12.7 The Second-Generation ALMO-EDA Method

12.7.5 ALMO-EDA with Implicit Solvent Models

In real-life applications, it is often desired to perform EDA under a solvent environment. Q-Chem 5.2 has made EDA2 compatible with PCM and SMD models. In these EDA calculations, the interaction energy to be decomposed is the energy difference between the solvated, fully relaxed complex and the individually solvated non-interacting fragments, which can still be partitioned into contributions from frozen interaction (FRZ), polarization (POL), and charge transfer (CT): Mao:2020b

ΔEINTs=EFulls-AEAs=ΔEFRZs+ΔEPOLs+ΔECTs (12.15)

Unlike many other EDA schemes in which the solvent contribution is treated as a correction to the gas-phase EDA results, in ALMO-EDA the effect of solvation is accounted for in the preparation of each intermediate state. The frozen interaction energy (ΔEFRZ) is defined as the energy change upon the formation of a solvated complex from several solvated non-interacting fragments without relaxing their orbitals, which can be further decomposed into permanent electrostatics (ELEC), Pauli repulsion (PAULI), and dispersion (DISP) contributions:

ΔEFRZs=EFRZs-AEAs=(EFRZs-EFRZv)-A(EAs-EAv)+EFRZv-AEAv=(ΔESOL+ΔEELECv)+ΔEPAULIv+ΔEDISPv=ΔEELECs+ΔEPAULIv+ΔEDISPv (12.16)

Note that the superscript “s" denotes intermediate state energies evaluated with the solvent contribution taken into account. We have also introduced a new term,

ΔESOL=(EFRZs-EFRZv)-A(EAs-EAv) (12.17)

to describe the loss/gain of solvation energy upon the formation of the frozen complex. The other three terms in eq. 12.16, ΔEELECv), ΔEPAULIv, and ΔEDISPv, are evaluated in the same way as in vacuum (as indicated by the superscripts “v") but with MOs of solvated fragments. As the existence of solvent mainly affects the electrostatic interaction between interacting moieties, which is exactly true at long range, we suggest that one can combine ΔESOL and ΔEELECv) (eq. 12.16) and report that as the electrostatic interaction within solvent environment (ΔEELECs).

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

ΔEPOLs=EPOLs-EFRZs (12.18)

where EPOLs is the converged SCF-MI energy with solvent. Similarly, the charge-transfer term is given by

ΔECTs=EFulls-EPOLs (12.19)

where EFulls is the full SCF energy evaluated with the presence of solvent.

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

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