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A new, efficient parallel algorithm for four-component relativistic generalized multiconfigurational quasidegenerate perturbation theory (GMC-QDPT) introducing Kramers symmetry is implemented. Because it utilizes the independence of the terms in the matrix element computations, this algorithm both speeds up the calculation and reduces the computational resources required for each node. In addition, the amount of memory for two-electron integrals is reduced to three-eigths by Kramers restriction. The algorithm is applied to the d-d excitation energies of the platinum halide complexes, [PtCl4](2-), [PtBr4](2-), and [PtCl6](2-) and to the 6p-7s and 6p-7p excitation energies of the radon atom. It is shown to provide high parallelization efficiency and accurate excitation energies that agree well with experimental data.

GMC-QDPTGMCJ. Comput. Chem. Jpn., Vol. 13, No. 1, pp. 32-42 (2014 GMC-QPDT GMC-QDPT3E 4E [PtCln] 2 − (n = 4, 6) d-d Table 3 87.4% 80.0 82.3% Table 5 GMC-PT GMC-PT 3.2 [2] H. Nakano, J. Chem. Phys., 99, 7983 (1993). [CrossRef] [3] H. Nakano, Chem. Phys. Lett., 207, 372 (1993). I2[CrossRef][4] K. Hirao, Chem. Phys. Lett., 190, 374 (1992). [CrossRef] [5] K. Hirao, Chem. Phys. Lett., 196, 397 (1992). [CrossRef] [6] I. Shavitt, L. R. Redmon, J. Chem. Phys., 73, 5711 (1980), and references therein. [CrossRef] [7] K. Freed, Lecture Notes in Chemistry (Springer, Berlin, 1989), Vol. 52, p. 1, and references therein.[8] H. Nakano, R. Uchiyama, K. Hirao, J. Comput. Chem., 23, 1166(2002. [Medline] [CrossRef][9] M. J. Vilkas, K. Koc, Y. Ishikawa, Chem. Phys. Lett., 296, 68 (1998). [CrossRef] [10] R. K. Chaudhuri, K. F. Freed, J. Chem. Phys., 122, 204111 (2005) The four-component relativistic general multiconfigurational quasidegenerate perturbation theory (GMC-QDPT) and its applications to some atomic and molecular systems are reviewed. An efficient and accurate approximation to the relativistic GMC-QDPT is also presented. In the approximation, the terms including core to virtual excitations in the second-order effective Hamiltonian are replaced with those of the conventional quasidegenerate perturbation theory.The approximation form, which we call semi-approximate second-order form, is applied to some molecular systems.The computed excitation energies and potential energy curves were in good agreement with the original GMC-QDPT values as well as available experimental data.

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