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--- exercises:common:sgcp [2025/06/19 02:28] – jglan
+++ exercises:common:sgcp [2025/06/19 02:54] (current) – [2. Comparison with CPMD and BOMD] jglan
@@ Line 9: / Line 9: @@
 [[ 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.
+**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        |  No (predictor-corrector) |
+| 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                 |
@@ Line 19: / Line 32: @@
 | 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  |
+. 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
+. 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
+. 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