This method keyword requests a perfect-pairing General Valence Bond (GVB-PP) calculation. GVB requires one parameter: the number of perfect-pairing pairs to split; for example:GVB(4). This parameter may also be specified with theNPairoption. The natural orbitals for the GVB pairs are taken from occupied and virtual orbitals of the initial guess determinant (described below).
Normally most of the difficult input for a GVB-PP calculation involves specifying the initial guess (Link 401). This often includes alteration of orbitals to ensure the correct identification of high-spin, perfect-pairing, and closed-shell orbitals and possible reduction of SCF symmetry to account for the localized orbitals which usually represent the lowest energy solution for GVB-PP.
The GVB program reads the number of orbitals in each GVB pair (in format 40I2). The number of lines read is fixed (and normally 1), so no terminating blank line is needed. For a molecule having spin multiplicity S, N GVB pairs, andn1, …,nNorbitals in each pair, orbitals from the initial guess are used in the following manner by the GVB program:
The S-1 highest occupied orbitals in the initial guess, which would have been singly occupied in an ROHF calculation, become high-spin orbitals.
The next lowerNoccupied orbitals, which would have been doubly occupied in an ROHF calculation, become the first natural orbitals of the GVB pairs.
Any remaining orbitals occupied in the guess stay closed-shell.
The lowestn1-1 virtual orbitals become natural orbitals 2 throughn1of the first GVB pair, then the nextn2-1 orbitals are assigned to pair 2, and so on. The GVB-PP scheme does not allow an orbital to be shared by more than one GVB pair.
Any remaining (virtual) orbitals from the initial guess become virtual orbitals in the GVB calculation.
GenerallyGuess=Alteris required to ensure that guess occupied orbitals, which will be used as first natural orbitals, match up with the correct guess virtual orbitals which will become the corresponding higher natural orbitals. Often it is helpful to start off withGuess=(Local,Only), examine the orbitals to determine alteration requirements, then doGuess=(Local,Alter)andGVB(NPair=N,Freeze)to allow the higher natural orbitals to become more appropriate. Finally the full calculation can be run withGuess=Readand all orbitals optimized in the GVB. If there is any confusion or concern with the orbitals breaking symmetry, the calculation should be done withSymm=NoSCFand initially withGuess=Local. In fact, this approach is generally recommended except for those very expert users.
If the number of orbitals in a pair is negative, the root of the CI to use for that pair and the pair’s initial GVB coefficients are read in format (I2,5D15.8). This is useful if a1Σor1Δ state is being represented as a GVB pair of the form x2± y2.
NPair
Gives the number of perfect-pairing pairs.GVB(N)is equivalent toGVB(NPair=N).NPair=0is acceptable and results in a closed-shell or spin-restricted SCF calculation.
InHam=N
Read inNHamiltonians (Fock operators, sets of coupling coefficients). This option may be combined with perfect-pairing pairs. Each Hamiltonian is read using the following syntax (format in parentheses):
| NO | # of orbitals in current Hamiltonian(I5) | |
| Fj | Occup. # (1.0=closed-shell)(D15.8) | |
| (AJ(I), I =1,NHam) | J coefficients(5D15.8) | |
| (AK(I), I =1,NHam) | K coefficients(5D15.8) |
OSS
Do a two electron, two orthogonal orbital open-shell singlet. This option may be combined with perfect-pairing pairs.OpenShellSingletis a synonym forOSS.
Freeze
Freeze closed-shell and open-shell orbitals, and first natural orbitals of GVB pairs, allowing only 2nd and higher orbitals to vary. This option is useful for starting off difficult wavefunctions.
Energies, analytic gradients, and numerical frequencies.
Here is a GVB(3/6) calculation performed on singlet methylene:
# GVB(3)/6-31G(d) Pop=Full Test Guess=(Local,LowSym,Alter) GVB(3) on CH2molecule specification1 4 0 2 3 9Guess=LowSym input2,3Guess=Alter input2 2 2GVB input
Each of the 3 valence electron pairs is split into a GVB pair. A preliminaryGuess=Onlycalculation was performed to determine the localized orbitals and which alterations would be required.
The perfect pairing GVB method includes the effects ofintra-pair correlation but not those ofinter-pair correlation. Consequently, GVB electrons pairs tend to be localized. In the case of singlet methylene, the carbon lone pair is localized even at the Hartree-Fock level. The canonical Hartree-Fock orbitals for the C-H bonds are delocalized into linear combinations (C-H1+ C-H2) and (C-H1- C-H2) having A1and B2symmetry, respectively. In order to allow the localization in the guess to produce separate bond pairs, these two irreducible representations must be combined. Similarly, the GVB calculation itself must be told not to impose the full molecular symmetry on the orbitals, which would force them to be delocalized. Combining the A1and B2representations and combining the A2and B1representations causes the calculation to impose only Cssymmetry on the individual orbitals, allowing separate GVB pairs for each bond. Since the resulting pairs for each bond will be equivalent, the resulting overall wavefunction and density will still have C2vsymmetry.
TheGuess=LowSymkeyword specifies that the irreducible representations of the molecular point group will be combined in the symmetry information used in a GVB calculation. It takes a single line of input consisting of giving the numbers of the irreducible representations to combine, where the numbers correspond to the order in which the representations are listed in the output file (they appear just after the standard orientation). For example, here is the output for a molecule with C2vsymmetry:
There are 4 symmetry adapted basis functions of A1 symmetry. There are 0 symmetry adapted basis functions of A2 symmetry. There are 1 symmetry adapted basis functions of B1 symmetry. There are 2 symmetry adapted basis functions of B2 symmetry.
Thus for C2vsymmetry, the order is A1, A2, B1, B2, referred to in theGuess=LowSyminput as 1 through 4, respectively. A zero separates groups of representations to be combined, and a nine ends the list. Thus, to combine A1 with B2 and A2 with B1, thereby lowering the SCF symmetry to Cs, the appropriate input line is:
1 4 0 2 3 9
Since this information always requires exactly one line, no blank line terminates this section.
The order of orbitals generated after localization by the initial guess in the first job step was C-1s C-H1C-H2C-2s for the occupied orbitals, and C-2p C-H1* C-H2* for the lowest virtual orbitals. Hence if no orbitals are interchanged, the C-2s lone pair would be correctly paired with the unoccupied p-orbital, but then the next lower occupied, C-H2, would be paired with the next higher virtual, C-H1*. So either the two bond occupied orbitals or the two bond virtual orbitals must be exchanged to match up the orbitals properly.
Finally, the one line of input to the GVB code indicates that there are 2 natural orbitals in each of the 3 GVB pairs.
Last update: 23 April 2013