J. Phys. Chem. 1992,96, 10725-10735
10725
Effect of Electron Correlation on the Electron Density Distribution and (Hyper)polarizability of Molecules Guus J. M.Veldem* and Dirk Feil Chemical Physics Laboratory, University of Twente, P.O. Box 21 7 , 7500 AE Enschede. The Netherlands (Received: March 13, 1992)
The influence of electron correlation, calculated with Mdler-Plesset perturbation theory, on the electron density distribution and (hyper)polarizabilityof molecules is discussed. Although the electron correlation contribution to the density is small compared with the total molecular density, it yields significant changes in atomic charges, compared to Hartree-Fock calculated values. In molecules with C==O bonds, atomic charges of the electron correlation density show a larger transferability between molecules than atomic charges calculated with the HartreeFock method. Two finite field methods and the sum over states method have been used to calculate the influence of an electric field of the molecules. The influence of electron correlation on the polarizability is small but can be quite large for the first hyperpolarizability, as seen, for example, in planar pnitroaniline.
1. Inboduction For calculating electronic properties in molecules the Hartree-Fock (HF) approximation is very popular. This method gives quite good results for a number of molecular properties and a large variety of molecules. It is well-known, however, that molecular energy differences, from molecular interactions, cannot be calculated accurately by using the H F approximation. Several methods are in use to improve the H F approximation. These advanced methods, often using the H F wave function as a starting point, mostly focus on the calculation of the total molecular energy of a system and derived properties. In understanding inter- and intramolecular bonding properties and. chemical reactions, knowledge concerning the electron density distribution in the systems is considered to be important. Fortunately, the effect of electron correlation on this distribution is small, explaining the ubiquitous role of Hartree-Fock methods in electron density studies. Not in all cases can correlation be neglected, as the history of calculation of the dipole moment of carbon m~noxidel-~ shows; Le., electron correlation is necessary to obtain the correct sign for the dipole moment of carbon monoxide. It can be expected that, in molecules with similar bonds, H F calculations give a distorted view of the electrostatic properties of the molecule. In most of the electron density studies, however, the H F method is used, and electron correlation effects are neglected. Only a few electron density distribution studiese13using more advanced methods than the conceptually simple HartretFock method are reported. Most of these are c o n f i i t i o n interaction (CI) calculationsusing single and double substitutions. When one restricts the configurations to those obtained by using single and double substitutions (CISD), the major part of the electron correlation is taken into account. Recently direct calculations of the effect of electron correlation on the electron density distribution of molecules have been performed by Wang and BoydI2J3using perturbation theory. They used Rayleigh-Schr&hger perturbation theory with the HF wave function as a starting point, as introduced by M ~ l l e and r Plesset. The computational demands of the Mdler-Plesset (MP) perturbation theory are much less than those of a CI calculation of approximately the same accuracy. The advantage of a CI calculation over an MP calculation is that the CI wave function is determined by a variational procedure. The MP perturbation theory, on the other hand, is size consistent; this is true for the CI method only when all possible substitutions are used (full CI). Wang and B o ~ d ' zstudied '~ the validity of the MP perturbation theory calculation,up to sccond order in the density, and compared it with a CISD calculation. They found for H2, N2, OF2, and H2C0 a very good agreement between both types of calculations. AmosI4-I6 investigated the influence of the electron correlation indirectly, by means of a multipole analysis of some diatomic molecules, using both the CI and MP methods. All ab initio studies of the influence of electron correlation on the electron density distribution and derived properties are re-
stricted to molecules consisting of only a few heavy atoms. To obtain information about electron correlation in larger molecules, we have studied the transferability of the electron density distribution and the electron correlation density for several molecules containing a C - 0 or a C - C bond. The contribution of MP2 on the dipole moment of some molecules will be discussed together with a charge density analysis of the origin of the dipole moment. We must realize that analyzing electron density distributions is not the only way to study electron correlation effects in molecules, but interesting information can be obtained from it. Electron correlation can be important in calculations of the polarizability and first hyperpolarizability. Most organic compounds that are interesting for nonlinear optics are quite large. For a molecule likepnitroanihe (PNA), CI and MP calculations can only be performed with moderate basis sets. We have performed calculations of the (hyper)polarizability of some small molecules and tried to extend the results to larger conjugated systems. 2. Theoretical Methods The quantum chemical methods we have used to calculate the electron density distributions, atomic moments, and effects of an electric field are the Hartree-Fock (HF) and M~ller-Plesset perturbation theory (MP2) methods (see section 2.1). 2.1. Merller-Plesset Perturbation Tbeory. Electron correlationl7-20 is defined as the difference between the exact solution of the total nonrelativistic Hamiltonian of a system, within the Bom-Oppenheimer approximation, and the approximated solution in the H F limit. It reflects the fact that the Hartree-Fock Hamiltonian contains the average, rather than the instantaneous, potential, and thus neglects the correlation between the motion of the electrons. Apart from this,there are also correlation effects related to relativistic effects and nuclear motion which will not be considered here. The expectation value of a single particle operator, like the charge density distribution and the dipole moment, will be constructed in the general case of a multideterminantal wave function. Maller-Plesset perturbation t h e ~ r y ' ~ J ~uses . ~ ' the H F wave function, in the spin unrestricted case (UHF), as a starting point. Starting from the H F wave function $o, the following multideterminantal wave function is constructed22 occ virt
= "(+o
OQ:
+ Ea ECL% + a
