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.
Similar content being viewed by others
References
Møller C, Plesset MS. Note on an approximation treatment for many-electron systems. Phys Rev, 1934, 46: 618–622
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
Schlegel HB. Potential energy curves using unrestricted Møller-Plesset perturbation theory with spin annihilation. J Chem Phys, 1986, 84: 4530–4534
Roothaan CC. Self-consistent field theory for open-shells of electronic systems. Rev Mod Phys, 1960, 32: 179–185
Hubač I, Čársky P. Correlation energy of open-shell systems. Phys Rev A, 1980, 22: 2392–2399
Amos RD, Andrews JS, Handy NC, Knowles PJ. Open-shell Møller-Plesset perturbation theory. Chem Phys Lett, 1991, 185: 256–264
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
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
Murray C, Davidson ER. Perturbation theory for open shell systems. Chem Phys Lett, 1991, 187: 451–454
Jayatilaka D, Lee TJ. The forms of spin orbitals for open-shell restricted Hartree-Fock reference functions. Chem Phys Lett, 1992, 199: 211–219
Lee TJ, Jayatilaka D. An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals. Chem Phys Lett, 1993, 201: 1–10
Kozlowski PM, Davidson ER. Construction of open shell perturbation theory invariant with respect to orbital degeneracy. Chem Phys Lett, 1994, 226: 440–446
Davidson ER. Construction of open shell perturbation theory. Chem Phys Lett, 1995, 241: 432–437
Murray CW, Handy NC. Comparison and assessment of different forms of open-shell perturbation theory. J Chem Phys, 1992, 97: 6509–6516
Lee TJ, Rendell AP, Dyall KG, Jayatilaka D. Open-shell restricted Hartree-Fock perturbation theory. J Chem Phys, 1994, 100: 7400–7409
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
Wheeler SE, Allen WD, Schaefer III HF. On the convergence of Z-averaged perturbation theory. J Chem Phys, 2008, 128: 074107
Chen F. A single reference perturbation theory beyond the Møller-Plesset partition. J Chem Theory Comput, 2009, 5, 931–936
Chen F, Davidson ER, Iwata S. New time-independent perturbation theory for the multireference problem. Int J Quantum Chem, 2002, 86: 256–264
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
Chen F. Numerical study on the size consistency of the multireference perturbation theory. Acta Phys-Chim Sin, 2007, 23: 1360–1364
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
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
Roos BO, Andersson K. Multiconfigurational perturbation theory with level shift. Chem Phys Lett, 1995, 245: 215–223
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
Werner H-J. Third-order multireference perturbation theory: The CASPT3 method. Mol Phys, 1996, 89: 645–661
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
Chen F. Computational Methods in Quantum Chemistry. Beijing: Science Press, 2008. 149–173
Szabo A, Ostlund NS. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. New York: Macmillan, 1982. 320–379
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
Yang CL, Zhang ZH, Ren TQ. Ab initio study of lutetium dimer. J Chem Phys, 2002, 116: 6656–6659
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
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
Huber KP, Herzberg G. Molecular Spectra and Molecular Structure IV: Constants of Diatomic Molecules. New York: Van Nostrand Reinhold, 1979
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
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
Hariharan PC, Pople JA. The influence of polarization functions on molecular orbital hydrogenation energies. Theor Chim Acta, 1973, 28: 213–222
Becke AD. Density-functional thermochemistry. J Chem Phys, 1993, 98: 5648–5652
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
Langhoff SR, Davidson ER. Configuration interaction calculations on the nitrogen molecule. Int J Quantum Chem, 1974, 8: 61–72
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11426-010-4199-1