Essentials of Computational Chemistry

Link
atom
LSCF
GHO
13.4 EMPIRICAL VALENCE BOND METHODS 477
A
A
A
r AB
r AB
r AB
MM region QM region
q ABC
B
qABC B
B
w ABCX
wABCX
w ABCX
q ABC
qBCX r BC
w
r BCXY
CX
C H qCXY C
qBCX r BC
r BC
C
q BCX
q CXH
X
w
r BCXY
CX
qCXY r CX
X
w BCXY
q CXY
X
Y
w CXYZ
Y
w CXYZ
Figure 13.6 Comparison of QM/MM partitioning schemes across covalent bonds. Included MM bond
stretch, angle bend, and torsion terms are indicated; those that are boxed are ignored by some authors.
Frozen orbitals are in gray for the LSCF and GHO methods
Analytic derivatives have been reported for both the LSCF and GHO models, making them
attractive options for MD simulations (Amara et al. 2000). Their generalization to ab initio
levels of theory through the use of core pseudopotentials (along the lines of the pseudohalogen
capping atoms described above) ensures that they will see continued development.
13.4 Empirical Valence Bond Methods
A method that has certain connections with QM/MM techniques even if it does not usually
involve simultaneous evaluation of QM and MM operators during a particular calculation
is the empirical valence bond method (EVB; Warshel and Weiss 1980). At the heart of the
EVB method is the notion that arbitrarily complex reactions may be modeled as the influence
of a surrounding environment on a fundamental process that may be represented by some
combination of valence bond resonance structures. For example, the proton transfer from
one water molecule to another may, at any point along the reaction path, be envisaged as
involving some admixture of the two VB wave functions corresponding formally to
1 = HO a –H ∗ + O b H2
2 = HO a− + H ∗ –O b H2 +
Y
Z
Z
Z
(13.8)
(13.9)