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exercises:common:sgcp [2025/06/19 02:29] jglanexercises:common:sgcp [2025/06/19 02:54] (current) – [2. Comparison with CPMD and BOMD] jglan
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 [[ https://doi.org/10.1021/acs.jpclett.0c01025 |J. Phys. Chem. Lett. 2020, 11, 9, 3724–3730]] [[ https://doi.org/10.1021/acs.jpclett.0c01025 |J. Phys. Chem. Lett. 2020, 11, 9, 3724–3730]]
  
-===Introduction===+====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. 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.
  
-===Comparison with CPMD and 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                | | Feature                          | CPMD          | BOMD         | SGCP                |
-| SCF at each step                  No          |  Yes        |  Partially (predictor-corrector) |+| SCF at each step                 | No          | Yes        |  Partially (predictor-corrector) |
 | Time step                        | Small (~0.1 fs) | Large (~1 fs) | Large (~1–2 fs)           | | Time step                        | Small (~0.1 fs) | Large (~1 fs) | Large (~1–2 fs)           |
 | Conserved quantity preservation  | Excellent     | Reasonable   | Excellent                 | | Conserved quantity preservation  | Excellent     | Reasonable   | Excellent                 |
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 | Works for small-gap systems      | Poor          | Good         | Good                      | | Works for small-gap systems      | Poor          | Good         | Good                      |
  
 +====3. ASPC Method====
 +ASPC Method: Always Stable Predictor Corrector
  
-Key Idea+ASPC is a **Gear-type integrator** for electronic wavefunctions:
  
-**Goal:** Retain the efficiency of CPMD while achieving BOMD-level accuracy.+Predictor:
  
-**Efficiency** Large time steps ; No full SCF loops   +\[ 
-- **Accuracy**:  Forces nearly indistinguishable from BOMD   +C_p(t_n) = \sum_{m=1}^{K} (-1)^{m+1} \cdot m \cdot B_m \cdot P_S(t_{n-m}) 
-**Stability** Effective for systems with vanishing band gaps   +\] 
-**Error Control**:  Controlled deviation from BO surface using adaptive correction+ 
 +where
 +Bm: Kolafa predictor coefficients 
 +- PS: 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: 
 + 
 +\[ 
 +M_I \ddot{R}_I = F_\text{BO} - (\gamma_D + \gamma_L)\dot{R}_I + \Xi_I 
 +\] 
 + 
 +- γD: implicit friction from ASPC   
 +γLLangevin thermostat   
 +ΞILangevin 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
  
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