Extended Tight Binding

This is a short tutorial on how to run GFN-xTB simulations with CP2K. The details on the theory and the original implementation can be found in Grimme2017 for GFN1-xTB and in Bannwarth2019 for GFN2-xTB.

The GFN-xTB methods are implemented either natively in CP2K or through the tblite library as described in Katbashev2025 and Alizadeh2026. The natively available methods are GFN0-xTB and GFN1-xTB, while the tblite library provides GFN1-xTB, IPEA1-xTB and GFN2-xTB.

In this tutorial after a brief theory recap, there is an example on how to run GFN2-xTB simulation with tblite and later there is an example on how to run GFN1-xTB with the native implementation.

Brief theory recap

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

\[ E_{\rm{\tiny{GFN1-xTB}}} = E_{\rm{\tiny{EL}}} + E_{\rm{\tiny{IES}}} + E_{\rm{\tiny{REP}}} + E_{\rm{\tiny{DISP}}} + E_{\rm{\tiny{XB}}} \, . \]

The GFN2-xTB, is defined similarly using anisotropic electrostatic (AES) in addition to isotropic contributions,

\[ E_{\rm{\tiny{GFN2-xTB}}} = E_{\rm{\tiny{EL}}} + E_{\rm{\tiny{AES}}} + E_{\rm{\tiny{REP}}} + E_{\rm{\tiny{DISP}}} \, . \]

1. Electronic energy

The electronic energy contribution,

\[ E_{\rm{\tiny{EL}}} = \sum_i^{\rm{\tiny{occ}}} n_i \langle \Psi_i | h_0 | \Psi_i \rangle - T_{\rm{\tiny{el}}} S_{\rm{\tiny{el}}} \, , \]

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 the electronic temperature times entropy term \(T_{\rm{\tiny{el}}}S_{\rm{\tiny{el}}}\) from fractional orbital occupations.

2. Electrostatic energy

The isotropic electrostatic energy contains a second-order contributions which are optimized self-consistently as well as third-order diagonal contributions,

\[ E_{\rm{\tiny{IES}}} = \frac{1}{2} \sum_{A,B} \sum_{{l}^A}\sum_{{l'}^B} p_l^A p_{{l'}}^B \gamma_{AB,ll'} + \frac{1}{3}\sum_{A} \Gamma_A q_A^3 \, . \]

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,

\[ p_l^A = p_l^{A_0} - \sum_{\nu}^{N_{\rm{\tiny{AO}}}} \sum_{\mu \in A, \mu \in l} S_{\mu \nu } P_{\mu \nu} \, , \]

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 \(\eta_A\).

In GFN2-xTB the electrostatic energy is extended to anisotropic electrostatic contributions,

\[ E_{\rm{\tiny{AES}}} = E_{\rm{\tiny{IES}}} + \sum_{A,B}\sum_{i} \mu_i q_B T_{AB,i} + \frac12\sum_{A,B}\sum_{ij} \mu_{A,i} \mu_{B,j} T_{AB,ij} + \sum_{A,B}\sum_{ij} \theta_{A,ij} q_B T_{AB,ij} \, , \]

including the atomic dipole moments \(\mu_A\) and atomic quadrupole moments \(\theta_A\). The interaction tensors \(T_{AB}\) are defined by

\[ T_{AB,i} = -f(R_{AB})\frac{R_{AB,i}}{R^3_{AB}} \, , \]

for the charge-dipole interaction and

\[ T_{AB,ij} = f(R_{AB})\frac{3R_{AB,i}R_{AB,j} - R^2_{AB}}{R^5_{AB}} \, , \]

for the dipole-dipole and charge-dipole interaction, both interaction tensors include a short-ranged damping function \(f\).

3. Repulsion

Repulsion is described via an atom-pairwise potential,

\[ E_{\rm{\tiny{REP}}} = \sum_{AB} \frac{Z_A^{\rm{\tiny{eff}}} Z_B^{\rm{\tiny{eff}}} }{R_{AB}} \exp^{- (\alpha_A \alpha_B)^{1/2} (R_{AB})^{k_f}} \, , \]

with the effective nuclear charge \(\mathbf{Z}^{\rm{\tiny{eff}}}\) as well as the global or element-specific parameters \(k_f\) and \(\alpha\).

4. Dispersion

Dispersion is included by the well-established D3 method in the BJ-damping scheme Grimme2010 for GFN1-xTB and using the D4 method with self-consistent charges for GFN2-xTB.

5. Corrections

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,

\[ E_{\rm{\tiny{GFN1-xTB+NONBOND}}} = E_{\rm{\tiny{GFN1-xTB}}} + E_{\rm{\tiny{NONBOND}}} \, . \]

The GFN-xTB input section

In this section the keywords for the native GFN-xTB implementation are described. The most important keywords and subsections of section XTB are:

  • CHECK_ATOMIC_CHARGES: the cubic charge diagonal contribution is checked to be numerically stable by switching the keyword to true.

  • USE_HALOGEN_CORRECTION: keyword to switch off contribution \(E_{\rm{\tiny{XB}}}\) to correct halogen interactions, default is to include this correction

  • 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

  • DO_EWALD: keyword to activate Ewald summation for periodic boundary conditions (PBC); has to be switched to true in case of PBC. Starting from CP2K 2026.2 the periodicity is directly taken from the cell definition, which makes this keyword obsolete.

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.

Input section for tblite

Available methods in the METHOD keyword are

  • GFN1: for GFN1-xTB method

  • GFN2: for GFN2-xTB method

  • IPEA1: for IPEA1-xTB version of GFN1-xTB

  • PARAM: read parameter file from filename provided via PARAM keyword, the format for the parameter file is following tblite structure as described in the documentation.

For enabling GFN-xTB methods via the tblite library, set the METHOD keyword to xTB and the GFN_TYPE in the XTB block to tblite. The TBLITE section allows to configure the input for the library, like selecting the actual GFN-xTB method via the METHOD keyword.

&QS
  METHOD xTB
  &XTB
    GFN_TYPE TBLITE
    SCC_MIXER AUTO
    &TBLITE
      METHOD GFN2
      ACCURACY 1.0
    &END TBLITE
  &END XTB
&END QS

The ACCURACY keyword controls the convergence thresholds of the electronic mixer in the tblite library. Lower values correspond to tighter convergence.

Simple examples

GFN-xTB ground-state energy based on Tblite

The following input is an example for calculating a single point calculation of ice-Ih crystal with GFN2-xTB method. Please note that k-points are fully supported for tblite in CP2K.

&GLOBAL
  PRINT_LEVEL LOW
  PROJECT ice_Ih_GFN2_k333
  RUN_TYPE ENERGY
&END GLOBAL

&FORCE_EVAL
  METHOD Quickstep
  &DFT
    &QS
      EPS_DEFAULT 1.0E-12
      METHOD xTB
      &XTB
        GFN_TYPE TBLITE
        &TBLITE
          METHOD GFN2
          ACCURACY 0.1
        &END TBLITE
      &END XTB
    &END QS
    &KPOINTS
      SCHEME MACDONALD 3 3 3 0.0 0.0 0.0
      FULL_GRID T
    &END KPOINTS
    &SCF
      EPS_SCF 1.0E-9
      MAX_SCF 300
      SCF_GUESS MOPAC
      &MIXING
        METHOD DIRECT_P_MIXING
        ALPHA 0.2
      &END MIXING
      &PRINT
        &RESTART OFF
        &END RESTART
      &END PRINT
    &END SCF
  &END DFT
  &SUBSYS
    &CELL
      PERIODIC XYZ
      A 7.678093000000 0.000000000000 0.000000000000
      B 3.839046000000 6.649423000000 0.000000000000
      C 0.000000000000 0.000000000000 7.234567000000
    &END CELL
    &COORD
      SCALED
      H   0.000007000000  0.334718000000  0.199799000000
      H   0.665252000000  0.000010000000  0.199780000000
      H   0.334714000000  0.665261000000  0.199791000000
      H   0.334760000000  0.999976000000  0.699786000000
      H   0.999980000000  0.665239000000  0.699800000000
      H   0.665240000000  0.334755000000  0.699799000000
      H   0.544461000000  0.000006000000  0.019584000000
      H  -0.000011000000  0.455520000000  0.019605000000
      H   0.455505000000  0.544480000000  0.019594000000
      H   0.455543000000  0.999980000000  0.519584000000
      H   0.999998000000  0.544446000000  0.519600000000
      H   0.544461000000  0.455524000000  0.519592000000
      H   0.332240000000  0.879481000000  0.984486000000
      H   0.211731000000  1.120507000000  0.984481000000
      H   0.879462000000  0.788265000000  0.984489000000
      H   0.788248000000  0.332255000000  0.984498000000
      H   0.667731000000  0.211748000000  0.984486000000
      H   0.120526000000  0.211703000000  0.484497000000
      H   0.667762000000  1.120506000000  0.484488000000
      H   0.788272000000  0.879477000000  0.484480000000
      H   0.211722000000  0.667743000000  0.484495000000
      H   0.332240000000  0.788252000000  0.484486000000
      H  -0.120503000000  0.332222000000  0.484499000000
      H   1.120486000000  0.667750000000  0.984491000000
      O   0.000009000000  0.331330000000  0.061616000000
      O   0.668637000000  0.000012000000  0.061595000000
      O   0.331326000000  0.668660000000  0.061608000000
      O   0.331370000000  0.999972000000  0.561601000000
      O   0.668637000000  0.331348000000  0.561616000000
      O   0.335676000000  0.999992000000  0.936746000000
      O   0.664294000000  0.335703000000  0.936768000000
      O   0.000012000000  0.335655000000  0.436771000000
      O   0.664333000000  0.999995000000  0.436740000000
      O   0.335670000000  0.664304000000  0.436760000000
      O   0.999979000000  0.668634000000  0.561617000000
      O   0.999974000000  0.664306000000  0.942299010000
    &END COORD
  &END SUBSYS
&END FORCE_EVAL

Unrestricted calculation with spGFN2-xTB

In case of open-shell calculations, a spin-polarization term can be enabled with the LSD keyword in CP2K. In this case, tblite automatically allows the usage of spGFN2-xTB for calculations as described in Neugebauer2023. An example for triplet oxygen is shown here.

&FORCE_EVAL
  &DFT
    LSD
    MULTIPLICITY 3
    &QS
      EPS_DEFAULT 1.00E-12
      METHOD xTB
      &XTB
        GFN_TYPE TBLITE
        SCC_MIXER TBLITE
        &TBLITE
          METHOD GFN2
        &END TBLITE
      &END XTB
    &END QS
    &SCF
      ADDED_MOS 1 3
      EPS_SCF 1.e-10
      MAX_SCF 200
      SCF_GUESS MOPAC
      &PRINT
        &RESTART OFF
        &END RESTART
      &END PRINT
    &END SCF
  &END DFT
  &SUBSYS
    &CELL
      ABC 20.0 20.0 20.0
      PERIODIC NONE
    &END CELL
    &COORD
      O     0.000000    0.000000    0.000000
      O     1.208000    0.000000    0.000000
    &END COORD
  &END SUBSYS
&END FORCE_EVAL

GFN1-xTB ground-state energy based on native Quickstep

The following input is a standard example for calculating GFN1-xTB ground-state energies using the native quickstep implementation XTB.

&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 and PARAM_FILE_NAME.

                  #####   #####        #          ####### ######   
                 #     # #     #      #              #    #     #  
                 #     # #           #    ##   ##    #    #     #  
                 #     #  #####     #      ## ##     #    ######   
                 #   # #       #   #        ###      #    #     #  
                 #    #  #     #  #        ## ##     #    #     #  
                  #### #  #####  #        ##   ##    #    ######   
                                                                   

 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.

 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.


&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