CP2K Open Source Molecular Dynamics

In this exercise, you will perform ab initio molecular dynamics using Second Generation Car-Parrinello (SGCP) molecular dynamics.

Please cite Phys. Rev. Lett. 98, 066401 , if you use this method.

Published work using SGCP method:

J. Phys. Chem. C 2018, 122, 42, 24068–24076

J. Phys. Chem. Lett. 2020, 11, 9, 3724–3730

1. Introduction

Second Generation CPMD (2ndG CPMD) is a molecular dynamics method that combines the efficiency of Car-Parrinello MD (CPMD) with the accuracy of Born-Oppenheimer MD (BOMD). It avoids fully self-consistent field (SCF) optimizations at each time step while enabling larger integration steps and maintaining accuracy close to BOMD.

Goal: Retain the efficiency of CPMD while achieving BOMD-level accuracy.

- Efficiency: Large time steps ; No full SCF loops

- Accuracy: Forces nearly indistinguishable from BOMD

- Stability: Effective for systems with vanishing band gaps

- Error Control: Controlled deviation from BO surface using adaptive correction

2. Comparison with CPMD and BOMD

Feature	CPMD	BOMD	SGCP
SCF at each step	No	Yes	Partially (predictor-corrector)
Time step	Small (~0.1 fs)	Large (~1 fs)	Large (~1–2 fs)
Conserved quantity preservation	Excellent	Reasonable	Excellent
On Born-Oppenheimer surface	Slightly above	Yes	Very close
Works for small-gap systems	Poor	Good	Good

3. ASPC Method

ASPC Method: Always Stable Predictor Corrector

ASPC is a Gear-type integrator for electronic wavefunctions:

Predictor:

$C_p(t_n) = \sum_{m=1}^{K} (-1)^{m+1} \cdot m \cdot B_m \cdot P_S(t_{n-m})$

where: - $B_m$ : Kolafa predictor coefficients - $P_S$ : projection onto the overlap matrix $S$

Corrector:

$C(t_n) = \omega \cdot \min[C_p(t_n)] + (1 - \omega) \cdot C_p(t_n), \quad \omega = \frac{K}{2K - 1}$

Langevin Dynamics & Dissipation Compensation

Because ASPC introduces small dissipation, Langevin-type equations are used to stabilize the dynamics:

$M_I \ddot{R}_I = F_\text{BO} - (\gamma_D + \gamma_L)\dot{R}_I + \Xi_I$

- $\gamma_D$ : implicit friction from ASPC - $\gamma_L$ : Langevin thermostat - $\Xi_I$ : Langevin random noise

4. How to Set Up in CP2K

Parameter	Purpose	Notes
EXTRAPOLATION_ORDER	Higher gives better predictor	1–4 typical, 0 for metallic is more stable
MAX_SCF_HIST	Controls SCF correction	≥2 helps smoother convergence
STEPSIZE	Time step in fs	~0.5–2 fs depending on system
PRECONDITIONER	Affects SCF convergence	`FULL_SINGLE_INVERSE` slightly better
NOISY_GAMMA (γ_D)	ASPC dissipation compensation	Adjust to control drift in T and energy
GAMMA (γ_L)	Langevin thermostat strength	Set to 0 for dissipation-only integration

1. ASPC Extrapolation

&FORCE_EVAL
  &DFT
     &QS
      EXTRAPOLATION ASPC
      EXTRAPOLATION_ORDER 0 # Higher gives better corrector 
     &END QS
     &SCF
      MAX_SCF_HIST 2
     &END SCF
  &END DFT
&END FORCE_EVAL

2. Langevin Thermostat

&MOTION
  &MD
    ENSEMBLE LANGEVIN
    &LANGEVIN
      GAMMA 0.005         ! γ_L
      NOISY_GAMMA 4.0E-4  ! γ_D
    &END LANGEVIN
  &END MD
&END MOTION

3. Atom-Specific γ_D (Optional)

&THERMAL_REGION
  DO_LANGEVIN_DEFAULT TRUE
  &DEFINE_REGION
    TEMPERATURE 500
    NOISY_GAMMA_REGION 4.E-4
    LIST 577..745
  &END DEFINE_REGION
&END THERMAL_REGION