the electronic ground state at each ionic step, i.e. using nitscf > 1 in the run command.

MD: Molecular dynamics. Ionic forces are computed and ionic positions are updated using the Verlet algorithm

\[R(t+dt) = 2 R(t) -R(t-dt) + \frac{dt^2}{m} F(t)\]This algorithm can be used to perform Born-Oppenheimer molecular dynamics (using nitscf > 1 in the run command) or Car-Parrinello molecular dynamics (nitscf not used). See also the wf_dyn variable.

BMD: Blocked Molecular dynamics. This algorithm updates ionic positions according to the MD algorithm (Verlet), but velocities are reset to zero whenever the total energy increases. This algorithm can be used for geometry optimization. It requires a full calculation of the electronic ground state at each ionic step, i.e. using nitscf > 1 in the run command.

- ALLOWED VALUES
- LOCKED, SD, SDA, CG, MD, BMD
- RELATED INFORMATION
- dt

## beta_RSH¶

## blHF¶

- NAME
**blHF**– bisection levels for Hartree-Fock exchange computation- DESCRIPTION
- The
**blHF**variable consists of three integer values*lx ly lz*that specify the number of recursive levels of bisection that must be perfomed on wave functions in the x, y, and z directions when computing the Hartree-Fock exchange energy. The values of blHF are only used if the variable btHF is non-zero. - ALLOWED VALUES
- positive integers
- RELATED INFORMATION
- btHF, bisection

## btHF¶

- NAME
**btHF**– bisection threshold for Hartree-Fock exchange computation- DESCRIPTION
- The
**btHF**variable defines the threshold used in the recursive bisection perfomed on wave functions when computing the Hartree-Fock exchange energy. If btHF is zero, no bisection is performed during Hartree-Fock exchange calculations. The default value of btHF is zero. - ALLOWED VALUES
- floating point numbers in [0,1]
- RELATED INFORMATION
- blHF, bisection

## cell¶

- NAME
**cell**- unit cell parameters- DESCRIPTION
The

**cell**variable contains the coordinates of the three lattice vectors defining the unit cell. The unit cell is defined using the**set**command with the following arguments**set cell***a1x a1y a1z a2x a2y a2z a3x a3y a3z*The lattice vectors are

\[ \begin{align}\begin{aligned}\vec{a}_1 = ( a_{1x}, a_{1y}, a_{1z} )^T\\\vec{a}_2 = ( a_{2x}, a_{2y}, a_{2z} )^T\\\vec{a}_3 = ( a_{3x}, a_{3y}, a_{3z} )^T\end{aligned}\end{align} \]and form the columns of the 3x3 lattice parameter matrix \(A\)

\[A = [ \vec{a}_1, \vec{a}_2, \vec{a}_3 ]\]The default value of all cell parameters is zero.

- ALLOWED VALUES
- positive real numbers
- RELATED INFORMATION
- ref_cell

## cell_dyn¶

- NAME
**cell_dyn**- cell dynamics control variable- DESCRIPTION
The

**cell_dyn**variable determines the algorithm used to update the unit cell during a simulation. The following values are allowed:LOCKED: The unit cell is not updated. This is the default.

SD: Steepest Descent. The unit cell is updated using the computed tress tensor and the steepest descent algorithm

\[a_{ij}(t+dt)=a_{ij}(t) + \frac{dt^2}{m_\Omega} \left( \sigma(t)-\sigma^{\rm ext}(t) \right) A(t)\]where \(\sigma\) is the stress tensor, \(\sigma^{\rm ext}\) is the externally applied stress (variable ext_stress), \(\Omega\) is the volume of the unit cell, \(m_\Omega\) is the mass of the unit cell (variable cell_mass), \(A\) is the 3x3 lattice parameter matrix (see cell variable) and \(dt\) is the time step (variable dt).

CG: Conjugate Gradient. The unit cell and the atomic positions are updated using the computed stress tensor and the atomic forces using a conjugate gradient algorithm. Note that both the unit cell and atomic positions are optmized simultaneously independently of the value of atoms_dyn.

- ALLOWED VALUES
- LOCKED, SD, CG
- RELATED INFORMATION
- cell, ref_cell, cell_lock

## cell_lock¶

- NAME
**cell_lock**- cell dynamics constraints control variable- DESCRIPTION
The

**cell_lock**variable is used to restrict the possible changes of the unit cell parameters. The allowed values are- OFF: No restrictions on the unit cell parameters are enforced. This is the default.
- A: The lattice vector \(\vec{a}_1\) is fixed.
- B: The lattice vector \(\vec{a}_2\) is fixed.
- C: The lattice vector \(\vec{a}_3\) is fixed.
- AB: The lattice vectors \(\vec{a}_1\) and \(\vec{a}_2\) are fixed.
- AC: The lattice vectors \(\vec{a}_1\) and \(\vec{a}_3\) are fixed.
- BC: The lattice vectors \(\vec{a}_2\) and \(\vec{a}_3\) are fixed.
- ABC: All lattice vectors are fixed. This is equivalent to
**cell_dyn**= LOCKED. - S: The shape of the unit cell is preserved. Lattice vectors can change length but not direction.
- AS: The lattice vector \(\vec{a}_1\) is fixed and the shape of the unit cell is preserved.
- BS: The lattice vector \(\vec{a}_2\) is fixed and the shape of the unit cell is preserved.
- CS: The lattice vector \(\vec{a}_3\) is fixed and the shape of the unit cell is preserved.
- ABS: The lattice vectors \(\vec{a}_1\) and \(\vec{a}_2\) are fixed and the shape of the unit cell is preserved.
- ACS: The lattice vectors \(\vec{a}_1\) and \(\vec{a}_3\) are fixed and the shape of the unit cell is preserved.
- BCS: The lattice vectors \(\vec{a}_2\) and \(\vec{a}_1\) are fixed and the shape of the unit cell is preserved.
- R: The aspect ratio of the unit cell is preserved. All lattice vectors are rescaled by the same constant.

- ALLOWED VALUES
- OFF, A, B, C, AB, AC, BC, ABC, S, AS, BS, CS, ABS, ACS, BCS, R
- RELATED INFORMATION
- cell, cell_dyn, cell_mass

## cell_mass¶

## charge_mix_coeff¶

- NAME
**charge_mix_coeff**- charge density mixing coefficient- DESCRIPTION
- The charge density mixing coefficient is used to update the electronic charge density during self-consistent iterations (see charge_mix_ndim). The default value is 0.5. Smaller values may be needed to ensure the convergence of self-consistent iterations in metallic systems.
- ALLOWED VALUES
- real values in the interval [0,1]
- RELATED INFORMATION
- charge_mix_rcut, charge_mix_ndim

## charge_mix_ndim¶

- NAME
**charge_mix_ndim**– dimension of Anderson acceleration of charge mixing- DESCRIPTION
The

**charge_mix_ndim**parameter determines how many previous charge density corrections are used in the Anderson acceleration of the charge mixing scheme. The new input charge density is computed according to\[\rho^{(k+1)}_{\rm in} = \bar{\rho} + \alpha \bar{f}\]where \(\alpha\) is the charge mixing coefficient (variable charge_mix_coeff) and \(\bar f\) is the least-squares residual in the subspace of dimension charge_mix_ndim spanned by the previous charge density corrections

\[\bar{f} = \delta \rho^{(k)} + \sum_{i=1}^n \theta_i (\delta\rho^{(k-i)}_{\rm in} - \delta\rho^{(k)}_{\rm in} )\]where \(\delta\rho^{(k)}=\rho^{(k)}_{\rm out} - \rho^{(k)}_{\rm in}\) is the difference between the output and input charge density of the self-consistent iteration k, and

\[\bar{\rho}=\rho^{(k)}_{\rm in} + \sum_{i=1}^n \theta_i (\rho^{(k-i)}_{\rm in} - \rho^{(k)}_{\rm in} )\]The coefficients are chosen so as to minimize \(||\bar f ||^2_2\) in a row-weighted least squares sense. The weight used in the LS calculation is the Kerker screening function

\[w(G) = \frac{G^2+q_0^2}{G^2}\]where \(q_0=2\pi/r_c\) and \(r_c\) is the charge mixing cutoff radius (variable charge_mix_rcut). The default value of charge_mix_ndim is 3.

- SPECIAL VALUES
Using charge_mix_ndim=0 leads to simple mixing

\[\rho^{(k+1)}_{\rm in} = \rho^{(k)}_{\rm in} + \alpha ( \rho^{(k)}_{\rm out} = \rho^{(k)}_{\rm in} )\]- ALLOWED VALUES
- non-negative integers
- RELATED INFORMATION
- charge_mix_rcut, charge_mix_coeff

## charge_mix_rcut¶

- NAME
**charge_mix_rcut**- charge mixing cutoff radius

DESCRIPTION

Thecharge_mix_rcutvariable is used to define the range of the Coulomb interaction in the Kerker screening function used in the charge density mixing scheme (see charge_mix_ndim). The default value of charge_mix_rcut is 10 a.u. If charge_mix_rcut is set to zero, no screening is used.

- ALLOWED VALUES
- positive real numbers
- RELATED INFORMATION
- charge_mix_ndim, charge_mix_ndim

## debug¶

- NAME
**debug**- debug parameters- DESCRIPTION
- The
**debug**variable is used to pass debug parameters to Qbox. It is not intended for normal use. - ALLOWED VALUES
- character strings

## delta_spin¶

- NAME
**delta_spin**– number of spin excitations- DESCRIPTION
The

**delta_spin**variable is used to modify the total spin of the system by promoting electrons from the minority spin determinant to the majority spin determinant in spin-polarized calculations. The value of delta_spin is the number of electrons promoted. Depending on the total number of electrons \(N_e\) and the value of delta_spin, the total spin takes values according to the following table :Ne delta_spin total_spin even 0 singlet odd 0 doublet even 1 triplet odd 1 quartet Higher total spin is obtained following the same pattern for larger values of delta_spin.

Note: the variable nspin must be set to 2 before delta_spin can be modified. The value of delta_spin cannot be larger than \(\lfloor N_e / 2 \rfloor\).

- ALLOWED VALUES
- non-negative integers
- RELATED INFORMATION
- nspin

## dt¶

## ecut¶

- NAME
**ecut**- plane wave basis energy cutoff- DESCRIPTION
- The
**ecut**variable determines the size of the plane wave basis used to define the electronic wave functions. It must given in Rydberg units. The wave function plane wave basis consists of all plane waves having a kinetic energy smaller than \(E_{\rm cut}\). The charge density and the total potential are described using a larger basis set that includes all plane waves with a kinetic energy smaller than \(4 E_{\rm cut}\). The default value of ecut is zero, in which case the plane wave basis contains one basis function: the plane wave of wave vector \(G=0\). - ALLOWED VALUES
- non-negative real numbers

## ecutprec¶

- NAME
**ecutprec**- preconditioning energy cutoff- DESCRIPTION
The

**ecutprec**variable defines the energy cutoff used in the preconditioner for electronic structure optimization. Corrections to the electronic wave functions are preconditioned in Fourier space using a diagonal preconditioning matrix K whose elements are defined by\[\begin{split}k(G) = \left\{ \begin{array}{ll} \frac{1}{2 E_{\rm cut}^{\rm prec}} & \frac{1}{2}G^2 < E_{\rm cut}^{\rm prec}\\ \frac{1}{G^2} & \frac{1}{2}G^2 \ge E_{\rm cut}^{\rm prec}\\ \end{array} \right.\end{split}\]The value of ecutprec must be given in Rydberg units. Preconditioning is only used if the wf_dyn variable is set to either PSD, PSDA or JD. If ecutprec = 0, an automatic preconditioner is used. The default value of ecutprec is zero (automatic preconditioning).

- ALLOWED VALUES
- non-negative real numbers smaller than or equal to ecut.
- RELATED INFORMATION
- ecut, wf_dyn

## ecuts¶

- NAME
**ecuts**- energy cutoff for stress confinement potential- DESCRIPTION
The ecuts variable defines the energy cutoff used in a confinement potential in Fourier space. The confinement potential is used when computing the stress tensor with variable cell size in order to ensure constant resolution as the unit cell changes size. The confinement energy is

\[E_{\rm conf} = \frac{1}{2} \sum_{n,G} |c_{n,G}|^2 G^2 f(G)\]where the \(c_{n,G}\) are wave function Fourier coefficients, and

\[f(G) = f_s \left( 1 - \frac{1}{1+{\rm exp}((G^2/2-E_{\rm cut}^s)/\sigma_s)} \right)\]and \(f_s=2, \sigma_s=1/2\). The default value of

**ecuts**is zero, in which case the confinement potential is not used.For a detailed description of the use of confinement potentials in constant pressure simulations, see

- P. Focher, G. L. Chiarotti, M. Bernasconi, et al. Structural Phase-Transformations Via 1St-Principles Simulation, Europhys. Lett. 26 (5): 345-351 (1994).
- M. Bernasconi, G. L. Chiarotti, P. Focher, et al. First-Principle Constant-Pressure Molecular-Dynamics, Journal of Physics and Chemistry of Solids 56 (3-4): 501-505 (1995).

- ALLOWED VALUES
- positive real numbers smaller than or equal to ecut
- RELATED INFORMATION
- stress, cell_dyn

## e_field¶

- NAME
**e_field**– total electric field- DESCRIPTION
- The
**e_field**variable defines the three components of the total electric field \(\vec{E}=(E_x,E_y,E_z)\). The field must be given in atomic units (1 Hartree/(electron Bohr) = \(5.1422\times 10^{11}\) V/m. The polarization variable must also be set in order to define the algorithm used to compute the electric dipole and quadrupole in the presence of the total electric field. The default value of**e_field**is zero. - ALLOWED VALUES
- three real numbers
- RELATED INFORMATION
- polarization

## emass¶

- NAME
**emass**- fictitious electronic mass for Car-Parrinello simulations- DESCRIPTION
- The
**emass**variable defines the fictitious electronic mass used in Car-Parrinello simulations. The default value is zero, in which case the fictitious electronic mass used in the calculation is \(m_e=2 E_{\rm cut} dt^2\). The value of emass is only relevant if the variable wf_dyn is set to MD (i.e. if the wave function dynamics is Car-Parrinello). It is ignored otherwise. - ALLOWED VALUES
- positive real values
- RELATED INFORMATION
- wf_dyn

## ext_stress¶

- NAME
**ext_stress**- external stress- DESCRIPTION
The

**ext_stress**variable determines the value of the externally applied stress. The ext_stress variable must be set using the following syntax:**set ext_stress***s_xx s_yy s_zz s_xy s_yz s_xz*where the values of the elements of the stress tensor must be given in GPa units. The external stress can be positive or negative. The default value is zero.

- ALLOWED VALUES
- real numbers
- RELATED INFORMATION
- stress

## fermi_temp¶

- NAME
**fermi_temp**- Fermi temperature for fractionally occupied states- DESCRIPTION
- The
**fermi_temp**variable determines the value of the Fermi temperature used to compute occupation factors for fractionally occupied states. The value must be given in degrees Kelvin. The default value is zero. - ALLOWED VALUES
- non-negative real numbers
- RELATED INFORMATION
- nempty

## iter_cmd¶

- NAME
**iter_cmd**- command or script to be executed every iter_cmd_period ionic steps- DESCRIPTION
- The
**iter_cmd**variable defines a command or script that is executed every iter_cmd_period ionic steps. If a single command must be executed, the full command (with arguments) can be used as the value of iter_cmd. If multiple commands are used, they must be written in a local script file, and the name of the script is used as the value of iter_cmd. - ALLOWED VALUES
- string
- RELATED INFORMATION
- iter_cmd_period

## iter_cmd_period¶

NAME iter_cmd_period –number of ionic steps between executions of iter_cmd

- DESCRIPTION
- The
**iter_cmd_period**variable defines the number of ionic steps that separate successive executions of the command (or script) defined by iter_cmd. The default value is 1. - ALLOWED VALUES
- positive integers
- RELATED INFORMATION
- iter_cmd

## mu_RSH¶

## nempty¶

- NAME
**nempty**- number of empty electronic states- DESCRIPTION
- The
**nempty**variable determines the number of electronic states that are included in the calculation in addition to the number of states needed to accommodate the total number of electrons. If nempty is non-zero, the eigenvalues and eigenvectors of the Kohn-Sham hamiltonian are computed at each electronic iteration and the charge density is recomputed from the eigenvectors using a Fermi distribution. The default value of nempty is zero. - ALLOWED VALUES
- non-negative integers
- RELATED INFORMATION
- fermi_temp

## net_charge¶

- NAME
**net_charge**- net charge of the system- DESCRIPTION
- The
**net_charge**variable is used to control the total amount of electronic charge in the calculation. If net_charge = 0, the total number of electrons is determined from the sum of the valence charges given in the species definition files and the system is neutral. If net_charge = -1, an extra electron is added to the system. If net_charge = 1, an electron is removed from the system. The default value is zero. - ALLOWED VALUES
- integers

## nrowmax¶

- NAME
**nrowmax**- maximum number of process grid rows- DESCRIPTION
- The
**nrowmax**variable determines the shape of the process grid used in parallel calculations. It is used to optimize performance when large numbers of parallel tasks are used. The default value is 32. Setting the value of nrowmax erases all information about the current wave functions. Performance is typically best for values comparable to the size of the charge density Fourier transform grid in the z direction (np2v in output). - ALLOWED VALUES
- positive integers

## nspin¶

- NAME
**nspin**- number of spin degrees of freedom- DESCRIPTION
- The
**nspin**variable is used to determine the number of spin components of the wave function. The default value is 1 (no spin polarization). - ALLOWED VALUES
- 1 or 2

## polarization¶

- NAME
**polarization**- algorithm used to compute the dipole and quadrupole moments- DESCRIPTION
The

**polarization**variable determines the algorithm used to compute the electric dipole and quadrupole. The allowed values are- OFF: The dipole and quadrupole are not computed. This is the default.
- MLWF: The electronic dipole is defined as the center of charge of maximally localized Wannier functions (MLWF).
- MLWF_REF: The electronic dipole is defined as the center of charge of maximally localized Wannier functions (MLWF) with the refinement correction proposed by M. Stengel and N. Spaldin, Phys. Rev. B73, 075121 (2006).
- MLWF_REF_Q: The electronic dipole is defined as for MLWF_REF and the quadrupole moment is computed.
- BERRY: The electronic dipole is computed using the definition based on the Berry phase as defined by I. Souza et al, Phys. Rev. Lett. 89, 117602 (2002).

The ionic, electronic and total dipole \(\vec d\) are computed and printed in units of (electron bohr). Note that the total dipole is only defined modulo an additive constant multiple of the lattice vectors in a periodic system. A dipole expressed in (electron bohr) can be converted to (Debye) using the relation 1 (electron Bohr) = 2.5417462 (Debye). Conversely, dipoles expressed in (Debye) can be converted to (electron bohr) using the relation 1 (Debye) = 0.39343031 (electron bohr).

If the total electric field (defined by the e_field variable) is non-zero, the calculation of the electronic ground state is performed using the electric enthalpy as defined by Souza et al., in order to impose a constant value of the total field. Note that \(\vec E\) is the total field, not the applied field.

The polarizability tensor of the system is defined as

\[\alpha_{ij} = \frac{\delta d_i}{\delta E_j}\]and is defined in units of (bohr

^{3}), \(\delta d_i\) in (electron bohr), and \(E_j\) in (hartree/(electron bohr)). The polarizability tensor \(\alpha_{ij}\) can be computed using calculations of the total dipole induced by small changes \(\delta E_j\) around \(\vec E = 0\).The change in dipole \(\delta d_i\) due to a small change in total field \(\delta E_j\) is computed using the centered finite difference expression

\[\delta d_i = \frac{1}{2} \left[ d_i(+\delta E_j)-d_i(-\delta E_j)\right]\]The polarizability tensor can then be expressed as

\[\alpha_{ij} = \frac{d_i(+\delta E_j)-d_i(-\delta E_j)}{2 \delta E_j}\]The full polarization tensor can be obtained using 6 calculations of the dipole (2 evaluations in 3 directions). Note that since the polarization due to a finite field includes linear and higher order terms, this calculation must be repeated with decreasing values of \(\delta E_j\) in order to obtain an accurate value of the linear polarizability.

In solids, the average polarization (dipole per unit volume) is defined as

\[\vec{P}=\frac{\vec d}{\Omega}\]where \(\Omega\) is the unit cell volume. The susceptibility tensor \(\chi\) and the dielectric tensor \(\epsilon\) (relative dielectric permittivity) are related by \(\epsilon = I + \chi\).

Using the SI unit convention,

\[\vec{D} = \epsilon_0 \vec{E} + \vec{P}\]and using atomic units, we have \(4 \pi \epsilon_0 = 1\) and the polarization can be expressed as

\[\vec{P}=\chi\epsilon_0\vec{E} = \frac{\chi}{4 \pi} \vec{E}\]A small change in total field \(\delta\vec{E}\) corresponds to a change of polarization

\[\delta\vec{P} = \frac{\chi}{4\pi} \, \delta\vec{E}\]If a sufficiently large unit cell is used, an estimate of the dielectric tensor can be computed using the finite-difference expression

\[\epsilon_{ij} = \delta_{ij} + 4\pi \frac{\delta P_i(+\delta E_j) - \delta P_i(-\delta E_j)}{2\delta E_j} = \delta_{ij} + \frac{4\pi}{\Omega} \frac{\delta d_i(+\delta E_j) - \delta d_i(-\delta E_j)}{2\delta E_j}\]or, in terms of the polarizability tensor,

\[\epsilon_{ij} = \delta_{ij} + \frac{4\pi}{\Omega} \alpha_{ij}\]

### Molecular polarizability¶

The polarizability computed from

\[\alpha_{ij} = \frac{\delta d_i}{\delta E_j}\]is the polarizability of an inifinite crystal that consists of the repeated unit cell. When computing the electronic properties of a molecule placed in a large, empty unit cell, the isotropic polarizability of a single isolated molecule can be evaluated using the Clausius-Mossotti relation

\[\alpha_{\rm CM} = \frac{3 \epsilon_0}{N} \frac{\epsilon - 1}{\epsilon + 2}\]where \(N = 1/\Omega\) is the number of molecules per unit volume. Using the above definitions of the dielectric tensor, we get

\[\alpha_{\rm CM} = \frac{\alpha}{1 + \frac{4 \pi}{3\Omega} \alpha}\]where \(\alpha\) is the isotropic polarizability

\[\alpha = \frac{1}{3}(\alpha_{11} + \alpha_{22} + \alpha_{33})\]

### Quadrupole moment¶

The quadrupole moment tensor is computed if the MLWF_REF_Q value is used. It is defined as

\[Q_{ij} = e \int_\Omega x_i x_j \rho(x) \, d^3 x\]in units of (electron bohr

^{2}). Note that this may differ from other definitions used in the literature, which may include a factor 1/2 in the above definition. The traceless quadrupole tensor defined as \(Q-({\rm tr} Q/3) I\) is also computed and printed. Some definitions used in the literature include an extra multiplicative factor of 3, or 3/2.The quadrupole moment is sometimes expressed in units of (Debye Å), related to (electron bohr

^{2}) by the expressions 1 (Debye Å) = 0.743476 (electron bohr^{2}) and 1 (electron bohr^{2}) = 1.3450336 (Debye Å) . The NIST Computational Chemistry Database (http://cccbdb.nist.gov) provides quadrupole moments of molecules in (Debye Å). A comparison of Qbox results with NIST values can be made using the relation:\[Q^{\rm NIST} {\rm (Debye Å)} = \frac{3}{2} 1.3450336 \; Q^{\rm Qbox} ({\rm e\; bohr}^2)\]Born effective charges are defined as the derivatives of ionic forces with respect to the total field

\[Z_{ij}^\alpha = \frac{\delta F_i^\alpha}{\delta E_j}\]whereis \(F_i^\alpha\) the ith component of the force on atom \(\alpha\). Born effective charges can be similarly computed using finite difference expressions.

As of release 1.64.0 the calculation of the polarization is only implemented at the \(\Gamma\) point of the Brillouin zone, for systems having no spin polarization.

- ALLOWED VALUES
- OFF, MLWF, MLWF_REF, MLWF_REF_Q, BERRY
- RELATED INFORMATION
- e_field

## ref_cell¶

- NAME
- ref_cell –reference unit cell
- DESCRIPTION
- The
**ref_cell**variable determines the size of the reference unit cell. The reference unit cell is used in constant pressure calculations to ensure constant resolution of the basis set as the unit cell changes size. The unit cell must always be enclosed in the reference unit cell during a constant pressure calculation. - ALLOWED VALUES
- positive real numbers
- RELATED INFORMATION
- cell

## scf_tol¶

- NAME
**scf_tol**– tolerance for convergence of SCF iterations

DESCRIPTION

Thescf_tolvariable determines the energy tolerance criterion for convergence of SCF iterations. The unit is (a.u.) (hartree). The default value is zero. The maximum number of SCF iterations is determined by the second argument of the run command: “runniter nitscf nite”. If scf_tol is set to a non-zero value and if the energy changes by less than scf_tol in three successive SCF iterations, the remaining SCF iterations are skipped. If scf_tol is zero, the number of SCF iterations isnitscf.

- ALLOWED VALUES
- non-negative real numbers
- RELATED INFORMATION
- run

## stress¶

- NAME
**stress**- stress calculation control variable- DESCRIPTION
- The
**stress**variable determines whether the stress tensor is calculated. The possible values are ON and OFF. The default is OFF. - ALLOWED VALUES
- ON, OFF
- RELATED INFORMATION
- ext_stress, cell_dyn

## thermostat¶

- NAME
**thermostat**- thermostat control variable- DESCRIPTION
The

**thermostat**variable determines what type of thermostat is used for constant temperature simulations. Valid choices areOFF: No thermostat is used. This is the default.

SCALING: Scaling of velocities. At each MD step, the velocities of all atoms are rescaled as

\[v_i := v_i (1 - \eta dt)\]where

\[\eta = \frac{1}{\tau} {\rm tanh} \frac{T-T_{\rm ref}}{\Delta}\]is the thermostat time constant (variable th_time), \(T\) is the instantaneous temperature computed from the ionic kinetic energy, \(T_{\rm ref}\) is the thermostat reference temperature (variable th_temp), and \(\Delta\) is the thermostat temperature width (variable th_width).

ANDERSEN: Andersen thermostat. The atoms are subjected to random collisions with particles drawn from a Maxwell distribution of velocities with temperature \(T_{\rm ref}\). The collision frequency is \(1/\tau\) where \(\tau\) is given by the variable th_time (see H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)).

LOWE: Lowe thermostat. Pairs of atoms are subjected to random collisions with a particle drawn from a Maxwell distribution of velocities with temperature \(T_{\rm ref}\). The collision frequency is \(1/\tau\) where \(\tau\) is given by the variable th_time. The Lowe thermostat is similar to the Andersen thermostat but conserves total momentum (see C. P. Lowe, Europhys. Lett. 47, 145 (1999)).

BDP: Bussi-Donadio-Parrinello thermostat. The stochastic thermostat described by Bussi, Donadio and Parrinello in J. Chem. Phys. 126, 014101 (2007) is used. The parameter \(\tau\) used in the BDP paper is the value of the variable th_time. The value of the variable th_width is ignored. When using the BDP thermostat, the value of <econst> printed on output corresponds to the conserved energy described in the above paper.

- ALLOWED VALUES
- OFF, SCALING, ANDERSON, LOWE, BDP
- RELATED INFORMATION
- th_temp, th_time, th_width

## th_temp¶

- NAME
**th_temp**- thermostat reference temperature- DESCRIPTION
- The
**th_temp**variable determines the thermostat reference temperature. The default is zero. See the thermostat variable. - ALLOWED VALUES
- non-negative real numbers
- RELATED INFORMATION
- thermostat, th_time, th_width

## th_time¶

- NAME
**th_time**- thermostat time constant- DESCRIPTION
- The
**th_time**variable determines the thermostat time constant. The time constant is a measure of the time over which the thermostat adjusts the temperature. See thermostat for details. The value of th_time must be given in atomic units of time. The default value is 5000 a.u. (~ 120 fs). - ALLOWED VALUES
- positive real numbers
- RELATED INFORMATION
- th_temp, th_width, thermostat

## th_width¶

- NAME
**th_width**- thermostat temperature window- DESCRIPTION
- The
**th_width**determines the value of the thermostat temperature width. See thermostat for details. The value of th_width must be given in degrees Kelvin. The default value is 100 K. - ALLOWED VALUES
- positive real numbers
- RELATED INFORMATION
- th_temp, th_time, thermostat

## vext¶

- NAME
**vext**- external potential file name- DESCRIPTION
The

**vext**variable contains the name of a file describing a periodic external potential. If the variable is set to a non-empty string, subsequent calculations will include the external potential. The variable can be reset by using:set vext NULL

which will revert to using no external potential. The file describing the external potential must be an XML file that conforms to the following example:

<?xml version="1.0" encoding="UTF-8"?> <fpmd:function3d xmlns:fpmd="http://www.quantum-simulation.org/ns/fpmd/fpmd-1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.quantum-simulation.org/ns/fpmd/fpmd-1.0 function3d.xsd" name="delta_v"> <domain a="16.0 0.0 0.0" b="0.0 16.0 0.0" c="0.0 0.0 16.0"/> <grid nx="64" ny="64" nz="64"/> <grid_function type="double" nx="64" ny="64" nz="64" encoding="base64"> AAAAAAAAAAAAAAAAAACgPwAAAAAAAMA/AAAAAAAA0j8AAAAAAADgPwAAAAAAAOk/AAAAAAAA8j8A AAAAAID4PwAAAAAAAABAAAAAAABABEAAAAAAAAAJQAAAAAAAQA5AAAAAAAAAEkAAAAAAACAVQAAA ... QAAAAAAAgABAAAAAAACA+T8AAAAAAADzPwAAAAAAAOs/AAAAAAAA4j8AAAAAAADWPwAAAAAAAMg/ AAAAAAAAuD8= </grid_function> </fpmd:function3d>

The values of the potential on the points defined by the grid are encoded using base64 encoding. The values are ordered as k,j,i with the i index changing fastest. See the file util/vext/mkvext.py for an example of how to generate an arbitrary external potential file. The value of the

**name**attribute can be arbitrary. The origin of coordinates of the (nx,ny,nz) grid corresponds to the atomic position (0,0,0) in the unit cell.- ALLOWED VALUES
- string

RELATED INFORMATION

## wf_diag¶

- NAME
**wf_diag**- diagonalization control variable

DESCRIPTION

The

wf_diagvariable determines whether eigenvectors and/or eigenvalues of the hamiltonian are computed after each optimization of the electronic structure. Valid choices are:

- T: True. Eigenvalues and eigenvectors are computed. Eigenvalues are printed on output in eV units.
- F: False. Eigenvalues and eigenvectors are not computed. This is the default.
- EIGVAL: Eigenvalues only. The eigenvalues are computed and printed, but eigenvectors are not computed.
- MLWF: Maximally localized Wannier Functions (MLWFs) are computed.
- MLWFC: The position of MLWF centers is computed and printed but MLWFs are not computed.
If empty states are added to the calculation (variable nempty > 0), the eigenvalues and eigenvectors are always computed.

- ALLOWED VALUES
- T, F, EIGVAL,MLWF,MLWFC

## wf_dyn¶

- NAME
**wf_dyn**– wave function dynamics control variable- DESCRIPTION
The

**wf_dyn**variable determines which algorithm is used to update the wave functions during electronic structure optimization. The choices areSD: Steepest Descent. This the default. Wavefunctions are updated as follows:

\[\Psi^{(k+1)} = \Psi^{(k)} - \alpha H \Psi^{(k)}\]where

\[\begin{split}\alpha = \left\{ \begin{array}{ll} \frac{1}{2 E_{\rm cut}} & m_e = 0 \\ \frac{dt^2}{m_e} & m_e > 0 \\ \end{array} \right.\end{split}\]and \(m_e\) is the fictitious electronic mass (variable emass). By default, \(m_e=0\). (Note that the SD algorithm is very inefficient and is not used in practice. It is provided for debugging purposes).

PSD: Preconditioned Steepest Descent. Wavefunctions are updated as follows:

\[\Psi^{(k+1)} = \Psi^{(k)} - \alpha K P_c H \Psi^{(k)}\]where K is a diagonal preconditioning matrix

\[k_{ij} = \delta_{ij} k(G)\]where

\[\begin{split}k(G) = \left\{ \begin{array}{ll} \frac{1}{2 E_{\rm cut}^{\rm prec}} & \frac{1}{2}G^2 < E_{\rm cut}^{\rm prec}\\ \frac{1}{G^2} & \frac{1}{2}G^2 \ge E_{\rm cut}^{\rm prec}\\ \end{array} \right.\end{split}\]and \(P_c\) is a projector on the orthogonal complement of the subspace spanned by all computed wave functions. The preconditioning matrix depends on the value of the variable ecutprec.

PSDA: Preconditioned Steepest Descent with Anderson acceleration. Wave functions are updated as with the PSD option, and convergence is accelerated by the Anderson scheme (D. G. Anderson,

*JACM*12, No 4, pp. 547-560 (1965)).JD: Jacobi-Davidson. Wave functions are updated using a preconditioned Jacobi-Davidson algorithm.

MD: Molecular Dynamics. Wave functions are updated using the Car-Parrinello scheme

\[\Psi^{(k+1)}_i = 2 \Psi^{(k)}_i - \Psi^{(k-1)}_i - \frac{dt^2}{m_e} H \Psi^{(k)}_i + \sum_j \Lambda_{ij} \Psi^{(k)}_j\]where holonomic constraints are used to enforce orthogonality.

LOCKED. Wavefunctions are not updated.

- ALLOWED VALUES
- SD, PSD, PSDA, JD, MD, LOCKED
- RELATED INFORMATION
- ecutprec

## xc¶

- NAME
**xc**- exchange-correlation functional control variable

DESCRIPTION

The

xcvariable determines which exchange-correlation functional is used in the electronic structure calculation. Valid choices are :

- LDA: Local Density Approximation, Ceperley-Alder data. This is the default.
- VWN: Local Density Approximation, parameterized by Vosko, Wilk and Nusair.
- PBE: Perdew-Burke-Ernzerhof GGA functional.
- PBE0: Hybrid density functional [C. Adamo and V. Barone, JCP 110, 6158 (1999)].
- BLYP: Becke-Lee-Yang-Parr functional.
- HF: Hartree-Fock.
- B3LYP: Three-parameter Becke-Lee-Yang-Parr hybrid density functional.
- HSE: Heyd-Scuseria-Ernzerhof 2006 hybrid density functional.
- RSH: Range-separated hybrid density functional [J. Skone et al. Phys. Rev. B 93, 235106 (2016)].
- BHandHLYP: Becke “half-and-half” LYP hybrid density functional.
The RSH functional uses the following definition of the electron self-energy

\[\Sigma = \alpha \Sigma^{\rm erf}(\mu) + \beta \Sigma^{\rm erfc}(\mu) + (1-\alpha) \Sigma^{\rm LR}_{\rm x}(\mu) + (1-\beta) \Sigma^{\rm SR}_{\rm x}(\mu)\]where the parameters \(\alpha, \beta, \mu\) have the values of the variables alpha_RSH, beta_RSH and mu_RSH respectively, and

\(\Sigma^{\rm erf}(\mu)\) is a screened exchange operator having an interaction potential \(\rm erf (\mu r) / r\)

\(\Sigma^{\rm erfc}(\mu)\) is a screened exchange operator having an interaction potential \(\rm erfc (\mu r) / r\)

\(\Sigma^{\rm LR}_{\rm x}(\mu)\) is the long-range semilocal PBE exchange potential

\(\Sigma^{\rm SR}_{\rm x}(\mu)\) is the short-range semilocal PBE exchange potential

The following table shows how some specific functionals are special cases of the RSH functional:

\(\alpha\) \(\beta\) \(\mu\) HSE 0 0.25 0.11 PBE0 0.25 0 \(\infty\) PBE 0 0 0 CAM-B3LYP 0.46 0.19 0.33 LC\(\mu\)PBE 1 0 0.4 If the RSH functional is selected, the default parameter values correspond to the HSE functional.

- ALLOWED VALUES
- LDA, VWN, PBE, PBE0, BLYP, HF, B3LYP, HSE, RSH, BHandHLYP