Next: 8.13.1 Example for computing Up: 8 PROGRAM CONTROL Previous: 8.12 Global Print Options


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 center 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.
  1 LXLX, LYLY, LZLZ one electron parts of products of
      angular momentum operators
  1 LXLY, LXLZ, LYLZ the symmetric combinations
      $\frac{1}{2} (\hat L_x \hat L_y+\hat L_y \hat L_x)$ etc. are computed
  1 LYLX, LZLX, LZLY same as previous
DM 1 DMX, DMY, DMZ dipole moments
SM 1 SMXX, SMYY, SMZZ, SMXY, SMXZ, SMYZ second moments
QM 1 QMXX, QMYY, QMZZ, QMXY, QMXZ, QMYZ, QMRR quadrupole moments and $R^2$
EF 1 EFX, EFY, EFZ electric field
FG 1 FGXX, FGYY, FGZZ, FGXY, FGXZ, FGYZ field gradients
  -1 LX, LY, LZ Angular momentum operators $\hat L_x$, $\hat L_y$, $\hat L_z$
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.



Subsections

Next: 8.13.1 Example for computing Up: 8 PROGRAM CONTROL Previous: 8.12 Global Print Options

P.J. Knowles and H.-J. Werner
molpro-support@tc.bham.ac.uk
Mar 8, 2000