5.6 Generating different GVB solutions
This section is for experienced GVB users. For conjugated molecules, there often exists multiple GVB solutions.
5.6.1 \( \sigma \) - \( \pi \) separated v.s. \( \sigma \) - \( \pi \) mixed solution
By default, the PM (Pipek-Mezey) localization method is used in constructing the initial guess of GVB orbitals. For example, if we calculate a benzene molecule,
%mem=48GB
%nprocshared=48
#p CASSCF/cc-pVDZ
mokit{}
0 1
C -0.90252711 0.46329723 0.00000000
C 0.49263289 0.46329723 0.00000000
C 1.19017089 1.67104823 0.00000000
C 0.49251689 2.87955723 -0.00119900
C -0.90230811 2.87947923 -0.00167800
C -1.59990911 1.67127323 -0.00068200
H -1.45228611 -0.48901977 0.00045000
H 1.04214089 -0.48921577 0.00131500
H 2.28985089 1.67112823 0.00063400
H 1.04271689 3.83170023 -0.00125800
H -1.45243011 3.83176023 -0.00263100
H -2.69951311 1.67145623 -0.00086200
we will obtain GVB(15) and CASSCF(6,6) natural orbitals, in which we can find 3 \( \pi \) bonding orbitals and 3 \( \pi \)* anti-bonding orbitals:
But if we deliberately change the orbital localization method as the Boys method:
mokit{LocalM=Boys}
then the \( \sigma \) - \( \pi \) orbitals are mixed during orbital localization,
and the GVB will converge to a lower-energy solution, but with \( \sigma \) - \( \pi \)
orbitals mixed. And we will probably get the complain information from automr
There is no active orbital/electron. AutoMR terminated.
The reason is this molecule has little multi-configurational or multi-reference
character...
This is because in the lower-energy GVB solution, there are no pure \( \pi \) orbitals, and the corresponding pair coefficients are totally different
CICOEF( 1)= 0.99795122275633, -0.06397934822390
CICOEF( 3)= 0.99795102014144, -0.06398250853672
CICOEF( 5)= 0.99794887464558, -0.06401596358426
CICOEF( 7)= 0.99608018865066, -0.08845483467657
CICOEF( 9)= 0.99607885713120, -0.08846982749052
CICOEF( 11)= 0.99607599571862, -0.08850203812992
CICOEF( 13)= 0.99602509688574, -0.08907303954478
CICOEF( 15)= 0.99602503059542, -0.08907378080778
CICOEF( 17)= 0.99602141489628, -0.08911420239227
CICOEF( 19)= 0.99591536359976, -0.09029168591829
CICOEF( 21)= 0.99591522848545, -0.09029317621383
CICOEF( 23)= 0.99591456661139, -0.09030047625144
CICOEF( 25)= 0.99591440686394, -0.09030223807220
CICOEF( 27)= 0.99591436826541, -0.09030266376197
CICOEF( 29)= 0.99591319014626, -0.09031565585597
It shows the symmetry of 3 C-C \( \sigma \) bonds, 6 C-H \( \sigma \) bonds,
and 6 \( \sigma \) - \( \pi \) mixing bonds ("banana" bonds). These pair coefficients
are of less multi-reference characteristics so that automr
thinks there is no
strongly correlated orbitals to be picked for CASSCF calculations.
5.6.2 closed-shell-like v.s. diradical-like solution
To be added.