howto:gfn1xtb

# How to run a GFN1-xTB calculation

This is a short tutorial on how to run GFN1-xTB computations. The details on the theory and the original implementation by Grimme can be found in https://pubs.acs.org/doi/full/10.1021/acs.jctc.7b00118. Please cite this paper if you were to use the GFN1-xTB module.

## Brief theory recap

The semi-empirical GFN1-xTB energy expression comprises contributions due to electronic (EL), atom-pairwise repulsion (REP), dispersion (DISP), and halogen-bonding (XB) terms,

\begin{equation}\label{gfnxtb1_plus_nonbonded} \begin{aligned} E_{\rm{\tiny{GFN1-xTB}}} = E_{\rm{\tiny{EL}}} + E_{\rm{\tiny{REP}}} + E_{\rm{\tiny{DISP}}} + E_{\rm{\tiny{XB}}} \, . \end{aligned} \end{equation}

1. The electronic energy contribution,

\begin{equation}\label{electronic_energy} \begin{aligned} E_{\rm{\tiny{EL}}} = \sum_i^{\rm{\tiny{occ}}} n_i \langle \Psi_i | h_0 | \Psi_i \rangle + \frac{1}{2} \sum_{A,B} \sum_{{l}^A}\sum_{{l'}^B} p_l^A p_{{l'}}^B \gamma_{AB,ll'} + \frac{1}{3}\sum_{A} \Gamma_A q_A^3 - T_{\rm{\tiny{el}}} S_{\rm{\tiny{el}}} \, , \end{aligned} \end{equation}

contains zeroth-order contributions based on a zeroth-order Hamiltonian $h_0$, the valence molecular orbitals $\Psi_i$, occupation numbers $n_i$ as well as second-order contributions which are optimized self-consistently as well as third-order diagonal contributions. The second order contributions are described using the semi-empirical electron repulsion operator $\gamma_{AB,ll'}$ which depends on the interatomic distance of atoms $A$ and $B$ as well as further empirical parameters that are specific for different angular momenta $l$ and $l'$. The monopole charges of the second-order expression are optimized self-consistently,

\begin{equation}\label{scc_charges} \begin{aligned} p_l^A = p_l^{A_0} - \sum_{\nu}^{N_{\rm{\tiny{AO}}}} \sum_{\mu \in A, \mu \in l} S_{\mu \nu } P_{\mu \nu} \, , \end{aligned} \end{equation}

referring to the atomic orbital overlap matrix $\mathbf{S}$ and the density matrix $\mathbf{P}$.

The remaining diagonal terms represent a cubic charge correction based on the Mulliken charge $q_A$ of atom $A$ and the charge derivative $\Gamma_A$ of the atomic Hubbard parameter $\eta_A$. Furthermore, the electronic temperature times entropy term $T_{\rm{\tiny{el}}}S_{\rm{\tiny{el}}}$ enables fractional orbital occupations.

2. Repulsion is described via an atom-pairwise potential,

\begin{equation}\label{repulsion} \begin{aligned} E_{\rm{\tiny{REP}}} = \sum_{AB} \frac{Z_A^{\rm{\tiny{eff}}} Z_B^{\rm{\tiny{eff}}} }{R_{AB}} \exp^{- (\alpha_A \alpha_B)^{1/2} (R_{AB})^{k_f}} \, , \end{aligned} \end{equation} with the effective nuclear charge $\mathbf{Z}^{\rm{\tiny{eff}}}$ as well as the global or element-specific parameters $k_f$ and $\alpha$.

3. Dispersion is included by the well-established D3 method in the BJ-damping schemehttps://aip.scitation.org/doi/10.1063/1.3382344.

4. Corrections for element-specific interactions are possible using either a halogen-bonding correction term (XB) or a generic nonbonding potential correction (NONBOND). Note that the generic nonbonding potential correction is CP2K specific and thus the so-obtained energy differs from the original GFN1-xTB method,

\begin{equation}\label{gfnxtb1_energy_expression} \begin{aligned} E_{\rm{\tiny{GFN1-xTB+NONBOND}}} = E_{\rm{\tiny{GFN1-xTB}}} + E_{\rm{\tiny{NONBOND}}} \, . \end{aligned} \end{equation}

## The GFN1-xTB input section

The most important keywords and subsections of section xTB are:

• DO_EWALD: keyword to activate Ewald summation for periodic boundary conditions (PBC); has to be switched to true in case of PBC
• USE_HALOGEN_INTERACTION: keyword to switch off contribution $E_{\rm{\tiny{XB}}}$ to correct halogen interactions, default is to include this correction
• CHECK_ATOMIC_CHARGES: the cubic charge diagonal contribution is checked to be numerically stable by switching the keyword to true.
• DO_NONBONDED: add a generic correction potential to correct bond- or atomic-specific interactions
• PARAMETER: it is possible to add this section with corresponding keywords to modify xTB parameters

The additional keywords COULOMB_INTERACTION, COULOMB_LR and TB3_INTERACTION are for debugging purposes only and it is recommended to use the default options here.

## Simple examples

### GFN1-xTB ground-state energy for

The following input is an examplary standard input for calculating GFN1-xTB ground-state energies.

periodic.inp
&GLOBAL
RUN_TYPE  ENERGY
PROJECT_NAME xtb
PRINT_LEVEL  MEDIUM
PREFERRED_DIAG_LIBRARY SL
&END GLOBAL
&FORCE_EVAL
METHOD QS
&DFT
&QS
METHOD XTB
&XTB
CHECK_ATOMIC_CHARGES F               ! Keyword to check if Mulliken charges are physically reasonable
DO_EWALD  T                          ! Ewald summation is required for periodic structures
USE_HALOGEN_CORRECTION T             ! Element-specific correction for halogen interactions (Cl, Br) with (O, N)
&END XTB
&END QS
&SCF
SCF_GUESS RESTART
MAX_SCF 50
EPS_SCF 1.E-6
&OT ON
PRECONDITIONER FULL_SINGLE_INVERSE
MINIMIZER DIIS
&END
&OUTER_SCF
MAX_SCF 200
EPS_SCF 1.E-6
&END OUTER_SCF
&END SCF
&END DFT
&SUBSYS
&TOPOLOGY
COORD_FILE_FORMAT  xyz
COORD_FILE_NAME  input.xyz
CONNECTIVITY OFF
&CENTER_COORDINATES
&END CENTER_COORDINATES
&END TOPOLOGY
&CELL
ABC  21.64 21.64 21.64
ALPHA_BETA_GAMMA 90.0 90.0 90.0
PERIODIC XYZ
&END CELL
&END SUBSYS
&END FORCE_EVAL


The so-obtained output is listing information on the chosen system-specific parameters. Note that parameters can be changed manually by adding a PARAMETER section to the xTB section and specifying corresponding keywords for the specific parameters with the adjusted values or by giving the path to the modified parameter file, adding the keywords PARAM_FILE_PATH pathname and PARAM_FILE_NAME filename.

cp2k
                  #####   #####        #          ####### ######
#     # #     #      #              #    #     #
#     # #           #    ##   ##    #    #     #
#     #  #####     #      ## ##     #    ######
#   # #       #   #        ###      #    #     #
#    #  #     #  #        ## ##     #    #     #
#### #  #####  #        ##   ##    #    ######

xTB| Parameter file                                              xTB_parameters
xTB| Basis expansion STO-NG                                                   6
xTB| Basis expansion STO-NG for Hydrogen                                      4
xTB| Halogen interaction potential                                            F
xTB| Halogen interaction potential cutoff radius                         20.000
xTB| Nonbonded interactions                                                   F
xTB| D3 Dispersion: Parameter                                         dftd3.dat
xTB| Huckel constants ks kp kd                        1.850     2.250     2.000
xTB| Huckel constants ksp k2sh                                  2.080     2.850
xTB| Mataga-Nishimoto exponent                                            2.000
xTB| Repulsion potential exponent                                         1.500
xTB| Coordination number scaling kcn(s) kcn(p) kc     0.006    -0.003    -0.005
xTB| Electronegativity scaling                                           -0.007
xTB| Halogen potential scaling kxr kx2                          1.300     0.440


Analogously to any other self-consistent field optimization (SCF) method, the output also includes the energy and convergence during the SCF steps with the finally converged GFN1-xTB energy.

cp2k
 SCF WAVEFUNCTION OPTIMIZATION

----------------------------------- OT ---------------------------------------
Minimizer      : DIIS                : direct inversion
in the iterative subspace
using   7 DIIS vectors
safer DIIS on
Preconditioner : FULL_SINGLE_INVERSE : inversion of
H + eS - 2*(Sc)(c^T*H*c+const)(Sc)^T
Precond_solver : DEFAULT
stepsize       :    0.08000000                  energy_gap     :    0.08000000
eps_taylor     :   0.10000E-15                  max_taylor     :             4
----------------------------------- OT ---------------------------------------

Step     Update method      Time    Convergence         Total energy    Change
------------------------------------------------------------------------------
1 OT DIIS     0.80E-01    0.5     0.01213502      -947.7483409153 -9.48E+02
2 OT DIIS     0.80E-01    0.3     0.00675007      -951.5762826800 -3.83E+00
3 OT DIIS     0.80E-01    0.3     0.00092877      -953.2164544959 -1.64E+00
4 OT DIIS     0.80E-01    0.3     0.00034159      -953.2591478247 -4.27E-02
5 OT DIIS     0.80E-01    0.3     0.00018348      -953.2687102329 -9.56E-03
6 OT DIIS     0.80E-01    0.3     0.00009265      -953.2707750500 -2.06E-03
7 OT DIIS     0.80E-01    0.3     0.00005495      -953.2714236504 -6.49E-04
8 OT DIIS     0.80E-01    0.3     0.00002612      -953.2716704946 -2.47E-04
9 OT DIIS     0.80E-01    0.3     0.00001585      -953.2717390500 -6.86E-05
10 OT DIIS     0.80E-01    0.3     0.00001020      -953.2717664315 -2.74E-05
11 OT DIIS     0.80E-01    0.3     0.00000564      -953.2717774258 -1.10E-05
12 OT DIIS     0.80E-01    0.3     0.00000354      -953.2717818198 -4.39E-06
13 OT DIIS     0.80E-01    0.3     0.00000206      -953.2717839406 -2.12E-06
14 OT DIIS     0.80E-01    0.3     0.00000127      -953.2717844831 -5.42E-07
15 OT DIIS     0.80E-01    0.3     0.00000077      -953.2717846336 -1.51E-07

*** SCF run converged in    15 steps ***

Core Hamiltonian energy:                                   -962.45147378153547
Repulsive potential energy:                                   8.84897617161771
Electronic energy:                                            0.76461561909348
DFTB3 3rd order energy:                                       0.33228335538302
Dispersion energy:                                           -0.76618599817727

Total energy:                                              -953.27178463361872

outer SCF iter =    1 RMS gradient =   0.77E-06 energy =       -953.2717846336
outer SCF loop converged in   1 iterations or   15 steps


### Adding a generic correction potential

It is possible to add a generic non bonded correction potential. The potential form can be chosen freely and needs to be specified by adding the keyword FUNCTION. Included parameters and variables have to be specified using the keywords VARIABLES and PARAMETERS. The section can be repeated as often as required and enables to include pairwise, element-specific correction potentials. The implementation also features analytic gradients for this option.

periodic_with_generic_correction_potential.inp
&GLOBAL
RUN_TYPE  ENERGY
PROJECT_NAME xtb
PRINT_LEVEL  MEDIUM
PREFERRED_DIAG_LIBRARY SL
&END GLOBAL
&FORCE_EVAL
METHOD QS
&DFT
&QS
METHOD XTB
&XTB
CHECK_ATOMIC_CHARGES F
DO_EWALD  T
USE_HALOGEN_CORRECTION T
DO_NONBONDED T                      ! Possible option to include a generic non-bonded potential
&NONBONDED                         ! Specification of the potential, keyword can be repeated
&GENPOT
ATOMS Kr Br
FUNCTION Aparam*exp(-Bparam*r)-Cparam/r**8  ! Potential formula has to be specified
PARAMETERS Aparam Bparam Cparam             ! Parameters included in the formula above
VALUES 70.0 1.0 0.0                         ! Explicit values for the parameters
VARIABLES r
RCUT 40.5
&END GENPOT
&END NONBONDED
&END XTB
&END QS
&SCF
SCF_GUESS RESTART
MAX_SCF 50
EPS_SCF 1.E-6
&OT ON
PRECONDITIONER FULL_SINGLE_INVERSE
MINIMIZER DIIS
&END
&OUTER_SCF
MAX_SCF 200
EPS_SCF 1.E-6
&END OUTER_SCF
&END SCF
&END DFT
&SUBSYS
&TOPOLOGY
COORD_FILE_FORMAT  xyz
COORD_FILE_NAME  input.xyz
CONNECTIVITY OFF
&CENTER_COORDINATES
&END CENTER_COORDINATES
&END TOPOLOGY
&CELL
ABC  21.64 21.64 21.64
ALPHA_BETA_GAMMA 90.0 90.0 90.0
PERIODIC XYZ
&END CELL
&END SUBSYS
&END FORCE_EVAL 