Formulation,
Implementation and Application of Second and Higher Derivatives
Using Coupled Cluster Theory
Prof. John Stanton
University of Texas
12:00 PM Monday, November 6, 2000
Classroom A101
Harvard-Smithsonian Center for Astrophysics
Abstract:
Perhaps the most important advances for facilitating widespread
application of molecular quantum mechanics to problems of interest
to chemists have been those associated with the development of
strategies for calculating analytic energy derivatives routinely
and efficiently. Beginning with Pulay's work on Hartree-Fock
derivatives, this field has been a focus of effort for many groups
for the last quarter century. Efficient implementations of analytic
first derivatives are now available for almost all methods that
constitute the alphabet soup of quantum chemical approaches,
and prove enormously useful in studying potential energy surfaces
governing molecular vibration and chemical reactions. Until recently,
analytic second derivative methods were limited to only the simplest
methods. In the last few years, methods have been developed for
the efficient calculation of analytic second derivatives of the
energy at levels of theory that include sophisticated treatments
of electron correlation. By using a strategy that differs markedly
from that usually advocated for analytic second derivative calculations,
it is possible to design algorithms that are free of disk-space
``bottlenecks''. These have been implemented for several levels
of many-body perturbation
theory and the coupled-cluster approximation, and allow the treatment
of systems containing more than 200 basis functions on modestly-equipped
workstations.
One of the more promising avenues for application of these
methods is in the calculation of quantities that more closely
resemble experimental observables than those traditionally obtained
by quantum chemistry. For example, fundamental frequencies are
measured in the laboratory while harmonic frequencies are routinely
reported in quantum-chemical studies,
effective rotational constants and internuclear distances are
measured while $B_e$ and $r_e$ values are most easily obtained
by calculation. However, more appropriate estimates of experimental
quantities can be achieved if anharmonic force fields are available
for the molecules of interest. Using analytic second derivative
techniques, all cubic and relevant (semidiagonal) quartic force
constants can be calculated efficiently and {\it accurately}
through an automated finite-difference procedure. In this talk,
the analytic second derivative
theory and its implementation are briefly discussed. Following
this, the method is illustrated by selected applications including
the vibration-rotation interaction constants of benzene, an empirical
deduction of the equilibrium structure of dioxirane, the fundamental
frequencies of diborane and highly accurate calculations of nuclear
magnetic shieldings.
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