Description
The MPn method keywords request a Hartree-Fock calculation (by default, RHF for singlets, UHF for higher multiplicities) followed by a Møller-Plesset correlation energy correction [ Moller34 C. Møller and M. S. Plesset, “Note on an approximation treatment for many-electron systems,” Phys. Rev., 46 (1934) 0618-22. DOI: ]:
- MP2: The Møller-Plesset expansion is truncated at second-order [ Frisch90b M. J. Frisch, M. Head-Gordon, and J. A. Pople, “Direct MP2 gradient method,” Chem. Phys. Lett., 166 (1990) 275-80. DOI: , Frisch90c M. J. Frisch, M. Head-Gordon, and J. A. Pople, “Semi-direct algorithms for the MP2 energy and gradient,” Chem. Phys. Lett., 166 (1990) 281-89. DOI: , Head-Gordon88a M. Head-Gordon, J. A. Pople, and M. J. Frisch, “MP2 energy evaluation by direct methods,” Chem. Phys. Lett., 153 (1988) 503-06. DOI: , Saebo89 S. Saebø and J. Almlöf, “Avoiding the integral storage bottleneck in LCAO calculations of electron correlation,” Chem. Phys. Lett., 154 (1989) 83-89. DOI: , Head-Gordon94 M. Head-Gordon and T. Head-Gordon, “Analytic MP2 Frequencies Without Fifth Order Storage: Theory and Application to Bifurcated Hydrogen Bonds in the Water Hexamer,” Chem. Phys. Lett., 220 (1994) 122-28. DOI: ].
- MP3: Third-order MP theory correction [ Pople76 J. A. Pople, J. S. Binkley, and R. Seeger, “Theoretical Models Incorporating Electron Correlation,” Int. J. Quantum Chem., Suppl. Y-10 (1976) 1-19. DOI: , Pople77 J. A. Pople, R. Seeger, and R. Krishnan, “Variational Configuration Interaction Methods and Comparison with Perturbation Theory,” Int. J. Quantum Chem., Suppl. Y-11 (1977) 149-63. DOI: ].
- MP4: Fourth-order MP theory correction [ Raghavachari78 K. Raghavachari and J. A. Pople, “Approximate 4th-order perturbation-theory of electron correlation energy,” Int. J. Quantum Chem., 14 (1978) 91-100. DOI: ], which defaults to full MP4 with single, double, triple and quadruple substitutions [ Raghavachari78 K. Raghavachari and J. A. Pople, “Approximate 4th-order perturbation-theory of electron correlation energy,” Int. J. Quantum Chem., 14 (1978) 91-100. DOI: , Raghavachari80 K. Raghavachari, M. J. Frisch, and J. A. Pople, “Contribution of triple substitutions to the electron correlation energy in fourth-order perturbation theory,” J. Chem. Phys., 72 (1980) 4244-45. DOI: ] (MP4(SDTQ)).
- MP4(DQ): Include only the space of double and quadruple substitutions in the MP expansion.
- MP4(SDQ): Include only single, double and quadruple substitutions.
- MP5: Fifth-order MP theory correction [ Raghavachari90 K. Raghavachari, J. A. Pople, E. S. Replogle, and M. Head-Gordon, “Fifth Order Møller-Plesset Perturbation Theory: Comparison of Existing Correlation Methods and Implementation of New Methods Correct to Fifth Order,” J. Phys. Chem., 94 (1990) 5579-86. DOI: ]. The MP5 code has been written for the open-shell case only, and so specifying MP5 defaults to a UMP5 calculation. This method requires O3V3 disk storage and scales as O4V4 in cpu time.
Analytic gradients are available for MP2 [ Frisch90b M. J. Frisch, M. Head-Gordon, and J. A. Pople, “Direct MP2 gradient method,” Chem. Phys. Lett., 166 (1990) 275-80. DOI: , Frisch90c M. J. Frisch, M. Head-Gordon, and J. A. Pople, “Semi-direct algorithms for the MP2 energy and gradient,” Chem. Phys. Lett., 166 (1990) 281-89. DOI: , Pople79 J. A. Pople, K. Raghavachari, H. B. Schlegel, and J. S. Binkley, “Derivative Studies in Hartree-Fock and Møller-Plesset Theories,” Int. J. Quantum Chem., Quant. Chem. Symp., S13 (1979) 225-41. DOI: , Handy84 N. C. Handy and H. F. Schaefer III, “On the evaluation of analytic energy derivatives for correlated wave-functions,” J. Chem. Phys., 81 (1984) 5031-33. DOI: ], MP3 and MP4(SDQ) [ Trucks88 G. W. Trucks, J. D. Watts, E. A. Salter, and R. J. Bartlett, “Analytical MBPT(4) Gradients,” Chem. Phys. Lett., 153 (1988) 490-95. DOI: , Trucks88a G. W. Trucks, E. A. Salter, C. Sosa, and R. J. Bartlett, “Theory and Implementation of the MBPT Density Matrix: An Application to One-Electron Properties,” Chem. Phys. Lett., 147 (1988) 359-66. DOI: ], and analytic frequencies are available for MP2 [ Head-Gordon94 M. Head-Gordon and T. Head-Gordon, “Analytic MP2 Frequencies Without Fifth Order Storage: Theory and Application to Bifurcated Hydrogen Bonds in the Water Hexamer,” Chem. Phys. Lett., 220 (1994) 122-28. DOI: ]. ROMP2, ROMP3 and ROMP4 energies are also available [ Knowles91 P. J. Knowles, J. S. Andrews, R. D. Amos, N. C. Handy, and J. A. Pople, “Restricted Møller-Plesset theory for open shell molecules,” Chem. Phys. Lett., 186 (1991) 130-36. DOI: , Lauderdale91 W. J. Lauderdale, J. F. Stanton, J. Gauss, J. D. Watts, and R. J. Bartlett, “Many-body perturbation theory with a restricted open-shell Hartree-Fock reference,” Chem. Phys. Lett., 187 (1991). DOI: , Lauderdale92 W. J. Lauderdale, J. F. Stanton, J. Gauss, J. D. Watts, and R. J. Bartlett, “Restricted open-shell Hartree-Fock based many-body perturbation theory: Theory and application of energy and gradient calculations,” J. Chem. Phys., 97 (1992). DOI: ].
Double-Hybrid Methods
Gaussian 16 also includes some double hybrid methods that combine exact HF exchange with an MP2-like correlation to a DFT calculation. These methods have the same computational cost as MP2 (rather than that of DFT). Gaussian 16 includes:
- Grimme’s B2PLYP [ Grimme06a S. Grimme, “Semiempirical hybrid density functional with perturbative second-order correlation,” J. Chem. Phys., 124 (2006) 034108. DOI: ] and mPW2PLYP [ Schwabe06 T. Schwabe and S. Grimme, “Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects,” Phys. Chem. Chem. Phys., 8 (2006) 4398. DOI: ] methods; the empirical dispersion corrected variations are specified by appending a D to the keyword name: e.g., B2PLYPD for B2PLYP with empirical dispersion [ Schwabe07 T. Schwabe and S. Grimme, “Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability,” Phys. Chem. Chem. Phys., 9 (2007) 3397. DOI: ].
- B2PLYPD3 requests the B2PLYP method combined with Grimme’s D3BJ dispersion [ Grimme11 S. Grimme, S. Ehrlich and L. Goerigk, “Effect of the damping function in dispersion corrected density functional theory,” J. Comp. Chem. 32 (2011) 1456-65. DOI: , Goerigk11 L. Goerigk and S. Grimme, “Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals—Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions,” J. Chem. Theory Comput., 7 (2011) 291-309. DOI: ].
- DSDPBEP86[ Kozuch11 S. Kozuch and J. M. L. Martin, “DSD-PBEP86: In search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections,” Phys. Chem. Chem. Phys., 2011, 13, 20104–20107, DOI: , Kozuch13 Kozuch, Sebastian; Martin, Jan M.L. “Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory&rdqui J. Comp. Chem., 34 (2013) pp 2327–2344. DOI: ], a dispersion-corrected double hybrid functional with Grimme’s D3BJ dispersion.
- The PBE0DH [ Bremond11 É. Brémond and C. Adamo, “Seeking for parameter-free double-hybrid functionals: The PBE0-DH model,” The Journal of Chemical Physics, 2011, 135, 024106. DOI: ] and PBEQIDH [ Bremond14 É. Brémond, J. C. Sancho-García, Á. J. Pérez-Jiménez and C. Adamo, “Communication: Double-hybrid functionals from adiabatic-connection: The QIDH model,” J. Chem. Phys., 2014, 141, 031101. DOI: ] double-hybrid functionals.
オプション
Options
Frozen Core Options
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the discussion of the FC options for full information.
Algorithm Selection Options for MP2 and Double Hybrid Methods
The appropriate algorithm for MP2 will be selected automatically based on the settings of %Mem and MaxDisk. Thus, the following options are almost never needed.
FullDirect
Forces the fully direct algorithm, which requires no external storage beyond that for the SCF. Requires a minimum of 2OVN words of main memory (O=number of occupied orbitals, V=number of virtual orbitals, N=number of basis functions). This is seldom a good choice, except for machines with very large main memory and limited disk.
TWInCore
Whether to store amplitudes and products in memory during higher-order post-SCF calculations. The default is to store these if possible, but to run off disk if memory is insufficient. TWInCore causes the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory storage.
SemiDirect
Forces the semi-direct algorithm.
Direct
Requests some sort of direct algorithm. The choice between in-core, fully direct and semidirect is made by the program based on memory and disk limits and the dimensions of the problem.
InCore
Forces the in-memory algorithm. This is very fast when it can be used, but requires N4/4 words of memory. It is normally used in conjunction with SCF=InCore. NoInCore prevents the use of the in-core algorithm.
適用範囲
Availability
MP2, B2PLYP methods, mPW2PLYP methods: Energies, analytic gradients, and analytic frequencies.
MP3, MP4(DQ) and MP4(SDQ): Energies, analytic gradients, and numerical frequencies.
MP4(SDTQ) and MP5: Analytic energies, numerical gradients, and numerical frequencies.
RO may be combined with MP2, MP3 and MP4 for energies only.
関連キーワード
Related Keywords
実例
Examples
The MP2 energy appears in the output as follows, labeled as EUMP2:
E2= -.3906492545D-01 EUMP2= -.75003727493390D+02
Here is the output from an MP4(SDTQ) calculation:
Time for triples= .04 seconds.
MP4(T)= -.55601167D-04
E3= -.10847902D-01 EUMP3= -.75014575395D+02
E4(DQ)= -.32068082D-02 UMP4(DQ)= -.75017782203D+02
E4(SDQ)= -.33238377D-02 UMP4(SDQ)= -.75017899233D+02
E4(SDTQ)= -.33794389D-02 UMP4(SDTQ)= -.75017954834D+02
The energy labeled EUMP3 is the MP3 energy, and the various MP4-level corrections appear after it, with the MP4(SDTQ) value coming in the final line.
The B2PLYP energy appears as follows in the output:
E2(B2PLYP) = -0.3262340664D-01 E(B2PLYP) = -0.39113226645200D+02