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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