ALBERT

Notes: First principles local density functional (LDF) calculations have been performed on a number of molecules to evaluate the use of this method in the theoretical prediction of electrical properties. Calculated dipoles and dipole polarizabilities show good agreement with both experimental and ab initio results based on second-order Møller–Plesset perturbation theory (MP2) calculations. Application to DNA base pairs provides information on the degree of nonadditivity in these interactions, as well as an example of the usefulness of LDF in the calculation of the properties of large molecular systems.

Notes: 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(ring), 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 construction of the two-dimensional potential surface of automerization. The following lowest vibrational energies were obtained for this surface (v1 and v2, the symmetric and antisymmetric CC stretches in D4h symmetry, are given in parentheses): 0 and 4.2 cm−1 (00+; 00−); 1526.1 and 1607.6 cm−1 (01+; 01−), 1480.9, and 1485.5 cm−1 (10+; 10−), and 791.6 cm−1 for the zero-point energy (00+). The computed splitting of the vibrational ground state implies the rate of automerization is k=2.5×1011 s−1 for temperatures close to absolute zero.

Notes: We have carried out nonlocal density-functional calculations of bond dissociation and isomerization energies of several polyatomic molecules in two schemes. In the first scheme, the nonlocal energy functional is incorporated into the optimization of both the electronic and nuclear degrees of freedom. In the second scheme, the nonlocal energy functional is only included in a non-self-consistent fashion in which we just use the molecular geometry and electron density determined by the corresponding local density calculations. Our study reveals that the differences of the energies are very small between these two schemes.

Notes: We derive expressions for molecular gradients and hessians for the case when the energy is evaluated using density functional theory. Although derivative expressions have been proposed previously, our derivation is based on the unitary exponential parameterization of the wavefunction, and our expressions are valid for local and non–local potentials. Density functional theory, although similar in implementation to standard SCF theory, differs in that it introduces an exchange–correlation term which is density dependent. The presence of such a quantity introduces additional derivative terms which are not present in standard approaches of electronic structure theory. Expressions are derived for both the exact Coulombic repulsion, as well as the case where the density is expressed as a fitted quantity. Given these choices our final equations offer a computationally tractable expression with particular emphasis on conditions which ensure that the computed quantities are numerically correct. We show that although the use of a fitted density allows significant computational savings in the energy and the first derivatives, it introduces additional computational complexity, beyond that normally encountered in traditional electronic structure methods, once second derivatives are evaluated. The evaluation of second derivatives also introduces derivatives of the exchange–correlation potential which have not been previously considered.The presence of such terms introduces the most serious computational complexity to the evaluation of any second derivative expression based on the density–functional formalism. Our derivation and analysis presents a computationally tractable procedure for the evaluation of all the terms required to compute the first and second derivatives with respect to perturbations such as nuclear coordinates, and external electric fields. Using a general set of response equations for the first order change in the wavefunction, we provide expressions for the evaluation of harmonic frequencies, infrared intensities, and molecular polarizabilities. Our final discussion assesses the computational consequences of using either an exact form for the density, or a fitted form. Although most of our discussion is cast in the form of a closed–shell formalism, extensions to an unrestricted (UHF) formalism are straightforward.

Notes: The potential energy surface of the (H2O)5 water cluster is examined using Kohn–Sham density functional theory, Hartree–Fock theory and second-order Møller–Plesset theory. Two distinct minima on the energy surface may be interconverted through the transfer of two hydrogen atoms, representing a possible mechanism for ionic dissociation in water clusters. Our calculations suggest a concerted mechanism where the two hydrogen atoms move simultaneously through a late transition state. © 1996 American Institute of Physics.