George Fitzgerald

Geometry optimization of solids using delocalized internal coordinates

A new algorithm is presented that uses delocalized internal coordinates to optimize structures of periodic systems. The algorithm employs translational symmetry to construct the B matrix. It requires generation of all unique primitive internals in the unit cell. B is subsequently used to generate a set of delocalized internals as described in the earlier work by Pulay, Baker and coworkers for molecular systems. A detailed analysis of the algorithm for bulk Si is given, and the performance of the method in applications to surface reactions and zeolites is briefly mentioned.

Analytic energy second derivatives for general MCSCF wave functions

Expressions for the determination of analytic energy second derivatives for general MCSCF wave functions are presented. Equations for two distinct approaches: (1) direct differentiation of the energy expression and associated Lagrangian condition; and (2) power series expansion of the Hamiltonian and exponential‐i‐lambda transformation of the wave function, are developed. The problem of the nonzero nullity of the Hessian, and the resultant existence of redundant variables in the coupled perturbed multiconfiguration Hartree Fock (CPMCHF) equations, is discussed and a straightforward solution proposed. The viability of the methods presented in this paper are illustrated by a sample calculation on formaldehyde, using a double zeta (DZ) basis set and including 325 MCSCF configurations in the state space.

Analytic energy second derivatives for general correlated wavefunctions, including a solution of the first-order coupled-perturbed configuration-interaction equations

Abstract The first theoretical method for the analytic determination of energy second derivatives for configuration-interaction wave-functions is presented. Several test cases are reported, the largest being an 8385 configuration formaldehyde wavefunction.

Theoretical study of the H+O3↔OH+O2↔O+HO2 system

The key features of the H+O3 potential energy surface have been determined using ab initio quantum mechanical methods. The electronic wave function used is a multiconfiguration Hartree–Fock wave function which provides a qualitatively correct description of various reactive channels. It is found that the H+O3→HO+O2 reaction proceeds along a nonplanar pathway in which the H atom descends vertically to the plane containing the ozone molecule to form an HO3 intermediate which then undergoes fragmentation. No planar transition state for a direct O‐atom abstraction could be located. The radical–radical O+HO2 reaction was found to have no energy barrier to formation of HO3 which was determined to subsequently decompose to HO+O2. The H‐atom abstraction reaction O+HO2→OH+O2 was found to have a small activation energy. The dynamical implications of these findings are discussed. The results are consistent with the observed vibrational excitation of the OH product in the H+O3 reaction. The key features of the H+O3 p...

Abinitio calculations on the energy of activation and tunneling in the automerization of cyclobutadiene

Results of ab initio two‐configuration CI‐SD/[3s2p1d/2s], MBPT(4), CCSD+T(CCSD), and CCSDT‐1 calculations are reported for the rectangular D2h equilibrium and square D4h transition structures of cyclobutadiene. The latter is a classic example of a multireference correlated method. The optimum CC and CH bond lengths found for the D4h transition structure are 1.448 and 1.093 A, respectively. The activation barrier for the automerization is 9.0 kcal/mol at the two‐reference GVB‐CISD level while the single reference CCSD gives 19.9, 14.4 for CCSD+T(CCSD) and finally a dramatic change to 9.5 at the highest CCSDT‐1 level. The importance of triples in overcoming the multireference character at the transition state is apparent. On the other hand, GVB‐CISD is simpler than CCSDT‐1 which attests to the importance of a qualitatively correct multireference starting point for this example. A less sophisticated computational method, GVB/4‐31G, which also gives a reasonable barrier of 10.2 kcal/mol was used for the const...

The open chain or chemically bonded structure of H2O4: The hydroperoxyl radical dimer

The straight chain isomer H–O–O–O–O–H of H2O4 is of considerable current interest in combustion and atmospheric chemistry. Ab initio quantum mechanical methods have been used to study the geometrical structure, energetics, and vibrational frequencies of this species. Double zeta (DZ) and double zeta plus polarization (DZ+P) basis sets have been used in this theoretical study, the latter designated O(9s5p1d/4s2p1d), H(4s1p/2s1p). These basis sets have been employed in conjunction with self–consistent field (SCF) and configuration interaction (CI) methods, including variationally up to 470 935 configurations. For the straight chain isomer, stationary points of symmetry C2h , Ci , and C1 have been identified, and correspond to Hessian indices 3,1, and 0, respectively. The equilibrium geometry, having no elements of symmetry at all, is relatively unique. The highest level of theory (unlinked cluster corrected DZ+P CI) predicts the straight chain structure of H2O4 to lie slightly lower in total energy than the...

Analytic energy derivative methods for excited singlet states of the same symmetry as the electronic ground state

The possibility of variational collapse of single configuration self‐consistent field (SCF) wave functions for excited electronic states becomes more serious when first and second derivatives of the energy (with respect to nuclear coordinates) are required. For a nonlinear molecule of four or more nuclei, there will almost inevitably be some displacement which removes all spatial symmetry, leaving the electronic state in question with the same spatial symmetry as the ground electronic state. For excited singlet states, a resolution of this problem is found by using the Davidson–Stenkamp method to guarantee orthogonality to the closed‐shell ground‐state wave function. The Davidson–Stenkamp wave function is then transformed to a conventional two‐configuration SCF wave function, to which analytic first and second derivative methods may be applied.

The cyclic, two‐hydrogen bond form of the HO2 dimer

Among possible forms of the hydroperoxyl radical dimer H2O4, one of the most appealing and plausible is the six‐membered ring 4. This cyclic isomer of H2O4 has been investigated using nonempirical molecular electronic structure theory. For the lowest triplet state of H2O4, the single configuration self‐consistent field (SCF) method was used in conjunction with double zeta (DZ) and double zeta plus polarization (DZ+P) basis sets. At both levels of theory, the six‐membered ring is predicted to be a minimum on the H2O4 potential energy hypersurface. The DZ SCF and DZ+P SCF dimerization energies are 4.5 and 4.9 kcal, respectively. Vibrational frequencies are predicted within the harmonic approximation and compared with the analogous monomer predictions and with the recent experimental findings of Diem, Tso, and Lee. It is concluded that the cyclic HO2 dimer is composed of two weak hydrogen bonds, each about one‐half the strength of that observed for the water dimer.

Benchmark and testing of the local density functional method for molecular systems

The prediction of molecular properties from computer simulations is playing an increasingly important role in the chemical and pharmaceutical industry (Dixon, 1987; Dixon et al., 1988a; 1988b). Although molecular modeling groups were already popular in the 1970’s with the promise of solving the rational drug design problem in a quantitative way, the available computational resources and software were not adequate for the task. With the more ready access by chemists to supercomputers in the 1980’s and the revolutions in theoretical developments, algorithm design and software implementation, it is now possible for computational science to have a quantitative impact on molecular design. The primary areas that have been responsible for this renaissance have been the development of force field methods including molecular dynamics and the more routine application of quantum chemical methods (Hehre et al., 1986) to increasingly more complex molecular systems of interest to the bench chemist. This chapter will focus on the latter application area.