8.13 One-electron operators and expectation values (GEXPEC)

The operators for which expectation values are requested, are specified by keywords on the global GEXPEC directive. 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 (if applicable).

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:

[G]EXPEC,opname[,][icen,[x,y,z]],...

where

opname

operator name (string), either generic or component.

icen

z-matrix row number or z-matrix symbol used to determine the origin (x,y,z must not be specified).
If icen$=0$ or blank, the origin must be specified in x,y,z

Several GEXPEC cards may follow each other, or several operators may be specified on one card.

Examples:

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:

Table 5: One-electron operators and their components

Generic	Parity	Components	Description
name
OV	1		Overlap
EKIN	1		Kinetic energy
POT	1		potential energy
DELT	1		delta function
DEL4	1		$\Delta^4$
DARW	1		one-electron Darwin term,
			i.e., DELT with appropriate factors
			summed over atoms.
MASSV	1		mass-velocity term,
			i.e., DEL4 with appropriate factor.
REL	1		total Cowan-Griffin Relativistic correction,
			i.e., DARW+MASSV.
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 $n$	multipole moments
QM	1	QMXX, QMYY, QMZZ, QMXY, QMXZ, QMYZ,	quadrupole moments and $R^2$
		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 $\hat L_x$, $\hat L_y$, $\hat L_z$
LOP2	1	LXLX, LYLY, LZLZ,	one electron parts of products of
		LXLY, LXLZ, LYLZ	angular momentum operators.
		The symmetric combinations	$\frac{1}{2} (\hat L_x \hat L_y+\hat L_y \hat L_x)$ 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). By default, the dipole moments are computed.