Chem3D Users Manual - CambridgeSoft

The Molecular Dynamics (MM2) command in the
Calculations menu can be used to compute a
molecular dynamics trajectory for a molecule or
fragment in Chem3D. A common use of molecular
dynamics is to explore the conformational space
accessible to a molecule, and to prepare sequences
of frames representing a molecule in motion. For
more information on Molecular Dynamics see
Chapter 9, “MM2 and MM3 Computations” on
page 151.
Molecular Dynamics Formulas
The molecular dynamics computation consists of a
series of steps that occur at a fixed interval, typically
about 2.0 fs (femtoseconds, 1.0 x 10 -15 seconds).
The Beeman algorithm for integrating the
equations of motion, with improved coefficients
(B. R. Brooks) is used to compute new positions
and velocities of each atom at each step.
Each atom (i) is moved according to the following
formula:
x i = x i + v i ∆t + (5a i – a
old
i ) (∆t) 2 /8
Similarly, each atom is moved for y and z, where x i ,
y i , and z i are the Cartesian coordinates of the atom,
v i is the velocity, a i is the acceleration, a
old
i is the
acceleration in the previous step, and ∆t is the time
between the current step and the previous step. The
potential energy and derivatives of potential energy
(g i ) are then computed with respect to the new
Cartesian coordinates.
New accelerations and velocities are computed at
each step according to the following formulas (m i is
the mass of the atom):
veryold old
a i = a i
a i
old
= a i
a i = –g i / m i
v i = v i + (3a i + 6a i
old
– a i
veryold
) ∆t / 8
Quantum Mechanics
Theory in Brief
The following information is intended to familiarize
you with the terminology of quantum mechanics
and to point out the areas where approximations
are made in semiempirical and ab initio methods.
For complete derivations of equations used in
quantum mechanics, you can refer to any quantum
chemistry text book.
Quantum mechanical methods describe molecules
in terms of explicit interactions between electrons
and nuclei. Both ab initio and semiempirical
methods are based on the following principles:
• Nuclei and electrons are distinguished from
each other.
• Electron-electron (usually averaged) and
electron-nuclear interactions are explicit.
• Interactions are governed by nuclear and
electron charges (i.e. potential energy) and
electron motions.
• Interactions determine the spatial distribution
of nuclei and electrons and their energies.
• Quantum mechanical methods are concerned
with approximate solutions to Schrödinger’s
wave equation.
HΨ = EΨ
• The Hamiltonian operator, H, contains
information describing the electrons and nuclei
in a system. The electronic wave function, Ψ,
describes the state of the electrons in terms of
their motion and position. E is the energy
associated with the particular state of the
electron.
NOTE: The Schrödinger equation is an
eigenequation, where the “H” operator, the
Hamiltonian, operates on the wave function to return
ChemOffice 2005/Chem3D Computation Concepts • 143
Quantum Mechanics Theory in Brief