The operators for which expectation values are requested, are specified by keywords on the global GEXPEC directive. By default, only dipole moments are computed. The first letter G is optional, but should be used to avoid confusion with program specific EXPEC cards, which have the same form as GEXPEC. For all operators specified on the GEXPEC card, expectation values are computed in all subsequent programs that generate the first-order density matix. This is always the case for variational wavefunctions, i.e., HF, DFT, MCSCF, MRCI. For non-variational wavefunctions such as MP2, QCISD, QCISD(T), CCSD, or CCSD(T) the density matix is not computed by default, since this requires considerable additional effort (solving z-vector equations). The GEXPEC directive does not affect such programs. In some cases [currently for MP2, QCISD, QCISD(T)] the EXPEC directive that is specific to those programs can be used to request the property calculation.
For a number of operators it is possible to use generic operator names, e.g., DM for dipole moments, which means that all three components DMX, DMY, and DMZ are computed. Alternatively, individual components may be requested.
The general format is as follows:
Several GEXPEC cards may follow each other, or several operators may be specified on one card.
GEXPEC,QM computes quadrupole moments with origin at (0,0,0),
GEXPEC,QM1 computes quadrupole moments with origin at centre 1.
GEXPEC,QM,O1 computes quadrupole moments with origin at atom O1.
GEXPEC,QM,,1,2,3 computes quadrupole moments with origin at (1,2,3).
The following table summarizes all available operators:
|DARW||1||one-electron Darwin term,|
|i.e., DELTA with appropriate factors|
|summed over atoms.|
|i.e., DEL4 with appropriate factor.|
|REL||1||total Cowan-Griffin Relativistic correction,|
|DM||1||DMX, DMY, DMZ||dipole moments|
|SM||1||XX, YY, ZZ, XY, XZ, YZ||second moments|
|TM||1||XXX, XXY, XXZ, XYY, XYZ,|
|XZZ, YYY, YYZ, YZZ, ZZZ||third moments|
|MLTPn||1||all unique Cartesian products of order||multipole moments|
|QM||1||QMXX, QMYY, QMZZ, QMXY, QMXZ, QMYZ,||quadrupole moments and|
|QMRR=XX + YY + ZZ,|
|QMXX=(3 XX - RR)/2,|
|QMXY=3 XY / 2 etc.|
|EF||1||EFX, EFY, EFZ||electric field|
|FG||1||FGXX, FGYY, FGZZ, FGXY, FGXZ, FGYZ||electric field gradients|
|DMS||1||DMSXX, DMSYX, DMSZX,|
|DMSXY, DMSYY, DMSZY,|
|DMSXZ, DMSYZ, DMSZZ||diamagnetic shielding tensor|
|LOP||-1||LX, LY, LZ||Angular momentum operators , ,|
|LOP2||1||LXLX, LYLY, LZLZ,||one electron parts of products of|
|LXLY, LXLZ, LYLZ||angular momentum operators.|
|The symmetric combinations||etc. are computed|
|VELO||-1||D/DX, D/DY, D/DZ||velocity|
|LS||-1||LSX, LSY, LSZ||spin-orbit operators|
|ECPLS||-1||ECPLSX, ECPLSY, ECPLSZ||ECP spin-orbit operators|
Expectation values are only nonzero for symmetric operators (parity=1). Other operators can be used to compute transition quantities (spin-orbit operators need a special treatment).