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Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method

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Abstract

We have analyzed the basis function series in molecular systems by optimization of orbital exponents in Gaussian-type functions (GTFs) including the electron correlation effects with multiconfiguration self-consistent field (MCSCF) and Møller–Plesset second-order perturbation (MP2) methods. First, we have derived and implemented the gradient formulas of MCSCF and MP2 energies with respect to GTF exponent, as well as GTF center and nuclear geometry, based on the fully variational molecular orbital (FVMO) method. Second, we have applied these electron-correlated FVMO methods to H2, LiH, and hydrocarbon (CH4, C2H6, C2H4, and C2H2) molecules. We have clearly demonstrated that the optimized exponent values with electron-correlated methods are different from those with simple Hartree–Fock method, since adequate basis functions for adequate virtual orbitals are indispensable to describe the accurate wave function and geometry for electron-correlated calculations.

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Acknowledgments

The present study has been supported in part by a Grant-in-Aid for Scientific Research and for the Priority Area by the Ministry of Education, Culture, Sports, Science and Technology (MT) and by a Grand-in-Aid for Young Scientists (Start-up) (No. 21850022) from the Japan Society for the Promotion of Science (JSPS) (TI).

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Correspondence to Masanori Tachikawa.

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Dedicated to Professor Akira Imamura on the occasion of his 77th birthday and published as part of the Imamura Festschrift Issue.

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Shimizu, N., Ishimoto, T. & Tachikawa, M. Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method. Theor Chem Acc 130, 679–685 (2011). https://doi.org/10.1007/s00214-011-1052-3

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