# GROMACS自由能计算中软核势的使用

• 2018-04-25 16:24:25

## Theory

The soft-core potential between two states A and B is defined as

$\begin{split} V_{sc}(r) &=(1-\lambda)V_A(r_A) + \lambda V_B(r_B) &=(1-\lambda)V_A(r) + \lambda V_B(r) \;\;\;\; \text{if } \alpha \sigma=0 r_A &= \left(\alpha \sigma_A^6 \lambda^p+r^6\right)^{1/6} r_B &= \left(\alpha \sigma_B^6 (1-\lambda)^p+r^6\right)^{1/6} \end{split}$

When $\alpha=0$ or $\sigma=0$, the soft-core potential degenerates to the original potential. $\alpha$ is usually about 0.5 and $p=1$ or $p=2$. The recommended combination is $\alpha=0.5, p=1$.

For LJ potential,

$\alg V &= { C_{12} \over r^{12} } - {C_6 \over r^6} V_{sc} &=C_{12}\left[{1-\lambda \over (\alpha \sigma^6 \lambda^p+r^6)^2} + {\lambda \over (\alpha \sigma^6(1-\lambda)^6+r^6)^2}\right] &-C_6 \left[{1-\lambda \over \alpha \sigma^6 \lambda^p+r^6} + {\lambda \over \alpha \sigma^6(1-\lambda)^6+r^6}\right] \ealg$

Some special cases

$\alg V_{sc}=0 &\Rightarrow V(r_A)=0 \; V(r_B)=0 r_A=r_B &\Rightarrow \lambda=0.5 \ealg$

If A state is totally decoupled, which means $V_A=0$, in this case

$\alg V_{sc}(r) &= \lambda V_B(r_B) &= \lambda \left\{ {C_{12} \over \left(\alpha \sigma^6 (1-\lambda)^p+r^6\right)^2} -{C_6 \over \alpha \sigma^6 (1-\lambda)^p+r^6} \right\} \ealg$

Define

$\alg s^6 &=\alpha\sigma^6 r_{sc} &= \left(r^6+ (1-\lambda)^p s^6\right)^{1/6} \min r_{sc} &= r &\;\; \text{when } \lambda=1 \max r_{sc} &= (r^6+s^6)^{1/6} &\;\; \text{when } \lambda=0 \ealg$

## GMX Options

In GMX, $\alpha, \sigma, p$ is corresponding to sc_alpha, sc_sigma, sc_power, respectively. The manual said

• sc-alpha: (0) the soft-core alpha parameter, a value of 0 results in linear interpolation of the LJ and Coulomb interactions

• sc-r-power: (6) the power of the radial term in the soft-core equation. Possible values are 6 and 48. 6 is more standard, and is the default. When 48 is used, then sc-alpha should generally be much lower (between 0.001 and 0.003).

• sc-power: (0) the power for lambda in the soft-core function, only the values 1 and 2 are supported

• sc-sigma: (0.3) [nm] the soft-core sigma for particles which have a C6 or C12 parameter equal to zero or a sigma smaller than sc-sigma

The description of sc-sigma is not correct, actually

$\sigma= \begin{cases} & \sigma^*=(C_{12}/C_{6})^{1/6} & \text{sc_sigma} \; \text{ if } C_6\times C_{12}=0 \end{cases}$

## Conclusion

• GROMACS calculates the interaction only If r_sc less than rvdw

• The r_sc for any distance should be in the range of the table files, otherwise GROMACS will use a unkown value

• If DispCorr is used, be sure C6 is the correct value

• If sc-alpha is not zero, be sure the $\s$ GROMACS used is the correct value

• If DispCorr not used, put total interaction in dispersion or repulsion column will force GROMACS to use sc-sigma

• If DispCorr is used and sc-alpha is not zero, be sure C6 and C12 are both correct

 随意赞赏 微信 支付宝
◆本文地址: , 转载请注明◆
◆评论问题: https://jerkwin.herokuapp.com/category/3/博客, 欢迎留言◆