[molpro-user] Transition dipole moment, phase convention

[Allan East]

Dear MOLPRO users:

    I have also seen some wavefunctions flip sign when I displace the 
geometry.  However, we have recently found something that looks very 
odd: a phase change within a MULTI run.

    We were computing CASSCF transition dipole moments from the ground 
A1 state to eight B2-symmetry states of C2v nitric oxide dimer, (NO)2.  
All but one of our runs suggests that there is just one diabatic state 
of strong intensity: a charge-transfer or charge-resonance (CR) state, 
denoted by MOLPRO as
+00 00 -00 00 and
-00 00 +00 00
in the output below.  All eight adiabatic states "borrow intensity" from 
this CR state to varying degrees.  The reason we know there is only one 
bright diabatic state is because we take the coefficient matrix and the 
adiabatic TDM's and deconvolute it (Gauss-Jordan elimination) to get the 
diabatic TDM's.  This results in just one bright diabatic state, 
regardless of basis set or geometry, EXCEPT for one run, which suggested 
three bright diabatic states.  With some sleuthing, we discovered that 
the problem was a phase change for adiabatic state #4 during the run.  
It was as if MOLPRO used one phase for it when it calculated the TDM for 
#4, but then used the opposite sign for it when it printed the table of 
coefficients.

Below are the printed TDM's for the eight adiabatic B2 states. 
 !MC MATR. ELEMENT <1.3|DMY|1.1>     -0.27908033  A.U. -0.70930498  DEBYE
 !MC MATR. ELEMENT <2.3|DMY|1.1>     -0.44873783  A.U. -1.14050309  DEBYE
 !MC MATR. ELEMENT <3.3|DMY|1.1>     -0.22007139  A.U. -0.55932903  DEBYE
 !MC MATR. ELEMENT <4.3|DMY|1.1>     -0.57769256  A.U. -1.46825186  DEBYE
 !MC MATR. ELEMENT <5.3|DMY|1.1>      0.13615376  A.U.  0.34604567  DEBYE
 !MC MATR. ELEMENT <6.3|DMY|1.1>      0.57552598  A.U.  1.46274533  DEBYE
 !MC MATR. ELEMENT <7.3|DMY|1.1>      0.04738081  A.U.  0.12042211  DEBYE
 !MC MATR. ELEMENT <8.3|DMY|1.1>     -0.93792215  A.U. -2.38380418  DEBYE

Our other runs suggest that the sign of the adiabatic-state TDM 
generally matches the sign of the CR-state coefficient in that adiabatic 
state.  Now, below is the relevant printout of the coefficient matrix:

 CI vector for state symmetry 2
 ------------------------------

 00+ 00 -00 00      0.0115718   0.1258424  -0.0151492   0.0368260
 00- 00 +00 00     -0.0115718  -0.1258424   0.0151492  -0.0368260
 +00 00 0-0 00     -0.6703766   0.0477829   0.0278655  -0.0230457
 -00 00 0+0 00      0.6703766  -0.0477829  -0.0278655   0.0230457
 +00 00 00- 00     -0.0155887  -0.6623023   0.0531727  -0.1128714
 -00 00 00+ 00      0.0155887   0.6623023  -0.0531727   0.1128714
 0+0 00 -00 00     -0.1815364   0.0324783   0.0153959  -0.1261730
 0-0 00 +00 00      0.1815364  -0.0324783  -0.0153959   0.1261730
 000 0+ 000 -0     -0.0104218  -0.0066836  -0.5373905  -0.1167052
 000 0- 000 +0      0.0104218   0.0066836   0.5373905   0.1167052
 +00 00 -00 00     -0.1292310  -0.1996674  -0.0934148   0.2726115 **
 -00 00 +00 00      0.1292310   0.1996674   0.0934148  -0.2726115 **
 000 +0 000 -0      0.0143860   0.0421109   0.3062086  -0.4891718
 000 -0 000 +0     -0.0143860  -0.0421109  -0.3062086   0.4891718
 000 +0 000 0-      0.0011618   0.0005808   0.3234205   0.3765773
 000 -0 000 0+     -0.0011618  -0.0005808  -0.3234205  -0.3765773

I added stars to highlight the rows of the CR diabatic state, and 
removed the columns for adiabatic states #5-#8.  Note that the signs 
across this row are not consistent with the signs of the first four 
TDMs.  Something happened to the signs of 0.2726115 (actually the entire 
column) between the TDM calculation and the printing of this coefficent 
here.

I verified the problem with another run, using the same conditions 
except that I first did the run at a displaced geometry, and then read 
in those orbitals/wavefunctions for the run at the desired geometry.  
The magnitudes of all TDM's and coeffecients matched, as expected. For 
the signs, MOLPRO flipped the phase of adiabatic state #2 for its TDM 
and its coefficients (yes, wierd, but yes phase is arbitrary), but only 
flipped the sign of the TDM for #4.  This gave correct, consistent 
results for state #4 in this verifying run, indicating that the original 
run reported above did something funny.

If this is a bug, our first guess is maybe there's an uncertainty in how 
MOLPRO handles the phase of added basis functions, which could affect 
the phase of entire states.  We had added extra diffuse functions in the 
following way:

basis
 sp,1,VTZ;C;SP,1,EVEN,2
 sp,2,VTZ;C;SP,2,EVEN,2
 df,1,AVTZ;c;
 df,2,AVTZ;c;
 endbasis

This level of detail may be too much for general posting, but I'm not 
100% sure I should send this to bug reports, so I thought I'd start here.

Sincerely,
Allan East
University of Regina, Canada