Correlated electronic structure wavefunction

The electronic structure of molecular systems interacting with the outer solvent is given by a correlated electronic structure wavefunction, which, coupled to solvent response theory, enables the calculations of molecular properties of solvated molecules such as ... 

Calculations of time-dependent electromagnetic properties of molecules at the correlated electronic structure level are conveniently carried out by the utilization of modern response theory [43-51], The transition of modern response theory for gas phase molecular systems to solvated molecules has been established [1-6] and these methods include the use of correlated electronic wavefunctions. These methods, reviewed here, have given rise a large number of computational approaches for calculating electric and magnetic molecular properties of solvated molecules. 

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

Ab initio modem valence bond theory, in its spin-coupled valence bond (SCVB) form, has proved very successful for accurate computations on ground and excited states of molecular systems. The compactness of the resulting wavefunctions allows direct and clear interpretation of correlated electronic structure. We concentrate in the present account on recent developments, typically involving the optimization of virtual orbitals via an approximate energy expression. These virtuals lead to higher accuracy for the final variational wavefunctions, but with even more compact functions. Particular attention is paid here to applications of the methodology to studies of intermolecular forces. 

We assume that standard Coulomb-correlated models for luminescent polymers [11] properly described the intrachain electronic structure of m-LPPP. In this case intrachain photoexcitation generate singlet excitons with odd parity wavefunctions (Bu), which are responsible for the spontaneous and stimulated emission. Since the pump energy in our experiments is about 0.5 eV larger than the optical ran... 

In the last few years, the improvements in computer hardware and software have allowed the simulation of molecules and materials with an increasing number of atoms. However, the most accurate electronic structure methods based on N-particle wavefunctions, for example, the configuration interaction (Cl) method or the coupled-cluster (CC) method, are computationally too expensive to be applied to large systems. There is a great need for treatments of electron correlation that scale favorably with the number of electrons. 

Section treats the spatial, angular momentum, and spin symmetries of the many-electron wavefunctions that are formed as antisymmetrized products of atomic or molecular orbitals. Proper coupling of angular momenta (orbital and spin) is covered here, and atomic and molecular term symbols are treated. The need to include Configuration Interaction to achieve qualitatively correct descriptions of certain species electronic structures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of chemical reactivity is also developed. 

The purpose of this review is to discuss the main conclusions for the electronic structure of benzenoid aromatic molecules of an approach which is much more general than either MO theory or classical VB theory. In particular, we describe some of the clear theoretical evidence which shows that the n electrons in such molecules are described well in terms of localized, non-orthogonal, singly-occupied orbitals. The characteristic properties of molecules such as benzene arise from a profoundly quantum mechanical phenomenon, namely the mode of coupling of the spins of the n electrons. This simple picture is furnished by spin-coupled theory, which incorporates from the start the most significant effects of electron correlation, but which retains a simple, clear-cut visuality. The spin-coupled representation of these systems is, to all intents and purposes, unaltered by the inclusion of additional electron correlation into the wavefunction. 

We start with a description of the spin-coupled wavefunction for the general case in which electron correlation is included for all of the electrons. We return later to the question of a-n separation. In the spin-coupled approach to molecular electronic structure, an A-electron system is described by N orbitals, all of which are allowed to be distinct and non-orthogonal. One consequence of the non-orthogonality of these singly-occupied orbitals is that there is usually more than one way of coupling together the spins of the individual electrons so as to achieve the required overall... 

The configuration interaction (Cl) treatment of electron correlation [83,95] is based on the simple idea that one can improve on the HF wavefunction, and hence energy, by adding on to the HF wavefunction terms that represent promotion of electrons from occupied to virtual MOs. The HF term and the additional terms each represent a particular electronic configuration, and the actual wavefunction and electronic structure of the system can be conceptualized as the result of the interaction of these configurations. This electron promotion, which makes it easier for electrons to avoid one another, is as we saw (Section 5.4.2) also the physical idea behind the Mpller-Plesset method the MP and Cl methods differ in their mathematical approaches. 

In this section, we briefly discuss some of the electronic structure methods which have been used in the calculations of the PE functions which are discussed in the following sections. There are variety of ab initio electronic structure methods which can be used for the calculation of the PE surface of the electronic ground state. Most widely used are Hartree-Fock (HF) based methods. In this approach, the electronic wavefunction of a closed-shell system is described by a determinant composed of restricted one-electron spin orbitals. The unrestricted HF (UHF) method can handle also open-shell electronic systems. The limitation of HF based methods is that they do not account for electron correlation effects. For the electronic ground state of closed-shell systems, electron correlation effects can be accounted for relatively easily by second-order Mpller-Plesset perturbation theory (MP2). In modern implementations of MP2, linear scaling with the size of the system has been achieved. It is thus possible to treat quite large molecules and clusters at this level of theory. 

The electronic structure methods are based primarily on two basic approximations (1) Born-Oppenheimer approximation that separates the nuclear motion from the electronic motion, and (2) Independent Particle approximation that allows one to describe the total electronic wavefunction in the form of one electron wavefunc-tions i.e. a Slater determinant [26], Together with electron spin, this is known as the Hartree-Fock (HF) approximation. The HF method can be of three types restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF) and restricted open Hartree-Fock (ROHF). In the RHF method, which is used for the singlet spin system, the same orbital spatial function is used for both electronic spins (a and (3). In the UHF method, electrons with a and (3 spins have different orbital spatial functions. However, this kind of wavefunction treatment yields an error known as spin contamination. In the case of ROHF method, for an open shell system paired electron spins have the same orbital spatial function. One of the shortcomings of the HF method is neglect of explicit electron correlation. Electron correlation is mainly caused by the instantaneous interaction between electrons which is not treated in an explicit way in the HF method. Therefore, several physical phenomena can not be explained using the HF method, for example, the dissociation of molecules. The deficiency of the HF method (RHF) at the dissociation limit of molecules can be partly overcome in the UHF method. However, for a satisfactory result, a method with electron correlation is necessary. 

Just as in correlated descriptions based on MO theory, it is neither practical nor desirable to include electron correlation for all of the electrons in large systems. In common with other strategies, the orbital space is partitioned into inactive , active and unoccupied or virtual subspaces. Electron correlation is incorporated only for the active space, which corresponds to that part of the electronic structure which interests us most. A convenient representation of a general spin-coupled wavefunction takes the form ... 

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