Gaussian 03 Online ManualLast update: 2 October 2006 | |

## CASSCFThis
method keyword requests a Complete Active Space Multiconfiguration SCF (MC-SCF)
[97,98,137,138,195,405].
An MC-SCF calculation is a combination of an SCF computation with a full CI involving
a subset of the orbitals; this subset is known as the By
default, the active space is defined assuming that the electrons come from the
highest occupied orbitals in the initial guess determinant and that the remaining
orbitals required for the active space come from the lowest virtuals of the initial
guess. Thus, for a 4-electron, 6-orbital CAS—specified as Enough occupied orbitals from the guess to provide 4 electrons. Thus, the 2 highest occupied MOs would be included. Enough virtual orbitals to make a total of 6 orbitals. Since 2 occupied orbitals were included, the lowest 4 virtual orbitals would become part of the active space.
Similarly, a 4 electron, 6 orbital CAS on
a triplet would include the highest 3 occupied orbitals (one of which is doubly
occupied and two singly occupied in the guess determinant) and the lowest 3 virtual
orbitals. In Normally, By default, CASSCF
calculations use a direct algorithm to avoid disk storage of integrals. A conventional
algorithm may be selected by including
Use A brief overview of the CASSCF method is given
in chapter 9 (exercises 5 and 6) and appendix A of
## VARIATIONSAn MP2-level electron correlation correction to the CASSCF energy may be computed during a CASSCF calculation by specifying the **MP2**keyword in addition to**CASSCF**within the route section [101].Calculations on excited states of molecular systems may be requested using the **NRoot**option. Note that a value of 1 specifies the ground state, not the first excited state (in contrast to usage with the**CIS**keyword).State-averaged CASSCF calculations may be performed using the **StateAverage**and**NRoot**options to specify the states to be used.Conical intersections and avoided crossings may be computed by including **Opt=Conical**in the route section of a CASSCF job (see the examples) [165,166,167].-
Approximate spin orbit coupling between two spin states can be computed during CASSCF calculations by including the **SpinOrbit**option [250,251,252,253,254,413,414]. The method used in*Gaussian 03*is based on reference [254]. It is available for the elements H through Cl.
In order to compute the spin orbit coupling, the integrals are computed in a one-electron approximation involving relativistic terms, and then effective charges are used that scale the Z value for each atom to empirically account for 2 electron effects. This value can be specified for each atom via the molecule specification nuclear parameters list.
Finally, note that such calculations will be state-averaged by default. The Restricted Active Space variation (RASSCF) [103] is now supported [104]. It is selected via the **RAS**option. RASSCF calculations partition the molecular orbitals into five sections: the lowest lying occupieds (doubly occupied in all configurations), the RAS1 space of doubly occupied MOs, the RAS2 space containing the most important orbitals for the problem, the RAS3 space of weakly occupied MOs and the remaining unoccupied orbitals. Thus, the active space in CASSCF calculations is divided into three parts in a RAS calculations, and allowed configurations are defined by specifying the minimum number of electrons that must be present in the RAS1 space and the maximum number that may be in the RAS3 space, in addition to the total number of electrons in the three RAS spaces. See the discussion of the**RAS**option for the methods for specifying these values.
The full Jacobi diagonalization method must be used if quadratic
convergence is required (see the
The default diagonalization
method is most efficient if the size of the CI problem is greater than about 50,
or the user can identify one or more dominant components in the eigenvector from
the onset of the calculation, via the initial trail vector. By default, the starting
vector is initialized in The
Guess=Read.The UNO
guess must be used with caution. Often, some of the natural orbitals which have
modest occupation are not the important ones for the process of interest. Consequently,
unless the entire valence space is being correlated (which is usually prohibitively
expensive), one normally runs one job which does a UHF calculation with
Energies, analytic gradients, and analytic and numerical frequencies. CASSCF may not be combined with any semi-empirical method. Analytic polarizabilities may not
be performed with the CASSCF method. Use You
can restart a CASSCF calculation by specifying
We will consider several of the most important uses of the CASSCF method in this section.
# HF/3-21G Guess=Only Pop=Reg Test The molecule being investigated
is 1,3-cyclobutadiene, a singlet with D The HOMO is orbital 14; therefore, orbitals 13 through 16 will comprise the active space. When we examine these orbitals, we see that only orbitals 14 and 15 are of the correct type. The molecule lies in the YZ-plane, so π orbitals will have significantly non-zero coefficients in the X direction. Here are the relevant coefficients for orbitals 10 and 13-16: Molecular Orbital Coefficients 10 13 14 15 16 O O O V V 3 1 C 2PX 0.29536 0.00000 0.34716 0.37752 0.00000 7 3PX 0.16911 0.00000 0.21750 0.24339 0.00000 12 2 C 2PX 0.29536 0.00000 0.34716 -0.37752 0.00000 16 3PX 0.16911 0.00000 0.21750 -0.24339 0.00000 21 3 C 2PX 0.29536 0.00000 -0.34716 -0.37752 0.00000 25 3PX 0.16911 0.00000 -0.21750 -0.24339 0.00000 30 4 C 2PX 0.29536 0.00000 -0.34716 0.37752 0.00000 34 3PX 0.16911 0.00000 -0.21750 0.24339 0.00000 Orbital 10 is clearly also a π orbital. If we look at higher virtual
orbitals, we will find that orbital 19 is also a π orbital. We have found our
four necessary orbitals, and can now use # CASSCF(4,4)/3-21G Guess=Alter Pop=Reg Test 1,3-Cyclobutadiene Singlet, D2H, Pi 4x4 CAS 0 1 TOTAL -152.836259 The value of It is also important to examine the one-electron density matrix, which appears next in the output: Final one electron symbolic density matrix: 1 2 3 4 1 0.191842D+01 2 -0.139172D-05 0.182680D+01 3 0.345450D-05 0.130613D-05 0.172679D+00 4 0.327584D-06 0.415187D-05 0.564187D-06 0.820965D-01 MCSCF converged. The diagonal elements indicate the approximate occupancies for each successive orbital in the active space. If any of these values is (essentially) zero, then that orbital was empty throughout the calculation; similarly, if any of them is essentially 2, then that orbital was doubly occupied throughout the CAS. In either case, there were no excitations into or out of the orbital in question, and there is probably a problem with the CASSCF calculation. In our case, the two "occupied" orbitals have values less than 2, and the other two orbitals in the active space have non-zero occupancies, so things are fine.
MP2 correction to the MCSCF energy is computed The string
PRIMARY BASIS FUNCTION= 1 2 1 2 2 SYMMETRY TYPE = 0 1 3 1 2 3 SYMMETRY TYPE = 0 2 3 1 2 The first line indicates the electron assignments for the reference configuration. This is a 4x4 CAS, so the primary basis function output indicates that there is an α and b electron in both orbitals 13 and 14 (the numbers refer to the orbitals in the active space, from lowest to highest, and the electron order in the output is: α α β β). In configuration 2, the α electron in orbital 13 remains there, the α electron from orbital 14 has been excited to orbital 15, the β electron in orbital 13 remains there, as does the β electron in orbital 14. Similarly, in configuration 3, there is a β electron in orbital 13, an α (from 13) and β electron in orbital 14, and an α electron in orbital 15.
%chk=CAS1 # CASSCF(2,4) 6-31+G(D) Guess=(Read,Alter) Pop=NaturalOrbital Test Geom=Check Alter the guess so that the three LUMOs are all the desired symmetry, and run the CAS 0,1 The second job step uses the
FINAL EIGENVALUES AND EIGENVECTORS VECTOR EIGENVALUES CORRESPONDING EIGENVECTOR If the two eigenvalues (the first entry in the lines labelled with a state number) are essentially the same, then the energies of the two states are the same, and it is a conical intersection. Otherwise, it is an avoided crossing.
**************************** spin-orbit coupling program **************************** Number of configs= 4 1st state is 1 The
spin orbit coupling is broken down into X, Y, and Z components, followed by its
total magnitude, which in this case is 55.2016070 cm
# CAS(16,18,RASSCF(1,2,3,4)) 6-31G(d) If this molecule is a neutral singlet, then this route defines
the following spaces: RAS1 with 2 orbitals, 3 or 4 electrons in all configurations;
RAS2 with 12 orbitals, 12 electrons in the reference configuration; and RAS3 with
4 orbitals, 0-3 electrons in all configurations. Thus, the RAS2 space will have
9 to 13 electrons in all configurations. The orbitals taken from the reference
determinant for the active space are (assuming a spin singlet) the 8 highest occupieds
and 10 lowest virtuals: i.e., same orbitals as for a regular |