Importance of van der Waals Interactions in QM/MM Simulations
Demian Riccardi, Guohui Li, and Qiang Cui*
Department of Chemistry and Theoretical Chemistry Institute, UniVersity of Wisconsin,
Madison, 1101 UniVersity AVe, Madison, Wisconsin 53706
ReceiVed: December 23, 2003; In Final Form: March 1, 2004
The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and
molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First,
a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the
self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-
bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was
then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized
set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems
include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the
radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction
potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the
enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent
structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and
potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The
differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were
explained in terms of the effects of the parameter set on solvation. The current study has made it clear that
efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase
should focus on components other than van der Waals interactions between QM and MM atoms.
1. Introduction
The analysis of chemical events in complex systems requires
a potential function that can describe electronic changes in the
region of interest. Current quantum mechanical approaches
provide such descriptions, but there are severe limitations in
the size of the systems that can be treated.
1,2
To investigate the
effects of the environment on chemical events, approximations
must be made with either an implicit or explicit approach. For
biological systems, the inclusion of the protein and solvent
environment is paramount,
3
and combined quantum mechanical
and molecular mechanical (QM/MM) methods
4-6
are a popular
choice for such investigations. QM/MM methods enable theo-
retical computations of complex chemical events in large
systems by partitioning the system into a quantum region and
a molecular mechanics region. The application of the QM/MM
method can provide atomistic details of catalytic mechanisms
corresponding to experimental observables, which is valuable
for both fundamental understanding of enzyme catalysis and
realistic applications such as protein engineering.
The total Hamiltonian for the molecular system under
consideration in the QM/MM framework is
where H ˆ
QM/MM
describes the interaction between the QM and
MM atoms governed by H ˆ
QM
and H ˆ
MM
, respectively. The
H ˆ
QM/MM
typically contains terms for the electrostatic, van der
Waals(vdW), and bonded interactions
The H ˆ
bonded
QM/MM
is required when partitioning a single molecule
into quantum and molecular mechanics regions, as is most
common for applications to protein systems. For such partition-
ing, the molecular mechanical bonding term is retained between
the boundary QM and MM atoms, whereas the valency of the
QM region is satisfied with the addition of link atoms
4
or frontier
bonds.
7,8
The purpose of the vdW term is to estimate dispersion
attractions that fall off as r
-6
and to prevent molecular collapse
being strongly repulsive at short interaction distances. In terms
of the magnitudes at typical interactomic distances, electrostatic
interactions usually overwhelm the vdW contributions, espe-
cially in polar systems such as enzymes. Due to the rapid
variation at short interatomic distances, however, the vdW
interactions (therefore vdW parameters) are important to the
equilibrium geometries of molecules treated by QM/MM in the
gas phase.
4,9-12
In the condensed phase, on the other hand, due
to averaging over a large number of configurations, the question
of how important the precision of QM/MM van der Waals
interactions is to the molecular properties of common interest
is an interesting one, which has not been systematically explored
in the past. Moreover, the vdW interaction between QM and
MM atoms in the condensed phase may not only affect the
enthalpy of direct interactions but also have a substantial
entropic component, and the possibility of enthalpy/entropy
compensation has not been analyzed in details in previous work.
In the current paper, we report a systematic analysis on the * To whom the correspondence should be addressed.
H ˆ) H ˆ
QM
+ H ˆ
QM/MM
+ H ˆ
MM
(1)
H ˆ
QM/MM
) H ˆ
vdW
QM/MM
+ H ˆ
elec
QM/MM
+ H ˆ
bonded
QM/MM
(2)
6467 J. Phys. Chem. B 2004, 108, 6467-6478
10.1021/jp037992q CCC: $27.50 © 2004 American Chemical Society
Published on Web 04/23/2004