12.7 Second-Generation ALMO-EDA Method

12.7.5 ALMO-EDA with Implicit Solvent Models

(June 30, 2021)

Since the majority of chemical processes occur in the condensed phase, it is often desirable to investigate intermolecular interactions in the presence of solvents. The solvation environment can affect intermolecular interactions in a variety of ways such that the gas-phase ALMO-EDA may not be capable of revealing the physical picture of these interactions correctly. To address this gap, Mao et al. have proposed the ALMO-EDA(solv) approach, 718 Mao Y. et al.
Chem. Sci.
(2021), 12, pp. 1398.
Link
which, unlike many other EDA schemes, incorporates the solvation effect in the evaluation of all the energy components. Currently, ALMO-EDA(solv) supports two widely used implicit solvent models: PCM and SMD (see Sec. 11.2). More solvation models will be made compatible in future releases of Q-Chem.

Within the ALMO-EDA(solv) scheme, the interaction energy to be decomposed is given by the energy difference between the solvated, fully relaxed complex and the sum of the energies of individually solvated, non-interacting fragments. 718 Mao Y. et al.
Chem. Sci.
(2021), 12, pp. 1398.
Link
As in gas-phase ALMO-EDA, the total interaction energy (INT) can be partitioned into frozen (FRZ), polarization (POL), and charge transfer (CT) contributions:

ΔEINT(s)=EFull(s)-AEA(s)=ΔEFRZ(s)+ΔEPOL(s)+ΔECT(s) (12.15)

Here the superscript “(s)” indicates that the energetic terms are evaluated with the solvent taken into account.

The frozen interaction energy (ΔEFRZ(s)) is defined as the energy change upon the formation of a solvated complex from several individually solvated non-interacting fragments without relaxing their orbitals, which can be further decomposed into permanent electrostatics (ELEC), Pauli repulsion (PAULI), and dispersion (DISP) contributions:

ΔEFRZ(s)=EFRZ(s)-AEA(s)=(EFRZ(s)-EFRZ(0))-A(EA(s)-EA(0))+EFRZ(0)-AEA(0)=ΔESOL+ΔEELEC(0)+ΔEPAULI(0)+ΔEDISP(0) (12.16)

Here we have introduced a new term,

ΔESOL=(EFRZ(s)-EFRZ(0))-A(EA(s)-EA(0)) (12.17)

to quantify the loss/gain of solvation energy upon the formation of the frozen complex. The other three terms in Eq. 12.16, ΔEELEC(0)), ΔEPAULI(0), and ΔEDISP(0), are evaluated in the same way as in vacuum 469 Horn P. R., Mao Y., Head-Gordon M.
J. Chem. Phys.
(2016), 144, pp. 114107.
Link
(as indicated by the superscripts “(0)") but using MOs of solvated fragments.

In the most general cases, the solvent contribution to the frozen interaction (ΔESOL) includes both electrostatic (ΔESOLel) and non-electrostatic (ΔESOLnon-el) components, which can be combined with the “gas-phase” ELEC and PAULI terms, respectively. In addition, we ignore the solvent contribution to dispersion, an effect that cannot be captured by dispersion-corrected DFT that ALMO-EDA(solv) is based upon, which leads to ΔEDISP(0)ΔEDISP(s). The decomposition of the frozen energy in the solvation environment (Eq. 12.16) can thus be rewritten as

ΔEFRZ(s)=(ΔEELEC(0)+ΔESOLel)+(ΔEPAULI(0)+ΔESOLnon-el)+ΔEDISP(0)=ΔEELEC(s)+ΔEPAULI(s)+ΔEDISP(s) (12.18)

Starting from the solvated frozen complex, one can relax the fragment orbitals using the SCFMI technique in presence of solvent. The associated energy lowering is defined as the polarization energy in ALMO-EDA(solv) (ΔEPOL(s)):

ΔEPOL(s)=EPOL(s)-EFRZ(s) (12.19)

where EPOL(s) is the converged SCFMI energy with solvent. Similarly, the charge-transfer term is given by

ΔECT(s)=EFull(s)-EPOL(s) (12.20)

where EFull(s) is the full SCF energy evaluated with the presence of solvent. With that, the solvation effects are implicitly incorporated in the POL and CT terms produced by the ALMO-EDA(solv) scheme.

Example 12.17  EDA calculation for the water-Mg2+ complex in PCM water.

$molecule
2 1
--
0 1
H1
H2 H1 1.55618
O1 H2 0.97619  H1 37.14891
--
2 1
Mg1 O1 scan    H2 127.14892  H1 180.0

scan = 1.91035
$end

$rem
   JOBTYPE           eda
   EDA2              2
   METHOD            wb97m-v
   BASIS             6-31+g(d)
   UNRESTRICTED      false
   SCF_ALGORITHM     diis
   SCF_CONVERGENCE   8
   MAX_SCF_CYCLES    200
   THRESH            14
   SYMMETRY          false
   SYM_IGNORE        true
   SOLVENT_METHOD    pcm
   EDA_CLS_DISP      true
$end

$PCM
   THEORY                     CPCM
   METHOD                     SWIG
   SOLVER                     INVERSION
   HPOINTS                    302
   HEAVYPOINTS                302
$END

$SOLVENT
   DIELECTRIC                 78.39
$END

View output

Example 12.18  EDA calculation for the water-Mg2+ complex in SMD water.

$molecule
2 1
--
0 1
H1
H2 H1 1.55618
O1 H2 0.97619  H1 37.14891
--
2 1
Mg1 O1 scan    H2 127.14892  H1 180.0

scan = 1.91035
$end

$rem
   JOBTYPE           eda
   EDA2              2
   METHOD            wb97m-v
   BASIS             6-31+g(d)
   UNRESTRICTED      false
   SCF_ALGORITHM     diis
   SCF_CONVERGENCE   8
   MAX_SCF_CYCLES    200
   THRESH            14
   SYMMETRY          false
   SYM_IGNORE        true
   SOLVENT_METHOD    smd
   EDA_CLS_DISP      true
$end

$smx
   solvent water
$end

View output