L1-regularization in quantum chemistry. The π-electron coupled cluster doubles theory
DOI:
https://doi.org/10.26565/2220-637X-2016-26-06Keywords:
coupled cluster theory, Moller-Plesset perturbation theory, L1-regularization, π-conjugated systemsAbstract
The possibility of using of L1-regularization in description of the many electron wave function structure has been discussed. The analysis of the configurational structure in semiempirical coupled cluster doubles theory (CCD) and second order Moller-Plesset perturbation theory (MP2) is presented as an example. The ranging lists of electron excited configurations as an approximation to exact solution of certain approach can be obtained. The qualitative similarity of regularized solutions for the above mentioned theories is demonstrated.
References
Tikhonov A. N., Arsenin V. Y. Solutions of ill-posed problems. New York, John Wiley & Sons, 1977. – 270 p.
Morozov V. A. Regulation Methods for ill-posed problems, CRC Press, 1993. – 273 с.
Binkers D., Dodge Y. Alternative Methods of Regression. New York.: John Wiley & Sons, 1993. – 228 p.
Chatterjee S., Hadi A. S. Regression Analysis by Example, J. Wiley & Sons.– 2006.– 375 p.
Tibshirani R. // J. Roy. Statist. Soc. 1996. – B58, № 1. – P. 267–288.
Hastie T., Tibshirani R., Wainwright M., Statistical Learning with Sparsity. The Lasso and Generalizations, CRC Press., 2015. 335 p.
Schmidt M. Least Squares Optimization with L1-Norm Regularization // CS542B Project Re-port. – 2005, 12 p. WEB page: http://www.cs.ubc.ca/~schmidtm/Documents/ 2005_Notes_Lasso.pdf.
Ozoliņš V., Lai R., Caflisch R., and Osher S. // Proc. Natl. Acad. Sci. USA. – V. 111(5). – P.1691–1696.
Cizek J., Paldus J. // Int. J. Quant. Chem. – 1971. – V. 5. – P. 359-379.
Bartlett R. J. // Ann. Rev. Phys. Chem. – 1981. – V. 32. – P. 359-401.
Brueckner K. A. // Phys. Rev. – 1955. – V. 100, № 1. – P. 36-45.
Bartlett R. J., Purvis G. D. // Int. J. Quant. Chem. – 1978. – V.14. – P. 561-581.
Bahamani S. Algorithms for Sparsity-Constrained Optimization. Springer, 2014. – 107 p.
Donoho D. L. // IEEE Transactions on Information Theory. – 1995. – V. 41, N 3.– P. 613-627.
Pariser R., Parr R. G. // J. Chem. Phys. – 1953. – V. 21. – P. 466-471.
Pople J. A. // Trans. Faraday Soc. – 1953. – V.49. – P. 1375-1385.
Onho K. // Theor. Chim. Acta. – 1964. – V. 2. – P. 219-227.
Zakharov A. B., Ivanov V. V. Adamowicz L. // J. Phys. Chem. C – 2014.– V. 118. – P. 8111 8121.
Schmidt M. W., Baldridge K. K., Boatz J. A., Elbert S. T., et al. // J. Comput. Chem. – 1993. – V. 14, № 1. – P. 1347-1363.
