MP2 through MP5 Keywords
Last Update: 12/31/2000

These method keywords request a Hartree-Fock calculation (RHF for singlets, UHF for higher multiplicities) followed by a Møller-Plesset correlation energy correction [47], truncated at second-order for MP2 [19,20, 21,23- 24,52], third order for MP3 [ 48,53], fourth-order for MP4 [49], and fifth-order for MP5 [51]. Analytic gradients are available for MP2 [20-21, 91-92], MP3 and MP4(SDQ) [ 93-94], and analytic frequencies are available for MP2 [23-24].

There are four basic algorithms for MP2 calculations and for producing transformed (MO) integrals on disk:

• Semi-Direct, which uses both main memory and external (disk) storage as available [ 21]. This is the default algorithm.

• Direct, which uses no external storage by recomputing the integrals as needed during the transformation.

• Conventional, which stores the transformed integrals on disk. This was the only method available in Gaussian 88, and the only method for generating MO integrals on disk in Gaussian 90. It is seldom a good choice on any but the smallest computer systems.

• In-core, in which all the AO integrals are generated and stored in main memory, then used without storing them externally.

The default is to decide between the in-core, direct, and semi-direct algorithms based on available memory and disk. The available disk can be specified via the MaxDisk keyword, either in the route section or (preferably) in the Default.Rou file (see chapter 6).

Note that selection of the direct or semi-direct MP2 and transformation algorithms is separate from selecting direct SCF (which is the default SCF algorithm in Gaussian 98). The E⁽²⁾ calculation or transformation then recomputes integrals as needed in the form required for vectorization.

MP4(DQ) is specified to use only the space of double and quadruple substitutions, MP4(SDQ) for single, double and quadruple substitutions, or MP4(SDTQ) for full MP4 with single, double, triple and quadruple substitutions [49-50]. Just specifying MP4 defaults to MP4(SDTQ).

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.

FC
This indicates "frozen-core," and it implies that inner-shells are excluded from the correlation calculation. This is the default calculation mode. Note that FC, Full, and RW and Window are mutually exclusive.

Full
This implies that all electrons are included in a correlation calculation.

RW
The "read window" option means that specific information about which orbitals are retained in the post-SCF calculation will be given in the input file. The additional input section consists of a line specifying the starting and ending orbitals to be retained, followed by a blank line. A value of zero indicates the first or last orbital, depending on where it is used. If the value for the first orbital is negative (-m), then the highest m orbitals are retained; the value for the last orbital is negative (-n), then the highest n orbitals are frozen. If m is positive and n is omitted, n defaults to 0. If m is negative and n is omitted, then the highest |m| occupied and lowest |m| virtual orbitals are retained.

Here are some examples for a calculation on C_⁴H_⁴:

0,0
Equivalent to Full.

5,0
Freezes the 4 core orbitals and keeps all virtual orbitals (equivalent to FC if the basis has a single zeta core).

5,-4
Freezes the four core orbitals and the highest four virtual orbitals. This is the appropriate frozen-core for a basis with a double-zeta core.

6,22
Retains orbitals 6 through 22 in the post-SCF. For example, since C₄H₄ has 28 electrons, if this is a closed shell calculation, there will be 14 occupied orbitals, 5 of which will be frozen, so the post-SCF calculation will involve 9 occupied orbitals (6-14) and 8 virtual orbitals (15-22).

-6
Retains orbitals 9 through 20.

ReadWindow
Is a synonym for RW.

Window=(m[,n])
Performs the same function as the ReadWindow option, but takes its input as parameters in the route section rather than from the input stream.

Note: CASSCF MP2 calculations use a different mechanism for specifying the frozen orbitals (see the NFC and NFV options to the CASSCF keyword).

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.

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.

Stingy
Compute MP2 frequencies in Stingy mode, trading CPU time for disk in intermediate results. Up to MaxDisk disk is still used, but the number of passes may be reduced (in Link 811). This is the default calculation mode. NoStingy says to do the integral transformation once rather than twice, at the expense of additional disk usage.

VeryStingy
Compute the MP2 frequencies using the minimum possible disk space. This option is designed only for very unusual environments where overall performance on multiple simultaneous Gaussian jobs is far more important than the efficiency of the MP2 frequency calculation.

MP2: Energies, analytic gradients, and analytic frequencies. MP3, MP4(SD) and MP4(SDQ): Energies, analytic gradients, and numerical frequencies. MP4(SDTQ) and MP5: Analytic energies, numerical gradients, and numerical frequencies.

HF Keyword, SCF, Transformation, MaxDisk

Energies. The MP2 energy appears in the output as follows, labeled as EUMP2:

 E2=        -.3906492545D-01 EUMP2=        -.75003727493390D+02

Energies for higher-order Møller-Plesset methods follow. 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 labelled EUMP3 is the MP3 energy, and the various MP4-level corrections appear after it, with the MP4(SDTQ) output coming in the final line (labeled UMP4(SDTQ)).

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