Coupled-cluster theory application

Single-root multireference Brillouin-Wigner coupled-cluster theory Applicability to the F-2 molecule... 

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. 

We do not pretend to give here an exhaustive account of all the possible applications ofNSS s into Quantum Chemistry. Some areas, which for sure can be studied from the nested summation point of view, like the Coupled Cluster Theory [14], are not included here. 

Use of Equation (1) in numerical work requires a means of generating x(r, r i(o) as well as the average charge density. Direct variational methods are not applicable to the expression for E itself, due to use of the virial theorem. However, both pc(r) and x(r, r ico) (39-42, 109-112) are computable with density-functional methods, thus permitting individual computations of E from Eq. (1) and investigations of the effects of various approximations for x(r, r ico). Within coupled-cluster theory, x(r, r ico) can be generated directly (53) from the definition in Eq. (3) then Eq. (1) yields the coupled-cluster energy in a new form, as an expectation value. 

Finally, Levchenko and Krylov (2004) have defined spin-flip versions of coupled cluster theories along lines similar to those previously described for SF-CISD. Applications to date have primarily been concerned with the accurate computation of electronically excited states, but the models are equally applicable to computing correlation energies for ground states. 

With increasing use of such models, methods are likely to become more concisely defined in the near future. At present, the models for which protocols and parameters have been most clearly defined and where a fair number of applications have appeared applying those models in a consistent fashion include the aheady noted AM1/TIP3P model (more generally AMl/OPLS when solvents other than water are employed in the MM region) and a similarly fashioned HF/3-21G/OPLS model (Freindorf and Gao 1996). Implementations carrying the QM level as far as coupled-cluster theory have been reported (Kongsted et al. 2003). 

P. Piecuch and J. Paldus, Phys. Rev. A, 49, 3479 (1994). Application of Hilbert-Space Coupled-Cluster Theory to Simple (H2 )2 Model Systems. II. Non-Planar Models. 

Korona T, Przybytek M, Jeziorski B. Time-independent coupled cluster theory of the polarization propagator. Implementation and application of the singles and doubles model to dynamic polarizabilities and Van der Waals constants, 2006. Submitted to Mol. Phys 104 2302-2316... 

Bartlett RJ (2005) How and why coupled-cluster theory became the pre-eminent method in an ab initio quantum chemistry. In Dykstra CE, Frenking G, Kim KS, Scuseria GE (eds) Theory and Applications of Computational Chemistry The First Forty Years, Elsevier Amsterdam, pp. 1191-1221. 

Mahapatra, U. S. Datta, B. Mukheijee, D. A size-consistent state-specific multireference coupled cluster theory Formal developments and molecular applications, J. Chem. Phys. 1999,110, 6171-6188. 

Thanks in part to the computational advances described in the preceding section, coupled cluster theory has developed into arguably the most accurate and computationally affordable method of modern computational quantum chemistry. The results of coupled cluster calculations are commonly found in the chemical physics literature, and, when the accuracy of experimental results is questioned, the CCSD(T) method is often used to settle the debate. In spite of this success, coupled cluster theory is far from applicable to all problems of chemical interest. The majority of the current research efforts may be divided into four overlapping categories ... 

A. Banerjee and J. Simons,/. Chem. Phys., 76,4548 (1982). Applications of Multiconfigura-tional Coupled-Cluster Theory. 

In Volume 5 of this series, R. J. Bartlett and J. E Stanton authored a popular tutorial on applications of post-Hartree-Fock methods. Here in Chapter 2, Dr. T. Daniel Crawford and Professor Henry F. Schaefer III explore coupled cluster theory in great depth. Despite the depth, the treatment is brilliantly clear. Beginning with fundamental concepts of cluster expansion of the wavefunction, the authors provide the formal theory and the derivation of the coupled cluster equations. This is followed by thorough explanations of diagrammatic representations, the connection to many-bodied perturbation theory, and computer implementation of the method. Directions for future developments are laid out. 

C. M. L. Rittby and R. J. Bartlett, Theor. Chim. Acta, 80, 469 (1991). Multireference Coupled-Cluster Theory in Fock Space With an Application to s-Tetrazine. 

Nonadditive effects in open-shell clusters have been investigated only recently and relatively little information is available on their importance and physical origin. From the theoretical point of view, open-shell systems are more difficult to study since the conventional, size-consistent computational tools of the theory of intermolecular forces, like the Mpller-Plesset perturbation theory, coupled cluster theory, or SAPT, are less suitable or less developed for applications to open-shell systems than to closed-shell ones. Moreover, there are many types of qualitatively different open-shell states, exhibiting different behavior and requiring different theoretical treatments. 

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

Taube, A. G., and Bartlett, R. J. [2008], Frozen natural orbital coupled-cluster theory Forces and application to decomposition of nitroethane, ]. Chem. Phys. 128, p. 164101, doi 10.1063/1.2902285,... 

The current volume presents the compilation of splendid contributions distributed over 21 chapters. The very first chapter contributed by Istvan Hargittai presents the historical account of development of structural chemistry. It also depicts some historical memories of scientists presented in the form of their pictures. This historical description covers a vast period of time. Intruder states pose serious problem in the multireference formulation based on Rayleigh-Schrodinger expansion. Ivan Hubac and Stephen Wilson discuss the ciurent development and future prospects of Many-Body Brillouin-Wigner theories to avoid the problem of intruder states in the next chapter. The third chapter written by Vladimir Ivanov and collaborators reveals the development of multireference state-specific coupled cluster theory. The next chapter from Maria Barysz discusses the development and application of relativistic effects in chemical problems while the fifth chapter contributed by Manthos Papadopoulos and coworkers describes electronic, vibrational and relativistic contributions to the linear and nonlinear optical properties of molecules. 

One of the most dramatic changes in the standard theoretical model used most widely in quantum chemistry occurred in the early 1990s. Until then, ab initio quantum chemical applications [1] typically used a Hartree-Fock (HF) starting point, followed in many cases by second-order Moller-Plesset perturbation theory. For small molecules requiring more accuracy, additional calculations were performed with coupled-cluster theory, quadratic configuration interaction, or related methods. While these techniques are still used widely, a substantial majority of the papers being published today are based on applications of density functional theory (DFT) [2]. Almost universally, the researchers use a functional due to Becke, whose papers in 1992 and 1993 contributed to this remarkable transformation that changed the entire landscape of quantum chemistry. 

The thesis begins with Section 2, where a brief history about the explicitly correlated approaches is presented. This is followed by Section 3 with general remarks about standard and explicitly correlated coupled-cluster theories. In Section 4, the details about the CCSD(F12) model relevant to the implementation in TuRBOMOLE are presented. The usefulness of the developed tool is illustrated with the application to the problems that are of interest to general chemistry. A very accurate determination of the reactions barrier heights of two CH3+CH4 reactions has been carried out (Section 5) and the atomization energies of 106 medium-size and small molecules were computed and compared with available experimental thermochemical data (Section 6). The ionization potentials and electron affinities of the atoms H, C, N, O and F were obtained and an agreement with the experimental values of the order of a fraction of a meV was reached (Section 7). Within all applications, the CCSD(F12) calculation was only a part of the whole computational procedure. The contributions from various levels of theory were taken into account to provide the final result, that could be successfully compared to the experiment. 

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