Computational chemistry coupled-cluster method

J. Noga, W. Klopper, and W. Kutzelnigg, in Recent Advances in Computational Chemistry, Vol. 3, Recent Advances in Coupled-Cluster Methods, R. J. Bartlett (ed.), World Scientific, Singapore (1997). 

Recent developments in computational chemistry have established the exact structure of carbocations by combining computational and experimental results.78,79 Furthermore, accurate 1H and 13C NMR chemical shifts of carbocations and other organic molecules can be calculated with the application of recent coupled cluster methods, such as GIAO-CCSD(T).80... 

In order to get more detailed information about, e.g., bond strengths and equilibrium geometries in transition metal systems it is necessary to include electron correlation. This can be done either by traditional ab initio quantum chemistry models, e.g., Cl-methods and coupled cluster methods, or by density functional theory (DFT) based methods. Correlated ab initio methods are often computationally very demanding, especially in cases where multi-reference based treatments are needed. Also, the computational cost of these methods increases dramatically with the size of the system. This implies that they can only be applied to rather small systems. 

The Soviet Union s military invasion of Czechoslovakia in August 1968 had a significant impact on the development of computational and theoretical chemistry in Canada. The troubles in Czechoslovakia led to Jiri Cizek and Joe Paldus accepting appointments at the University of Waterloo in 1968. Their many achievements include the first ab initio study of the coupled cluster method.104... 

R.J. Bartlett (Ed.), Recent advances in coupled-cluster methods, Recent advances in computational chemistry, Vol. 3, World Scientific Publishing, Singapore, 1997. 

These values of f can then be used as a new Iq vector for the next application of Eq. (4.24). This multidimensional Newton-Raphson procedure, which involves the solution of a large number of coupled linear equations, is then repeated until the At values are sufficiently small (convergence). Given the set of f J amplitudes, Eq. (4.16) can then be used to compute E. Although the first applications of the coupled cluster method to quantum chemistry did employ this Newton Raphson scheme, the numerical problems involved... 

J. Kim, J.Y. Lee, S. Lee, B.J. Mhin, and K.S. Kim, J. Chem. Phys., 102, 310 (1995). This paper reports normal mode analysis for potential energy hypersurfaces computed by various methods of quantum chemistry. I have chosen the coupled cluster method [CCSD(T) see Chapter 10] as an illustration. 

Ehara M, Nakatsuji H (2010) In Catsky P, Ptildus J, Pittner J (eds) Recent progress in coupled cluster methods, vol 11, Challenges tmd advtmces in computational chemistry tmd physics. Springer, Dordrecht/Heidelberg/London/New York, p 79... 

There are many ways to compute the ground-state wavefunction Tq, such as configuration-interaction techniques and coupled-cluster methods, widely studied by the ab-initio theoretical-chemistry community. These methods however show a unfavorable scaling with the number of electrons and still cannot be applied to model large systems of increasing interest (e.g. in nano-bio-science). The main limitation is that these methods focus on the many-electron wavefunction T which contains N variables. 

As I have argued, errors are seldom computed by independent ab inito criteria in any of the calculations in theoretical chemistry which I discuss. Only the Self-Consistent Field calculations provide an upper bound whereas Many-Body Perturbation Theory and Coupled Cluster methods do not. More importantly perhaps, none of these methods computes a lower bound. As was remarked earlier the calculation of the ground state energies of atoms has been achieved to a remarkable degree of accuracy and similarly calculations on small or even medium sized molecules have given encouraging results. However, whether one can draw the conclusion that chemistry has been reduced rather depends on one s criteria of reduction. If we are to define approximate reduction as has been suggested in this paper then it must be concluded that chemistry is not even approximately reduced to quantum mechanics. The point I wish to emphasize is that we should not be misled by the apparent quantitative successes achieved and should appreciate the full nature of the approximation procedures employed. 

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