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On the performance of the open-shell perturbation theory

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Abstract

A few open-shell molecules are taken as examples in order to examine the performance of the open-shell perturbation theory for electron correlation (J Chem Theory Comput, 2009, 5: 931–936). The convergence of the perturbation series is shown to be stable for the doublet state of NH2 at both the equilibrium and stretched geometries. The equilibrium bond lengths, and harmonic and anharmonic vibrational frequencies are calculated for NO(X 2Π), OH(X 2Π), CH(X 2Π) and NH(X 2Σ) with different second-order perturbation theories at the cc-pVDZ, cc-pVTZ and cc-pVQZ levels. The ground state energies of BeF(X 2Σ+), MgH(X 2Σ+) and the HCCl triplet state have also been computed with various perturbation theories and compared with configuration interaction with single and double excitations (CISD) and CISD + Davidson correction. The energy difference between the formaldehyde (H2CO+) and hydroxymethylene (HCOH+) radical cations has been computed. Our perturbation theory predicts correctly that H2CO+ is more stable than HCOH+. However, calculations using UMP2, CASPT2, the Z-averaged perturbation theory and restricted Møller-Plesset theory fail even to produce the correct sign of the energy difference.

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References

  1. Møller C, Plesset MS. Note on an approximation treatment for many-electron systems. Phys Rev, 1934, 46: 618–622

    Article  Google Scholar 

  2. Gill P MW, Pople JA, Radom L, Nobes RH. Why does unrestricted Møller-Plesset perturbation theory converge so slowly for spin-contaminated wave functions? J Chem Phys, 1988, 89: 7307–7314

    Article  CAS  Google Scholar 

  3. Schlegel HB. Potential energy curves using unrestricted Møller-Plesset perturbation theory with spin annihilation. J Chem Phys, 1986, 84: 4530–4534

    Article  CAS  Google Scholar 

  4. Roothaan CC. Self-consistent field theory for open-shells of electronic systems. Rev Mod Phys, 1960, 32: 179–185

    Article  Google Scholar 

  5. Hubač I, Čársky P. Correlation energy of open-shell systems. Phys Rev A, 1980, 22: 2392–2399

    Article  Google Scholar 

  6. Amos RD, Andrews JS, Handy NC, Knowles PJ. Open-shell Møller-Plesset perturbation theory. Chem Phys Lett, 1991, 185: 256–264

    Article  CAS  Google Scholar 

  7. Knowles PJ, Andrews JS, Amos RD, Handy NC, Pople JA. Restricted Møller-Plesset theory for open-shell molecules. Chem Phys Lett, 1991, 186: 130–136

    Article  CAS  Google Scholar 

  8. Lauderdale WJ, Stanton JF, Gauss J, Watts JD, Bartlett RJ. Many-body perturbation theory with a restricted open-shell Hartree-Fock reference. Chem Phys Lett, 1991, 187: 21–28

    Article  CAS  Google Scholar 

  9. Murray C, Davidson ER. Perturbation theory for open shell systems. Chem Phys Lett, 1991, 187: 451–454

    Article  CAS  Google Scholar 

  10. Jayatilaka D, Lee TJ. The forms of spin orbitals for open-shell restricted Hartree-Fock reference functions. Chem Phys Lett, 1992, 199: 211–219

    Article  CAS  Google Scholar 

  11. Lee TJ, Jayatilaka D. An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals. Chem Phys Lett, 1993, 201: 1–10

    Article  CAS  Google Scholar 

  12. Kozlowski PM, Davidson ER. Construction of open shell perturbation theory invariant with respect to orbital degeneracy. Chem Phys Lett, 1994, 226: 440–446

    Article  CAS  Google Scholar 

  13. Davidson ER. Construction of open shell perturbation theory. Chem Phys Lett, 1995, 241: 432–437

    Article  CAS  Google Scholar 

  14. Murray CW, Handy NC. Comparison and assessment of different forms of open-shell perturbation theory. J Chem Phys, 1992, 97: 6509–6516

    Article  CAS  Google Scholar 

  15. Lee TJ, Rendell AP, Dyall KG, Jayatilaka D. Open-shell restricted Hartree-Fock perturbation theory. J Chem Phys, 1994, 100: 7400–7409

    Article  CAS  Google Scholar 

  16. Davidson ER, Jarzecki AA. Multi-reference perturbation theory. In: Hirao K. ed. Recent Advances in Computational Chemistry. Vol 4. Singapore: World Scientific, 1999. 31–36

    Google Scholar 

  17. Wheeler SE, Allen WD, Schaefer III HF. On the convergence of Z-averaged perturbation theory. J Chem Phys, 2008, 128: 074107

    Article  CAS  Google Scholar 

  18. Chen F. A single reference perturbation theory beyond the Møller-Plesset partition. J Chem Theory Comput, 2009, 5, 931–936

    Google Scholar 

  19. Chen F, Davidson ER, Iwata S. New time-independent perturbation theory for the multireference problem. Int J Quantum Chem, 2002, 86: 256–264

    Article  CAS  Google Scholar 

  20. Chen F. Theoretical study on the size consistency of the second and third order energies of the multireference perturbation theory. Sci China Ser B-Chem, 2007, 50: 483–487

    Article  CAS  Google Scholar 

  21. Chen F. Numerical study on the size consistency of the multireference perturbation theory. Acta Phys-Chim Sin, 2007, 23: 1360–1364

    Article  CAS  Google Scholar 

  22. Ma NL, Smith BJ, Radom L. The energy difference between formaldehyde and hydroxymethylene radical cations: Failure of unrestricted (UMP2) and restricted (RMP2) Møller-Plesset procedures. Chem Phys Lett, 1992, 193: 386–394

    Article  CAS  Google Scholar 

  23. Andersson K, Malmqvist P-A, Roos BO. Second-order perturbation theory with a complete active space self-consistent field reference function. J Chem Phys, 1992, 96, 1218-1226

    Google Scholar 

  24. Roos BO, Andersson K. Multiconfigurational perturbation theory with level shift. Chem Phys Lett, 1995, 245: 215–223

    Article  CAS  Google Scholar 

  25. Andersson K. Different forms of the zeroth-order Hamiltonian in second-order perturbation theory with a complete active space self-consistent field reference function. Theor Chim Acta, 1995, 91: 31–46

    Article  CAS  Google Scholar 

  26. Werner H-J. Third-order multireference perturbation theory: The CASPT3 method. Mol Phys, 1996, 89: 645–661

    Article  CAS  Google Scholar 

  27. Celani P, Werner H-J. Multireference perturbation theory for large restricted and selected active space reference wave functions. J Chem Phys, 2000, 112: 5546–5557

    Article  CAS  Google Scholar 

  28. Chen F. Computational Methods in Quantum Chemistry. Beijing: Science Press, 2008. 149–173

    Google Scholar 

  29. Szabo A, Ostlund NS. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. New York: Macmillan, 1982. 320–379

    Google Scholar 

  30. Murrell JN, Sorbie KS. New analytic form for the potential energy curves of stable diatomic states. J Chem Soc Faraday Trans, 1974, 270: 1552–1556

    Article  Google Scholar 

  31. Yang CL, Zhang ZH, Ren TQ. Ab initio study of lutetium dimer. J Chem Phys, 2002, 116: 6656–6659

    Article  CAS  Google Scholar 

  32. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Natsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA. General atomic and molecular electronic structure system. J Comput Chem, 1993, 14: 1347–1363

    Article  CAS  Google Scholar 

  33. Dunning TH. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys, 1989, 90: 1007–1023

    Article  CAS  Google Scholar 

  34. Huber KP, Herzberg G. Molecular Spectra and Molecular Structure IV: Constants of Diatomic Molecules. New York: Van Nostrand Reinhold, 1979

    Book  Google Scholar 

  35. Werner, H-J, Knowles PJ, Lindh R, Manby FR, Schütz M, Celani P, Korona T, Mitrushenkov A, Rauhut G, Adler TB, Amos RD, Bernhardsson A, Berning A, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Goll E, Hampel C, Hetzer G, Hrenar T, Knizia G, Köppl C, Liu Y, Lloyd AW, Mata RA, May AJ, McNicholas SJ, Meyer W, Mura ME, Nicklass A, Palmieri P, Pflüger K, Pitzer R, Reiher M, Schumann U, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Wang M, Wolf A. MOLPRO, version 2009.1, A package of ab initio programs. See http://www.molpro.net

  36. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck, AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA. Gaussian 03W, Revision D.01. Wallingford, CT: Gaussian, Inc., 2004

    Google Scholar 

  37. Hariharan PC, Pople JA. The influence of polarization functions on molecular orbital hydrogenation energies. Theor Chim Acta, 1973, 28: 213–222

    Article  CAS  Google Scholar 

  38. Becke AD. Density-functional thermochemistry. J Chem Phys, 1993, 98: 5648–5652

    Article  CAS  Google Scholar 

  39. Lee CT, Yang WT, Parr RG. Development of the Colle-Salvetti correlation energy formula into a functional of the electron density. Phys Rev B, 1988, 37: 785–789

    Article  CAS  Google Scholar 

  40. Langhoff SR, Davidson ER. Configuration interaction calculations on the nitrogen molecule. Int J Quantum Chem, 1974, 8: 61–72

    Article  CAS  Google Scholar 

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Chen, F., Wei, M. & Liu, W. On the performance of the open-shell perturbation theory. Sci. China Chem. 54, 446–453 (2011). https://doi.org/10.1007/s11426-010-4199-1

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