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Manual: Migrate howto:newtonx from wiki (Orig. Author: Anna Hehn)

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molecular_dynamics
metadynamics
path_integrals
Surface Hopping with NEWTON-X <https://www.cp2k.org/howto:newtonx>
newton-x
i-PI <https://www.cp2k.org/howto:ipi>
Gibbs Ensemble Monte Carlo <https://www.cp2k.org/howto:gemc>
Langevin Dynamics <https://www.cp2k.org/howto:langevin_regions>

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# Surface Hopping with NEWTON-X
This is a short tutorial on how to use the CP2K-NEWTONX interface to a) generate initial conditions
to compute photoabsorption spectra and b) to run non-adiabatic dynamics simulations using orbital
derivative couplings. A more comprehensive tutorial on all NEWTONX features, including a
documentation of the required specifications for the CP2K interface, can be found on the NEWTONX
homepage, <https://newtonx.org/documentation-tutorials/>.
## Brief theory recap
The interface enables to use electronic-structure data from CP2K and combine it with the surface
hopping module of NEWTONX. Excitation energies $\Omega^M$ and excited-state eigenvectors
$\mathbf{X}^M$ to describe the excited state $M$ are provided by CP2K, relying on the Tamm-Dancoff
eigenvalue problem,
$$
\mathbf{A} \mathbf{X}^M &= \Omega^M \mathbf{S} \mathbf{X}^M \, , \\
\sum_{\kappa k} [ F_{\mu \kappa \sigma} \delta_{ik} - F_{ik \sigma} S_{\mu \kappa} ] X^M_{\kappa k \sigma} + \sum_{\lambda} K_{\mu \lambda \sigma} [\mathbf{D}^{{\rm{\tiny{X}}}M}] C_{\lambda i \sigma} &= \sum_{\kappa} \Omega^M S_{\mu \kappa} X^M_{\kappa i \sigma} \, ,
$$
with $\mathbf{S}$ representing the conventional atomic-orbital overlap matrix, $\mathbf{F}$ the
Kohn-Sham matrix, $\mathbf{K}$ the kernel comprising -- depending on the chosen functional --
Coulomb, exchange and exchange-correlation contributions, and $\mathbf{C}$ the molecular orbital
coefficients. $\mu, \nu, \dots$ denote atomic orbitals, $i, j, \dots$ occupied molecular orbitals.
The corresponding excited-state gradient is obtained setting up a variational Lagrangian and taking
the derivative with respect to the nuclear coordinates $\mathbf{R}$ (see also
[](../properties/tddft)).
By performing a TDDFPT computation, excitation energies $\Omega^M (\mathbf{R}(t))$, excited-state
eigenvectors $\mathbf{X}^M (\mathbf{R}(t))$ and corresponding excited-state gradients
$\nabla \Omega^M (\mathbf{R}(t))$ are provided by CP2K. On the so-defined potential energy surfaces,
the nuclei are propagated classically relying on the surface hopping code of NEWTONX,
$$
\mathbf{R}(t + \Delta t) &= \mathbf{R} (t) + \mathbf{v} (t) \Delta t + \frac{1}{2} \mathbf{a}(t) \Delta t^2 \, ,\\
\mathbf{v} (t + \Delta t) &= \mathbf{v} (t) + \frac{1}{2} (\mathbf{a} (t) + \mathbf{a} (t+ \Delta t) ) \Delta t \, , \\
\mathbf{a} (t) &= - \frac{1}{m} \nabla \Omega^M (\mathbf{R}(t)) \, .
$$
The coefficients $c^M (t)$ of the total wave function $\Psi (\mathbf{R}(t))$ over all excited states
$M$ are obtained implying hopping probabilities $P_{M\rightarrow N}$ of Tully's surface hopping,
$$
\Psi (\mathbf{R}(t)) &= \sum_{M} c^{M} (t) \Psi^M (\mathbf{R}(t)) \\
i \frac{{\rm{d}} c^M (t)}{{\rm{d}}t} &= \sum_N c^N (t) \left ( \delta_{MN} E_N (\mathbf{R}(t)) - i \sigma_{MN} (t) \right ) \, , \\
P_{M \rightarrow N} &= {\rm{max}} \left [ 0, \frac{-2 \Delta t}{| c^M|^2} {\rm{Re}} (c^M c^{N \ast}) \sigma_{MN} \right ] \, .
$$
The therefore required non-adiabatic time derivative couplings $\sigma_{MN}$ can be obtained relying
on semi-empirical models (Baeck-An; please cite
[Barbatti et al., Open Research Europe 1, 49 (2021)](https://doi.org/10.12688/openreseurope.13624.1).)
or as numerical time derivative couplings (orbital time derivative (OD); please cite
[Ryabinkin et al., J. Phys. Chem. Lett. 6, 4200 (2015)](https://doi.org/10.1021/acs.jpclett.5b02062);
[Barbatti et al., Molecules 21, 1603 (2016)](https://doi.org/10.3390/molecules21111603).), with the
corresponding molecular orbital overlap matrix $\mathbf{S}^{{\rm{\tiny{t-\Delta t,t}}}}$ being
provided by CP2K,
$$
\sigma_{MN}^{{\rm{\tiny{OD}}}} &= \sum_{ia} X_{ia}^{M} \frac{\partial }{\partial t} X_{ia}^N + \sum_{iab} X_{ia}^M X_{ib}^N S_{ab}^{{\rm{\tiny{t-\Delta t,t}}}} - \sum_{ija} P_{ij} X_{ia}^M X_{ja}^N
S_{ji}^{{\rm{\tiny{t-\Delta t,t}}}} \\
S_{pq}^{{\rm{\tiny{t - \Delta t , t}}}} &= \frac{\langle \phi_i (\mathbf{R}(t- \Delta t )) | \phi_j (\mathbf{R} (t)) \rangle}{\Delta t} \, .
$$
$a,b, \dots$ denote virtual molecular orbitals.
## General input setup
The input sections for TDDFPT energy and gradient computations are described in
[](../properties/tddft). To furthermore provide the required CP2K output, subsequently read in by
NEWTONX, the following print statements have to be added to the CP2K input files:
- [FORCE_EVAL.PRINT.FORCES](#CP2K_INPUT.FORCE_EVAL.PRINT.FORCES): prints the excited-state forces
- [TDDFPT.PRINT.NAMD_PRINT](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.PRINT.NAMD_PRINT) with keyword
option [PRINT_PHASES](#CP2K_INPUT.FORCE_EVAL.PROPERTIES.TDDFPT.PRINT.NAMD_PRINT.PRINT_PHASES):
prints the excited-state eigenvectors in MO format as well as the corresponding phases.
- [VIBRATIONAL_ANALYSIS.PRINT.NAMD_PRINT](#CP2K_INPUT.VIBRATIONAL_ANALYSIS.PRINT.NAMD_PRINT): prints
normal modes to generate initial conditions It should furthermore be noted that cartesian
coordinates have to be provided in terms of the external file `coord.cp2k` and that the number of
atoms has to be specified in the CP2K input file in the [SUBSYS](#CP2K_INPUT.FORCE_EVAL.SUBSYS)
section.
## A) Initial conditions and photoabsorption spectra
The following tutorial to obtain photoabsorption spectra is based on section 2 of
<https://vdv.dcf.mybluehost.me/nx/wp-content/uploads/2020/02/tutorial-2_2.pdf>. For the
electronic-structure calculation with CP2K, a `cp2k.inp` and `cp2k.par` file as well as a coordinate
file named `coord.cp2k` has to be provided in a subdirectory called `JOB_AD`. Furthermore, a
vibrational analysis computation has to be performed to provide cartesian normal modes, with the
input file including the corresponding `NAMD print` section.
Examplary input files for computing the absorption spectrum as well as for performing a vibrational
analysis for a single water molecule with CP2K are given below:
```none
&GLOBAL
PROJECT excited_states_for_h2o
RUN_TYPE ENERGY
PREFERRED_DIAG_LIBRARY SL
PRINT_LEVEL medium
&END GLOBAL
&FORCE_EVAL
&PRINT # print statement for ground-state or excited-state forces
&FORCES
&END FORCES
&END PRINT
METHOD Quickstep
&PROPERTIES
&TDDFPT # TDDFPT input section to compute 10 excited states
&DIPOLE_MOMENTS
DIPOLE_FORM LENGTH
&END DIPOLE_MOMENTS
KERNEL FULL
NSTATES 10
MAX_ITER 100
MAX_KV 20
CONVERGENCE [eV] 1.0e-5
RKS_TRIPLETS F
&PRINT # NAMD print section to print excited-state eigenvectors
&NAMD_PRINT
PRINT_VIRTUALS T
PRINT_PHASES T
&END NAMD_PRINT
&END PRINT
&END TDDFPT
&END PROPERTIES
&DFT
&QS
METHOD GAPW
EPS_DEFAULT 1.0E-17
&END QS
&SCF
SCF_GUESS restart
&OT
PRECONDITIONER FULL_ALL
MINIMIZER DIIS
&END OT
&OUTER_SCF
MAX_SCF 900
EPS_SCF 1.0E-7
&END OUTER_SCF
MAX_SCF 10
EPS_SCF 1.0E-7
&END SCF
POTENTIAL_FILE_NAME POTENTIAL
BASIS_SET_FILE_NAME EMSL_BASIS_SETS
&MGRID
CUTOFF 1000
REL_CUTOFF 100
NGRIDS 5
&END MGRID
&POISSON
PERIODIC NONE
PSOLVER MT
&END
&XC
&XC_FUNCTIONAL PBE
&END XC_FUNCTIONAL
&END XC
&END DFT
&SUBSYS
&CELL
ABC 8.0 8.0 8.0
PERIODIC NONE
&END CELL
# Coordinates are provided externally for the interface
&COORD
@include coord.cp2k
&END COORD
&TOPOLOGY
&CENTER_COORDINATES T
&END
NATOMS 3 # specifying number of atoms for NEWTONX
CONNECTIVITY OFF
&END TOPOLOGY
&KIND H
BASIS_SET 6-311Gxx
POTENTIAL ALL
&END KIND
&KIND O
BASIS_SET 6-311Gxx
POTENTIAL ALL
&END KIND
&END SUBSYS
&END FORCE_EVAL
```
```none
&GLOBAL
PROJECT normal_modes_for_h2o
RUN_TYPE VIBRATIONAL_ANALYSIS #computing normal modes to generate initial conditions
PREFERRED_DIAG_LIBRARY SL
PRINT_LEVEL medium
&END GLOBAL
&FORCE_EVAL
&PRINT
&FORCES
&END FORCES
&END PRINT
METHOD Quickstep
&DFT
&QS
METHOD GAPW # GAPW enables comparison with all-electron molecular program codes like Turbomole
EPS_DEFAULT 1.0E-17
&END QS
&SCF
SCF_GUESS restart
&OT
PRECONDITIONER FULL_ALL
MINIMIZER DIIS
&END OT
&OUTER_SCF
MAX_SCF 900
EPS_SCF 1.0E-7
&END OUTER_SCF
MAX_SCF 10
EPS_SCF 1.0E-7
&END SCF
POTENTIAL_FILE_NAME POTENTIAL
BASIS_SET_FILE_NAME EMSL_BASIS_SETS
&MGRID
CUTOFF 1000
REL_CUTOFF 100
NGRIDS 5
&END MGRID
&POISSON
PERIODIC NONE
PSOLVER MT
&END
&XC
&XC_FUNCTIONAL PBE
&END XC_FUNCTIONAL
&END XC
&END DFT
&SUBSYS
&CELL
ABC 8.0 8.0 8.0
PERIODIC NONE
&END CELL
# coordinates must be provided as external file for NEWTONX
&COORD
@include coord.cp2k
&END COORD
&TOPOLOGY
&CENTER_COORDINATES T
&END
NATOMS 3
CONNECTIVITY OFF
&END TOPOLOGY
&KIND H
BASIS_SET 6-311Gxx
POTENTIAL ALL
&END KIND
&KIND O
BASIS_SET 6-311Gxx
POTENTIAL ALL
&END KIND
&END SUBSYS
&END FORCE_EVAL
&VIBRATIONAL_ANALYSIS
&PRINT
&NAMD_PRINT # keyword to enable printing of cartesian normal modes
&END NAMD_PRINT
&END PRINT
DX 0.001
&END VIBRATIONAL_ANALYSIS
```
The input file `cp2k.par` includes all specifications regarding the executable and parallelization
setup.
```none
parallel = 16
exec = cp2k.psmp
```
Furthermore, a `initqp_input` file has to be generated for NEWTONX following the instructions given
in the NEWTONX tutorial. Specifications for CP2K in the `initqp_input` file are the following:
- The file comprising the normal modes of the CP2K frequency computation -- for the above input
provided as `normal_modes_for_h2o-VIBRATIONS-1.eig`-- has to be specified as
`file_nmodes = normal_modes_for_h2o-VIBRATIONS-1.eig`.
- The electronic structure program has to be specified as CP2K by defining `iprog = 10`.
```none
&dat
nact = 2
iprog = 10
numat = 3
npoints = 500
file_geom = geom
file_nmodes = normal_modes_for_h2o-VIBRATIONS-1.eig
anh_f = 1
rescale = n
temp = 0
ics_flg = n
chk_e = 1
nis = 1
nfs = 11
kvert = 1
de = 100
prog = 14
iseed = 0
lvprt = 1
/
```
After providing the excited-state CP2K computation based on input file `h2o_cp2k.inp` in the
subdirectory `JOB_AD`, the normal modes `normal_modes_for_h2o-VIBRATIONS-1.eig` of the frequency
computation and the `initqp_input` file for NEWTONX, the script initcond.pl of NEWTONX can be
executed to generate initial conditions. The resulting initcond-output file of NEWTONX, it is first
stated that the read-in cartesian normal modes are transferred to mass-weighted normal modes.
```none
Cartesian normal modes (1/sqrt(amu))
0.00 0.00 0.00 0.00 0.00 0.00 1523.92 3851.12
0.0000 -0.0492 0.0001 -0.1268 0.5632 -0.0083 0.0000 -0.0000
-0.0886 0.0000 -0.0000 -0.0169 0.0047 0.5777 0.0000 -0.0000
-0.0000 -0.0000 -0.0000 0.5630 0.1269 0.0155 -0.0715 0.0487
0.0001 0.3905 -0.0004 -0.1267 0.5632 -0.0082 -0.4184 -0.5910
0.7043 0.0008 0.7071 -0.0162 0.0040 0.5768 0.0000 0.0000
-0.0001 -0.5885 0.0007 0.5630 0.1270 0.0155 0.5678 -0.3867
0.0000 0.3905 -0.0004 -0.1267 0.5632 -0.0083 0.4184 0.5910
0.7043 -0.0009 -0.7071 -0.0170 0.0051 0.5768 0.0000 0.0000
-0.0000 0.5885 -0.0007 0.5630 0.1269 0.0154 0.5678 -0.3867
3986.44
0.0712
-0.0000
0.0000
-0.5650
0.0000
-0.4222
-0.5650
0.0000
0.4222
Mass weighted normal modes
Frequencies will be multiplied by ANH_F = 1.00000
0.00 0.00 0.00 0.00 0.00 0.00 1523.92 3851.12
0.0001 -0.1967 0.0006 -0.5069 2.2526 -0.0330 0.0000 -0.0000
-0.3543 0.0000 -0.0000 -0.0677 0.0186 2.3104 0.0000 -0.0000
-0.0001 -0.0000 -0.0002 2.2517 0.5077 0.0619 -0.2861 0.1949
0.0001 0.3920 -0.0004 -0.1272 0.5654 -0.0083 -0.4200 -0.5933
0.7071 0.0008 0.7099 -0.0162 0.0040 0.5791 0.0000 0.0000
-0.0001 -0.5908 0.0007 0.5652 0.1275 0.0155 0.5700 -0.3882
0.0000 0.3921 -0.0004 -0.1272 0.5654 -0.0083 0.4200 0.5933
0.7071 -0.0009 -0.7099 -0.0171 0.0051 0.5790 0.0000 0.0000
-0.0000 0.5908 -0.0007 0.5652 0.1274 0.0155 0.5700 -0.3882
3986.44
0.2847
-0.0000
0.0000
-0.5672
0.0000
-0.4238
-0.5672
0.0000
0.4238
```
The thereon based initial conditions are summarized in external output files for each state, dubbed
"final_output_XXX", comprising information on the various geometries and velocities as examplarily
given below:
```none
Initial condition = 1
Geometry in COLUMBUS and NX input format:
o 8.0 5.00630777 5.00000001 4.46399957 15.99491464
h 1.0 6.37684065 5.00000128 5.50815661 1.00782504
h 1.0 3.52303474 5.00000149 5.58297278 1.00782504
Velocity in NX input format:
-0.000089112 0.000000000 -0.000020915
0.000417197 0.000000002 0.000694479
0.000997296 0.000000013 -0.000362483
Epot of initial state (eV): 0.0865 Epot of final state (eV): 19.0799
Vertical excitation (eV): 18.9935 Is Ev in the required range? YES
Ekin of initial state (eV): 0.0479 Etot of initial state (eV): 0.1343
Oscillator strength: 0.1221
State: 10
```
Based on the initial conditions, the broadened photoabsorption spectrum can be computed with the
nxinp script. As outlined in section 2.7 of the cited NEWTONX tutorial, the so-obtained output file
`cross-section.dat` comprises the data points of the computed photoabsorption spectrum as visualized
below:
## B) Non-adiabatic dynamics using orbital determinant derivatives