Molecular properties coupled-cluster theory

Since its introduction into quantum chemistry in the late 1960s by Qzek and Paldus, " coupled cluster theory has emerged as perhaps the most reliable, yet computationally affordable method for the approximate solution of the electronic Schrodinger equation and the prediction of molecular properties. The purpose of this chapter is to provide computational chemists who seek a deeper knowledge of coupled cluster theory with the background necessary to understand the extensive literature on this important ab initio technique. 

Hald, K. Molecular properties in Coupled-Cluster theory. Ph.D. Thesis, University of Aarhus (2002)... 

The efficient computation of molecular response properties such as optical rotation is of paramount importance, and schemes for reducing the computational effort required for high-accuracy methods such as coupled cluster theory become even more crucial for larger, chemically relevant molecules. However, algorithmic improvements must not come at the expense of the overall accuracy of the theory, and the EOM-CCl approach of Sekino and Bartlett provides a reasonable com-... 

Ab-initio methods based on solution of the Hartree-Fock equations are well established (Ref 14), and are used in routine molecular and electronic calculations on small organic and inorganic molecules. For such molecules, extremely accurate predictions of many spectroscopic properties can be made using methods such as CAS-CI, MCSCF, coupled-cluster theory, and multireference methods. Recent advances in supercomputer technology coupled with improved algorithms have made it possible to perform full Cl calculations for small systems. Due to their size and complexity, such calculations have been limited mostly to diatomic molecules. However, where cost is not a problem, it is quite feasible to perform full Cl calculations on quite large systems, and such calculations have been carried out on small energetic molecules by Haskins and Cook at RARDE (Ref 16). 

The aim of this book is to present the basic aspects of the molecular response function theory for molecular systems in solution described with the Polarizable Continuum Model, giving special emphasis both to the physical basis of the theory and to its quantum chemical formalism. The QM formalism will be presented in the form of the coupled-cluster theory, as it is the most recent and less known formulation for the QM calculation of molecular properties within the PCM... 

In the previous sections we have shown how it is possible to obtain a coherent generalization of the coupled-cluster theory to the description of the ground state properties of molecular solutes. In this section we will show how a similar generalization can be obtained for the EOM-coupled cluster theory, for the description of the excited states properties of solvated molecules. 

The calculation of molecular properties can be carried out at three distinct levels (i) ab initio, (ii) semi-empirical, (iii) empirical. Ab initio methods have increased enormously in accuracy and efficiency in the last two decades and are the focus of our discussion here. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Moller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become very popular, since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field G2 Theory Geometry Optimization 1 Gradient Theory Inter-molecular Interactions by Perturbation Theory Molecular Magnetic Properties NMR Chemical Shift Computation Ab Initio NMR Chemical Shift Computation Structural Applications Self-consistent Reaction Field Methods Spin Contamination. 

For reasons of computational practicality and efficiency, molecular electronic coupled-cluster energies are determined using a nonvariational projection technique. The chief deficiency of this approach is not so much the loss of boundedness (since the coupled-cluster energy is nevertheless rather accurate), but the difficulties that it creates for the calculation of properties as the conditions for the Hellmann-Feynman theorem are not satisfied - even in the limit of a eomplete one-electron basis. Fortunately, as discussed in Section 4.2.8, this situation may be remedied by the construction of a variational Lagrangian [14]. In this formulation, the conditions of the Hellmann-Feynman theorem are fulfilled and molecular properties may be calculated by a proeedure that is essentially the same as for variational wave functions. The Lagrangian formulation of the energy is also related to a variational treatment of coupled-cluster theory applicable to excited states, as discussed in Section 13.6. 

According to (13.5.8), first-order molecular properties may in coupled-cluster theory be calculated... 

Sous J, Goel P, Nooijen M. Similarity transformed equation of motion coupled cluster theory revisited a benchmark study of valence excited states. Mol Phys. 2013 112 616-638. Trofimov AB, Krivdina IL, Weller J, Schimer J. Algebraic-diagrammatic construction propagator approach to molecular response properties. Chem Phys. 2006 329 1-10. 

The reasons for not invoking the variation principle in the optimization of the wave function are given in Chapter 13, which provides a detailed account of coupled-cluster theory. We here only note that the loss of the variational property characteristic of the exact wave function is unfortunate, but only mildly so. Thus, even though the coupled-cluster method does not provide an upper bound to the FCI energy, the energy is usually so accurate that the absence of an upper bound does not matter anyway. Also, because of the Lagrangian method of Section 4.2.8, the complications that arise in connection with the evaluation of molecular properties for the nonvariational coupled-cluster model are of little practical consequence. 

Rapid convergence of molecular properties with respect to the excitation rank is obtained with the systematic approximations of coupled-cluster (CC) theory... 

The single-reference coupled cluster (CC) theory [1-5] has become a standard computational tool for studying ground-state molecular properties [6-10]. The basic approximations, such as CCSD (coupled cluster singles and doubles approach) [11-15], and the noniterative CCSD[T] [16,17] and CCSD(T) [18] methods, in which the cleverly designed corrections due to... 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Our present focus is on density functional theory and coupled cluster methods for describing molecular systems interacting with a structured environment, and we focus on the derivation of linear response properties and compare the expressions that we obtain for the two different electronic structure methods. Based on linear response... 

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