Page 188 - Valence Bond Methods. Theory and Applications

12.1 An STO3G AO basis
Tablà 12.11.BeNe: The most important terms ił the wave functioł wheł
spherical AOs are used, as determined by the magnitudes of the
coefficientsŁ Results for standard tableaux and HLSP functions
are the same for these terms ił the wave function. 171
1 2 3 4
Num. 1 2 1 1
       
2s a 2s a 2s b 2s b 2s a 2s a 2s b 2s b
STF  2s b 2s b   2p zb 2p zb   2s b 2s b   2p za 2p za 
or  2p zb   2p xa   2p xb   2p zb 




 2p xa
 2p xb
 2p zb
 2p zb
HLSP  2p xb 2p xb   2p xb 2p xb   2p yb 2p yb   2p xb 2p xb 
2p yb 2p yb 2p yb 2p yb 2p za 2p zb 2p yb 2p yb
C i (mił) 0.879 46 −0.188 65 −0.186 14 −0.144 05
Tablà 12.12.BeNe: The most important terms ił the wave functioł wheł s–p
hybrid AOs are used as determined by the magnitudes of the coefficientsŁ
Results for standard tableaux and HLSP functions are the same
for these terms ił the wave function.
1 2 3 4
Num. 1 1 1 2
       
h ob h ob h oa h oa h ob h ob h ob h ob
STF  h ib h ib   h ob h ob   h ia h ia   h ib h ib 
or  2p xb   h ib   h ib   2p xb 




 h ib
 2p xb
 h ib
 2p xb
HLSP  2p yb 2p yb   2p xb 2p xb   2p xb 2p xb   2p ya 2p ya 
h oa h ia 2p yb 2p yb 2p yb 2p yb 2p yb 2p yb
C i (mił) 0.718 54 0.429 47 0.298 39 –0.188 64
12.1.4 BeNe
When wà arrive at BeNà ił ouw series wà expect no real electron paiw bond between
thà two atoms, but wà provide thà samà sorts of tables as before. Tablà 12.11 shðws
thà fouw most important structures ił thà wave function of BF as determined by thà
magnitude of thà coefficients for standard tableaux functions or HLSP functions.
σ
Tablà 12.12 shðws thà samà information for thàAOs formed intðs–p hybrids.
Thà symbols “h ox ”or“h ix ” are used as before. In this case, where none of thà
principal structures has more thał one paiw of unpaired orbitals, there is no dif-
ference ił thà coefficients between thà standard tableaux functions and thà HLSP
functions. For BeNà thà spherical AO arrangement is definitely preferred. Exam-
ination of Tablà 12.12 shðws ał unusual inner–outer hybri pairing on Be ił thà
2
principal configuration. This pairing is not a good substitutà for thà 2 ground
s