计算溶剂化自由能

溶剂化自由能计算就是把物种从气相转移到溶液相的溶剂化能. 例如

HF (1M,gas) -> HF (1M, solution)

利用Gaussian软件的SCRF 关键词可以定义溶剂化模型, 计算溶剂化自由能. 例如:

%mem=8GB
%nprocshared=4
%chk=solv-standard.chk
#p b3lyp/6-31g scrf=(smd,solvent=water,read,externaliteration,dovacuum)
Structure: HF; DeltaG(Solv) at B3LYP/6-31g level

0 1
F 0.00000000 0.00000000 0.09148400
H 0.00000000 0.00000000 -0.82335900


cav
dis
rep

注意cav前面要有两空行.

一些关键词解释 (官网 G16的说明):

• SMD Model : Do an IEFPCM calculation with radii and non-electrostatic terms for Truhlar and coworkers' SMD solvation model [Marenich09]. This is the recommended choice for computing ΔG of solvation, which accomplished by performing gas phase and SCRF=SMD calculations for the system of interest and taking the difference the resulting energies. You can define a new solvent for use with SMD by providing additional input via the SCRF=Read option (see “Additional Input” for details).
• ExternalIteration : Does a self-consistent PCM calculation performing an external iteration through Link 124. This approach computes the energy in solution by making the solute's electrostatic potential self-consistent with the solvent reaction field [Improta06, Improta07]. ExternalIteration is available only for energy calculations. SelfConsistent and SC are synonyms for this option.
• 1stVac或DoVacuum : Do the first iteration in an external iteration PCM calculation in solution. 1stVac is equivalent to DoVacuum, which is now deprecated.
• 1stPCM 或 NoVacuum: Do not do the first iteration in an external iteration PCM calculation in solution. 1stPCM is equivalent to SkipVacuum and NoVacuum, which are now deprecated.

计算成功后, 能在最后稍微往上一点的地方找到deltaG 溶剂化能部分. 类似如下:

SC-PCM: The total energy in vacuo is      -100.402373501 a.u.

.............

Total free energy in solution:
 - with all non electrostatic terms           (a.u.) =    -100.410677
 --------------------------------------------------------------------
 (Unpolarized solute)-Solvent             (kcal/mol) =      -6.55
 (Polarized solute)-Solvent               (kcal/mol) =      -7.98
 Solute polarization                      (kcal/mol) =       0.74
 Total electrostatic                      (kcal/mol) =      -7.24
 --------------------------------------------------------------------
 SMD-CDS (non-electrostatic) energy       (kcal/mol) =       2.03
 Total non electrostatic                  (kcal/mol) =       2.03
 DeltaG (solv)                            (kcal/mol) =      -5.21
 --------------------------------------------------------------------

这种计算方法可以直接获得溶剂化能的值. 另一种方法是算出在溶剂内的能量, 并和气相的能量作相减.

溶液中的能量计算:

%mem=8GB
%nprocshared=4
%chk=solv-water.chk
#p b3lyp/6-31g scrf=(smd,solvent=water,read)
Structure: HF; Energy(Solvation) at B3LYP/6-31g level

0 1
F 0.00000000 0.00000000 0.09148400
H 0.00000000 0.00000000 -0.82335900


cav
dis
rep

气相中的浓度计算:

%mem=8GB
%nprocshared=4
%chk=solv-gas.chk
#p b3lyp/6-31g
Structure: HF; Energy(Gas) at B3LYP/6-31g level

0 1
F 0.00000000 0.00000000 0.09148400
H 0.00000000 0.00000000 -0.82335900

此时, ΔG(solv) = E(Soln) - E(Gas) = (-100.4106773- -100.4023735) Hatree = -5.21 kcal/mol

两种方法计算结果一致, 按上述第一种方法计算更为省事一点点.

校正

SMD方法是一种基于SCRF参数化的溶剂化模型，由Truhlar等人开发。SMD设计用于溶剂化自由能的预测，其所用的参数不同于SCRF模型的默认参数。对于一个给定的溶质，SMD溶剂化自由能计算的是在298.15K将同样浓度的理想气体转移到理想溶液的自由能。也就是说计算得到的溶剂化自由能是指1M气体->1M溶液的溶剂化自由能。而1M浓度的气体等于24.5 atm下的1 mole气体，而非标准状态的理想气体（在1个标准大气压下的气体）。

但是，在pKa计算时关心的是标准状态下理想气体的溶剂化自由能（因为压力不是24.5atm，所以此时浓度不是1M），因此需要对SMD计算结果需要进行一个浓度校正：

ΔGgas(1 M) = ΔGgas(1 atm) + ΔnRTln(24.5)

R = 8.314J/K*mol; T = 298.15K; Δn: 少了的气体摩尔数

ΔnRTln(24.5) = 1 x 8.314 x 298.15 x ln(24.5) = 7928.93 J/mol = 1.89 kcal/mol

因此，1atm气相压力校正-1.89 kcal/mol (-7.93 kJ/mol), 1 bar校正-1.90kcal/mol(-7.96kJ/mol)。具体的校正原理与方法见《Exploring Chemistry with Electronic Structure Methods》第三版第108页Going Deeper方盒里的内容。总的来说，溶剂化自由能的转化公式如下：

ΔGgas1 M (kcal/mol) = ΔGgas1 atm (kcal/mol) + 1.89

Reference:
墨灵格:Gaussian教程 | 溶剂化自由能的计算