The simplest ab initio calculations possible use the Hartree-Fock (HF) Self-Consistent Field (SCF) method having the program name SCF in the MOLCAS suite. It is possible to calculate the HF energy once we have calculated the integrals using the SEWARD module, although MOLCAS can perform a direct SCF calculation in which the two-electron integrals are not stored on disk. The MOLCAS implementation performs a closed-shell (all electrons are paired in orbitals) calculation. It is not possible to perform an Open-shell Hartree-Fock (ROHF). calculation with the SEWARD. The SCF input for a Hartree-Fock calculation of a water molecule is given in figure 3.2 which continues our calculations on the water molecule.
The first keyword used is TITLe. As with the SEWARD program, the lines following the keyword up to, but not including, the next keyword are printed in the output of SCF and can be as verbose as required (up to ten lines).
The only compulsory keyword for SCF is OCCUpied
which specifies the number of occupied orbitals in each symmetry grouping
listed in the SEWARD output and given in
Figure 3.2. The basis label and type give an
impression of the possible molecular orbital that will be obtained in
the SCF calculation. For example, the first basis function in the 
irreducible representation is an 
type on the oxygen indicating the
oxygen 1 orbital. Note, also, that the fourth basis function is centered on
the hydrogens, has an type and is symmetric on both hydrogens as
indicated by both hydrogens having a phase of 1, unlike the sixth basis function
which has a phase of 1 on center 2 (input H1) and -1 on center 3
(generated H1).
Figure 3.2. Sample input requesting the SCF module to
calculate the ground Hartree-Fock energy for a neutral water molecule
in C
symmetry.
&SCF &END Title Water - A Tutorial The SCF energy of water is calculated using C2v symmetry Occupied 3 1 0 1 OccNumbers 2.0 2.0 2.0 2.0 2.0 IVO End of Input
Figure 3.2. Symmetry adapted Basis Functions from a SEWARD output.
Irreducible representation : a1
Basis function(s) of irrep: z
Basis Label Type Center Phase
1 O1 1s0 1 1
2 O1 1s0 1 1
3 O1 2p0 1 1
4 H1 1s0 2 1 3 1
Irreducible representation : b1
Basis function(s) of irrep: x, xz, Ry
Basis Label Type Center Phase
5 O1 2p1+ 1 1
6 H1 1s0 2 1 3 -1
Irreducible representation : b2
Basis function(s) of irrep: y, yz, Rx
Basis Label Type Center Phase
7 O1 2p1- 1 1
We have ten electrons to ascribe to five orbitals to describe a neutral water molecule in the ground state. Several techniques exist for correct allocation of electrons. As a test of the electron allocation, the energy obtained should be the same with and without symmetry. Water is a simple case, more so when using the minimal basis set. In this case, the third irreducible representation is not listed in the SEWARD output as there are no basis functions in that representation. That is why the third number after the OCCUpied keyword is zero. Keyword AUFBau can be of great help in difficult cases but it must be used with caution because the right result is not always guaranteed.
The next keyword, OCCNumbers, is not required in this case as the default occupation for each orbital is 2.0. It is useful for defining open-shell systems for later calculation by the RASSCF and other modules. Any number between 0.0 and 2.0 can be specified for any number of orbitals. An example input containing partially filled orbitals can be seen on section 4.1.1. The program will perform a calculation with ``fractionally" occupied closed shells. Such a calculation is without physical meaning (except in the true closed shell case), but may be used to produce improved starting orbitals for other program modules of MOLCAS. The occupations for each representation are grouped linewise for clarity. Note that we have used the option IVO. This it is not advisable when you use a positively charged moeity to generate starting orbitals, since it will generally generate too compact valence orbitals.
Performing the Hartree-Fock calculation introduces some important aspects of the transfer of data between the MOLCAS program modules. Recall that the SEWARD module produces two integral files symbolically linked to ONEINT and ORDINT and actually called, in our case, water.OneInt and water.OrdInt, respectively. The simplest procedure to ensure that the SCF module uses the integral files is to insert a line in the shell script in Figure 3.1 immediately after the molcas run seward command requesting the SCF module. Because the two integral files are present in the working directory when the SCF module is performed, MOLCAS automatically links them to the symbolic names. The SCF input can either be included in the same file as the SEWARD input or in a separate file.
If the integral files were not deleted in a previous calculation (using the rm -r $WorkDir command in Figure 3.1) then the SEWARD calculation need not be repeated. Furthermore, integral files need not be in the working directory if they are linked by the user to their respective symbolic names. Integral files, however, are often very large making it desirous to remove them after the calculation is complete. The linking of files to their symbolic names is useful in other case, such as input orbitals.
If one wants to use any input orbitals for the SCF program the option LUMOrb must be used. If an specific file wants to be used it should be linked to INPORB, but if is is the default $Project.ScfOrb file the program will complain. Input and output orbital files in SCF should be named differently. Ona can copy $Project.ScfOrb for instance to $Project.ScfOld and link this name to INPORB.
The SCF output includes the title from the input as well as the title from the SEWARD input because we used the integrals generated by SEWARD. The output also contains the cartesian coordinates of the molecule and orbital specifications including the number of frozen, occupied and virtual (secondary) orbitals in each symmetry. This is followed by details regarding the SCF algorithm including convergence criteria and iteration limits. The energy convergence information includes the one-electron, two-electron, and total energies for each iteration. This is followed by the final results including the final energy and molecular orbitals for each symmetry.
The molecular orbital (MO) information lists the orbital energy, the electron occupation (which doesn't change from the input values for a Hartree-Fock calculation) and the coefficients of the basis functions contributing to that MO. For a minimal basis set, the basis functions correspond directly to the atomic orbitals. Using larger basis sets means that a combination of the basis functions will be used for each atomic orbital and more so for the MOs. The MOs from the first symmetry species are given in Figure 3.2. The first MO has an energy of -20.5611 hartree and an occupation of 2.0. The major contribution is from the first basis function label `O1 1s0' meaning an s type function centered on the oxygen atom. The orbital energy and the coefficient indicates that it is the MO based largely on the oxygen 1s atomic orbital.
Figure 3.2. Molecular orbitals from the first symmetry species of a
calculation of water using C symmetry and a minimal basis set.
ORBITAL 1 2 3 4
EneRGY -20.5611 -1.3467 -.5957 .0000
Occ. NO. 2.0000 2.0000 2.0000 .0000
1 O1 1s0 1.0000 -.0131 -.0264 -.0797
2 O1 1s0 .0011 .8608 -.4646 -.7760
3 O1 2p0 .0017 .1392 .7809 -.7749
4 H1 1s0 -.0009 .2330 .4849 1.5386
The second MO has a major contribution from the second oxygen 1s basis function indicating a mostly oxygen 2s construction. Note that it is the absolute value of the coefficient that determines it importance. The sign is important for determining the orthogonality of its orbitals and whether the atomic orbitals contributions with overlap constructively (bonding) or destructively (anti-bonding). The former occurs in this MO as indicated by the positive sign on the oxygen 2s and the hydrogen 1s orbitals, showing a bonding interaction between them. The latter occurs in the third MO, where the relative sign is reversed.
The third MO has an energy of -0.5957 hartree and major contributions from the second oxygen 1s basis function, the oxygen 2p0 basis function and the hydrogen 1s basis functions which are symmetrically situated on each hydrogen (see Figure 3.2). The mixing of the oxygen 2s and 2p0 basis functions leads to a hybrid orbital that points away from the two hydrogens, to which it is weakly antibonding.
A similar analysis of the fourth orbital reveals that it is the strongly anti-bonding orbital partner to the third MO. The oxygen 2p0 basis function is negative which reverses the overlap characteristics.
The molecular orbital information is followed by a Mulliken charge analysis by input center and basis function. This provides a measure of the electronic charge of each atomic center.
Towards the end of the SCF section of the MOLCAS output various properties of the molecule are displayed. By default the first (dipole) and second cartesian moments and the quadrupoles are displayed. The inclusion of the FLDG keyword (with zero (0) on the next line) with cause the electric field gradients at each atomic center to be calculated and displayed. There are several other properties that can be calculated in this fashion using the variational MOLCAS programs - SCF and RASSCF when producing a CASSCF wave function.
The SCF module uses the integral files computed by SEWARD. It produces a orbital file with the symbolic name SCFORB which contains all the MO information. This is then available for use in subsequent MOLCAS modules. The SCF module also adds information to the COMFILE.