Multireference self-consistent-field calculation

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

This calculation is typically performed in some form of a restricted configuration interaction (Cl) expansion (CASSCF [complete active space self consistent field], MRCI [multireference configuration interaction]). The perturbation V is represented by the operators and The perturbed wave function F and energy E satisfy the equation... 

Multireference configuration interaction (MRCI) calculations based on valence complete active space self-consistent field (CASSCF) wave functions with the quadruples corrections (-I-Q) [25-30] were used to determine the excitation energies of the N and P atoms using the AVQZ basis set. 

The calculations were performed with several different levels of correlation treatment Hartree-Fock (HF), configuration interaction with single and double excitations (SDCI), Multiconfiguration self consistent field (CAS), and multireference configuration interaction (MRCI). Relativistic efferts were accounted for using either the Douglas-Kroll method or a relativistic effective core potential approach (RECP). 

In this section we will introduce some wavefunction-based methods to calculate photoabsorption spectra. The Hartree-Fock method itself is a wavefunction-based approach to solve the static Schrodinger equation. For excited states one has to account for time-dependent phenomena as in the density-based approaches. Therefore, we will start with a short review of time-dependent Hartree-Fock. Several more advanced methods are available as well, e.g. configuration interaction (Cl), multireference configuration interaction (MRCI), multireference Moller-Plesset (MRMP), or complete active space self-consistent field (CASSCF), to name only a few. Also flavours of the coupled-cluster approach (equations-of-motion CC and linear-response CQ are used to calculate excited states. However, all these methods are applicable only to fairly small molecules due to their high computational costs. These approaches are therefore discussed only in a more phenomenological way here, and many post-Hartree-Fock methods are explicitly not included. 

There is far less reported experience for the HF studies of electronic excited states (ESs). Especially, highly, doubly and core hole excited (ionized) states are not often studied. It is clear that existing ground state self-consistent field (SCF) methods cannot be directly applied to excited states of the same symmetry or of the same spin multiplicity as a lower state because of the so-called variational collapse i.e., the optimization procedure will find only the lowest solution of a given symmetry or a given spin multiplicity. Therefore, such calculations for ES cannot be considered as routine. The most powerful scheme for accurate treatment of ESs is based on multireference methods [2-8]. They typically provide an accuracy of about 0.1 eV but require the expense of much computational cost. Thus, it can be quite difficult to carry out the corresponding calculations. Such methods are, however, indispensable to study systems where... 

The Multireference Space. The calculations of the embedded-cluster wavefunctions have a first step where multiconfigurational self-consistent field wavefunctions and energies are calculated using complete and/or restricted active spaces (CASSCF [32-34] and/or RASSCF [35,36]). The lanthanide 4/, 5d, and 6s shells must be included in the active space for the calculation of the 4/, 4f 5d, and manifolds, N being the num-... 

MP methods have been developed for both spin-restricted HF (RHF), spin-unrestricted HF (UHF), and restricted open-shell HF (ROHF) wavefunctions to investigate both closed- and open-shell systems (see Table 2). For the calculation of electron systems with multireference character such as biradicals various multireference state (MRS) MP methods have been developed (Table 2). All these methods describe atoms, molecules, and reaction systems in the gas phase. However, many chemical reactions take place in solution phases. For this purpose, MP methods are available that start from a solvent corrected wavefunction where mostly polarizable continuum models are used (see Self-consistent Reaction Field Methods). 

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