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MP Methods

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]:

  • MP2: The Møller-Plesset expansion is truncated at second-order [Frisch90b, Frisch90c, Head-Gordon88a, Saebo89, Head-Gordon94].
  • MP3: Third-order MP theory correction [Pople76, Pople77].
  • MP4: Fourth-order MP theory correction [Raghavachari78], which defaults to full MP4 with single, double, triple and quadruple substitutions [Raghavachari78, Raghavachari80] (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]. 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, Frisch90c, Pople79, Handy84], MP3 and MP4(SDQ) [Trucks88, Trucks88a], and analytic frequencies are available for MP2 [Head-Gordon94]. ROMP2, ROMP3 and ROMP4 energies are also available [Knowles91, Lauderdale91, Lauderdale92].

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] and mPW2PLYP [Schwabe06] 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].
  • B2PLYPD3 requests the B2PLYP method combined with Grimme’s D3BJ dispersion [Grimme11, Goerigk11].
  • DSDPBEP86 [Kozuch11], a dispersion-corrected double hybrid functional.
  • The PBE0DH [Bremond11] and PBEQIDH [Bremond14] double-hybrid functionals.

Frozen Core Options


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.


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.


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.


Forces the semi-direct algorithm.


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.


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.

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.

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

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