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The adiabatic correction to the ring puckering potential of oxetane
Volunw 108. number 4
CHEMICAL
THE ADIABATIC Hanell
CORREClJON
PHYSICS
13 July 1984
LETTERS
TO THE RING PUCKERING
POTENTIAL
OF OXETANE
SELLERS
LIepat-nttertt of Cltctttist~~~. Lottisiatta Tech Uttiversiiy, Rtcsrott. Lottisiatta 71_3!_7.US.4
Rcccivcd 5 April 1984
The adiabatic correction to the iiartree-Fock ring puckering potential of osetme is presented along with the adiabatic correction to potenthl functionsof IIz_ CO, and CO?. The oxetane calculation allows the identification of the source of the disrtgeement between theory and experiment for the barrier to ring planarity.
l_ Introduction
Is;, =
Osetane (trinletllylene aside) is at present an interesting molecule from a theoreical viewpoint because of the wuesolved disagreement between experiment4 results [l-l?] and the results ofab initio calculations [ 13,141 pertaining to the barrier to ring planarity. This barrier to ring planarity (of about 15 c111-~ j is well established experimentally and, hence. its existence is not questioned. However, no ab initio calculation
to date
served
barrier.
nlinded from
has been able to account It would
chemists
to know
the theoretical
the disagreement. The candidates are neglect
be useful what
treatment
for the ob-
to theoretically it is that
that
is nksing
is responsible
for
for the source of the disagreement
of electron
correlation_
vibrational
nlodu-
lation, the adiabatic correction, and diabatic effects (the possibility that this is a basis set effect has been ruled out [7]). Pulay et al. [ 131 have attributed about 13 cm-* of the barrier to vibrational modulation, but, this falls far short of reconciling the difference between the ab initio and experimental potential functions_ At present the expense of a definitive configuration-interaction calculation of the ring puckering potential of oxetane makes it prudent to first examine other possible sources of the disagreement. The adiabatic correction to a potential surface for a given nuclear degree of freedom can be written as LlSl 0 009-2614/84/S 03.00 0 Elsevier Science Publishers INorth-Holland Phvsics Publishing Division)
B-V.
(n’/2flJ)(~’ j +‘1 .
(1)
where E,, is the adiabatic correction to the electronic energy and is a function of the nuclear coordinates, kJ is the IXKSassociated with the nuclear degree of freedom in question, CPis the usual Born-Oppenheimer electronic wavefunction (the primes indicate differentiation with respect to the nuclear degree of freedom). and the bra-ket notation indicates integration over the electronic coordinates only. From eq. (1) it is seen that the adiabatic correction is proportional to the square magnitude of the vector describing the rate of change of the electronic wavefunction with respect to the nuclear degree of freedom. Since the s!lape of the oxetane molecule changes dramatically as it passes from a puckered configuration through the planar ring structure, it is reasonable to think that the rapidly changing molecular shape may contribute to a’ and the adiabatic correction, E,,.
2. Calculations
For a closed shell. single determinant function eq. (1) becomes [ 151 &
= (?i’/ZM) Tr(SD’SD’j4
SCF wave-
+ D’PDS + DQ + DPDPIZ) (9
where D is the closed shell density matrix (D = 2Ce and C is the matrix of LCAO coefficients of the oc339
_
Volume
108. number
Table 1 The adiabatic
CHEMICAL
4
correction
PHYSICS
LETTERS Table 3 The adiabatic of co2
for iI2
13 July
correction
for rhc asymmetric
R (.A)
El (CIII-~)
E2 (cm-‘)
0.4
11.7
0.6
10.9 10.1 9.2
10.2 8.6
0.0 0.1
8.07 8.12
0.7
8.3
7.2
0.2
8.36
0.Y
7.5
6.3
0.3
8.11
0.9
6.6
5.5
1 .o
5.8
4.8
0.4 0.5 0.6
8.44 8.46 9.29
P =)
0.5
cupied MOs), S is the basis function overlap matrix, P and Q are overlap matrices involving one and two differentiated basis functions, respectively, defined clscwherc [ 15j. Orbital following was assumed in the caluclation of the P and Q matrices. The derivatives of the density matrix were obtained numerically by the two-point
central
difference
approximation.
As a
matter of general interest we present the adiabatic correction to potential functions of H2, CO, and CO2 in tables
1-4
(sonic
of these
data
were
presented
in
ref. lib]). Table 1 contains the adiabatic correction (in cn- 1) to the bond stretching potential of H2 obtained from the llartrce-Fock wavcfunction employing the 4-21C and 4-21C** basis sets 1171. The effect of the more flexible wdvefunction can be seen. Table 2 contains the adiabatic correction (obtained with the 4-21G basis) to the bond stretching potential of CO. TIE data of tables 1 and 2 show the adiabatic correclion tending to zero as the diatomic electronic wavcI‘tmc~ion becomes less sensitive to changes in the bond length at larger intcrnuclcar distances. Tables 3 and 4 contain the adiltbatic correction to the asymmetric and symmetric stretching modes of CO,. rcspcctively. obtained with the 4-71 G basis. The asym-
---_
__~____
_--Ii
I:’ (CIIl--’ )
( t-i)
II.6
21.70
I).7
9.43
11.8 0.9
_5 .-‘0 3.111
t .I)
2.40
1.1 --.
MO
--
- . ..--
I.2 -
-
I.Hh I.73
stretching
1984
mode
E (cm-‘)
0.7
11.60
0.8
16.28
a) Q is the normalized asymmetric combination of the two bond stretching displacement coordinates. The refcrencc bond ien< WBS 1.162 A.
metric and symmetric stretching coordinates (denoted by Q in tables 3 and 4) are 2- l12(SR1 - 6Rz) and 2- l12(6R1 + 6R ?),respectively, where 6RI is a bond stretching displacement coordinate. The reference bond length was taken to be 1-162 8, The associated masses of the asymmetric and symmetric stretching coordinates arc the corresponding elements of the inverse of the Wilson G matrix and are 4.3633 and 15.9949 amu. respectively. In none of these cases is the adiabatic correction significant for usual chemical problems. (To get the dimuonium adiabatic corrections from the Ii1 valuesone needs only to apply mass correction.) The adiabatic correction to the ring puckering potential of oxctanc WIS caluclatcd using the 4-2 IG
p II)
I:’ ( clll-1
-0.8
6.6 1 3.46 2.63 2.13
-0.6 - o..t -0.2 (I.11
0.2 (1.4 0.6
1.77 1.72 1.x5 1.91
)
Volume
108. number
Table 5 Tbc adiabatic osef~nc
CHEMICAL
4
PHYSICS
LETTERS
13 July
1984
Acknowledgement correcrion
for the ring puckering
T a)
E (cm-’
0.00 0.32 0.73
0.994 0.995 0.980
mode
of
The author thanks Professor J.E. Boggs and the University of Texas at Austin Computation Center for providing the computer time for these calculations. The author also thanks Louisiana Tech University for paying the phone bill.
1
a) 7 is half the sum of the four ring torsions.
References basis (=$X$
at values
of the
1pi, where
ring
{pi}
puckering is
coordinate,
the set of oxetane
5 ring
dihedral angles) of 0.0.32, and 0.72 radians. The other 3N - 7 = 23 vibrational coordinates were fully
relaxed at these values of 7 [I 3]_ To obtain accurate density matrix derivatives we executed SCF calculations using positive and negative deviations in T of 0.02 rad about
the central values. The associated mass of the ring puckering vibration is a function of the puckering coordinate
[I] [2 ] [3] 141 IS) [6]
and has the values (obtained
from the inverse of the Wilson G matrix) of 3.3417. 3.4053, and 3.6887 amu A2/rad2 for r = 0.0.32. and 0.72 rad, respectively.
Table 5 gives the adiabatic correction to the ring puckering potential of oxetane. It is seen that the adiabatic correction contributes essentially nothing to the ring puckering potential. Since the ring puckering vibration of oxetane is a very slow vibration, it is hyghly unlikely that diabatic effects are important. It is reasonable to conclude that the case of oxetane repfesents a failure of the Hartree-Fock method. Pulay has given the explanation that the Hartree-Fock method overestimates the ring strain energy in oxetane [ 181. Hence, a good quality CI calculation should bring theory and experiment
into agreement.
17 ]
S.I. Chnn. J. Zinn. J. Fernnndez nnd W-D. Gwinn, 1. Chem. Phys. 33 (1960) 1643. S.1. Ghan. J. Zinn and W. D. Gwinn, J. Chem. Phys. 33 (1960) 295. S.I. Cban, J. Zinn and W-D. Gwinn. J. Chcm. Phys. 34 (1961) !319. S.I. Chm, T.R. Borgcrs, J.W. Russell, H.L. Srrauss and \\‘.D. Cwinn. J. Chcm. Phys. 44 (1966) 1103. II. Wicscr. .?I. Danyluk and R.A. Kpdd. J. Mol. Spectr?.. 43 (1972) 382. I. Foltynowicz. J. Konarski and hl. Kreglelvski. J. Mol. Spcct*. 67 (1981‘) 19. G. Banhcghyi, P. Pulay and C. Fograsi. Spectrochinl.
Acta 39 (1983) 76 1. 181 R.A. Crcswcll and LRI. Mills. J. Mol. Spcctry. [9] [IO] [ 111 [ 121 [ 131
51 ( 1974) 392. P.D. Blakkinson and A.G. Robiettc. J. bloL Spectry_ 51 (1974) 413. R.A. CrcsweU. Mol. Pbys. 30 ( 1975) 217. J. Jokisaari and J. Kauppinen, J. Chrm. Pbyr 59 (1973) 2260. R.A. Kydd. II. Wicser and W_ Kiefer. Spcctrochim. Acta 39 (1983) 173. P. Puiuy, C. Banhegyi. T. Jonvik and J.E. Boggs. Paper TX14.9th Austin Symposium on hIoiccuku Structure
(1982). [ 141 P.N. Skanckc.
C. Foogarasi and J.E. Bogs, J. Mol. Structure 62 (1980) 259. [ 151 11.Sellers and P. Pulay, Chem. Phys Letters 103 (19%) 463. [ 161 H. Sellers. Paper Th16. 10111 Austin Symposium on hlolccular Structure (I 984). [ 171 P. I’ulay, G. Fogarasi, F. Pang and J.E. Bogs. J. Ant. Chem. SW. 101 (1979) 2150. [ 181 P. May, private communication (February 1984).
341
CHEMICAL
THE ADIABATIC Hanell
CORREClJON
PHYSICS
13 July 1984
LETTERS
TO THE RING PUCKERING
POTENTIAL
OF OXETANE
SELLERS
LIepat-nttertt of Cltctttist~~~. Lottisiatta Tech Uttiversiiy, Rtcsrott. Lottisiatta 71_3!_7.US.4
Rcccivcd 5 April 1984
The adiabatic correction to the iiartree-Fock ring puckering potential of osetme is presented along with the adiabatic correction to potenthl functionsof IIz_ CO, and CO?. The oxetane calculation allows the identification of the source of the disrtgeement between theory and experiment for the barrier to ring planarity.
l_ Introduction
Is;, =
Osetane (trinletllylene aside) is at present an interesting molecule from a theoreical viewpoint because of the wuesolved disagreement between experiment4 results [l-l?] and the results ofab initio calculations [ 13,141 pertaining to the barrier to ring planarity. This barrier to ring planarity (of about 15 c111-~ j is well established experimentally and, hence. its existence is not questioned. However, no ab initio calculation
to date
served
barrier.
nlinded from
has been able to account It would
chemists
to know
the theoretical
the disagreement. The candidates are neglect
be useful what
treatment
for the ob-
to theoretically it is that
that
is nksing
is responsible
for
for the source of the disagreement
of electron
correlation_
vibrational
nlodu-
lation, the adiabatic correction, and diabatic effects (the possibility that this is a basis set effect has been ruled out [7]). Pulay et al. [ 131 have attributed about 13 cm-* of the barrier to vibrational modulation, but, this falls far short of reconciling the difference between the ab initio and experimental potential functions_ At present the expense of a definitive configuration-interaction calculation of the ring puckering potential of oxetane makes it prudent to first examine other possible sources of the disagreement. The adiabatic correction to a potential surface for a given nuclear degree of freedom can be written as LlSl 0 009-2614/84/S 03.00 0 Elsevier Science Publishers INorth-Holland Phvsics Publishing Division)
B-V.
(n’/2flJ)(~’ j +‘1 .
(1)
where E,, is the adiabatic correction to the electronic energy and is a function of the nuclear coordinates, kJ is the IXKSassociated with the nuclear degree of freedom in question, CPis the usual Born-Oppenheimer electronic wavefunction (the primes indicate differentiation with respect to the nuclear degree of freedom). and the bra-ket notation indicates integration over the electronic coordinates only. From eq. (1) it is seen that the adiabatic correction is proportional to the square magnitude of the vector describing the rate of change of the electronic wavefunction with respect to the nuclear degree of freedom. Since the s!lape of the oxetane molecule changes dramatically as it passes from a puckered configuration through the planar ring structure, it is reasonable to think that the rapidly changing molecular shape may contribute to a’ and the adiabatic correction, E,,.
2. Calculations
For a closed shell. single determinant function eq. (1) becomes [ 151 &
= (?i’/ZM) Tr(SD’SD’j4
SCF wave-
+ D’PDS + DQ + DPDPIZ) (9
where D is the closed shell density matrix (D = 2Ce and C is the matrix of LCAO coefficients of the oc339
_
Volume
108. number
Table 1 The adiabatic
CHEMICAL
4
correction
PHYSICS
LETTERS Table 3 The adiabatic of co2
for iI2
13 July
correction
for rhc asymmetric
R (.A)
El (CIII-~)
E2 (cm-‘)
0.4
11.7
0.6
10.9 10.1 9.2
10.2 8.6
0.0 0.1
8.07 8.12
0.7
8.3
7.2
0.2
8.36
0.Y
7.5
6.3
0.3
8.11
0.9
6.6
5.5
1 .o
5.8
4.8
0.4 0.5 0.6
8.44 8.46 9.29
P =)
0.5
cupied MOs), S is the basis function overlap matrix, P and Q are overlap matrices involving one and two differentiated basis functions, respectively, defined clscwherc [ 15j. Orbital following was assumed in the caluclation of the P and Q matrices. The derivatives of the density matrix were obtained numerically by the two-point
central
difference
approximation.
As a
matter of general interest we present the adiabatic correction to potential functions of H2, CO, and CO2 in tables
1-4
(sonic
of these
data
were
presented
in
ref. lib]). Table 1 contains the adiabatic correction (in cn- 1) to the bond stretching potential of H2 obtained from the llartrce-Fock wavcfunction employing the 4-21C and 4-21C** basis sets 1171. The effect of the more flexible wdvefunction can be seen. Table 2 contains the adiabatic correction (obtained with the 4-21G basis) to the bond stretching potential of CO. TIE data of tables 1 and 2 show the adiabatic correclion tending to zero as the diatomic electronic wavcI‘tmc~ion becomes less sensitive to changes in the bond length at larger intcrnuclcar distances. Tables 3 and 4 contain the adiltbatic correction to the asymmetric and symmetric stretching modes of CO,. rcspcctively. obtained with the 4-71 G basis. The asym-
---_
__~____
_--Ii
I:’ (CIIl--’ )
( t-i)
II.6
21.70
I).7
9.43
11.8 0.9
_5 .-‘0 3.111
t .I)
2.40
1.1 --.
MO
--
- . ..--
I.2 -
-
I.Hh I.73
stretching
1984
mode
E (cm-‘)
0.7
11.60
0.8
16.28
a) Q is the normalized asymmetric combination of the two bond stretching displacement coordinates. The refcrencc bond ien< WBS 1.162 A.
metric and symmetric stretching coordinates (denoted by Q in tables 3 and 4) are 2- l12(SR1 - 6Rz) and 2- l12(6R1 + 6R ?),respectively, where 6RI is a bond stretching displacement coordinate. The reference bond length was taken to be 1-162 8, The associated masses of the asymmetric and symmetric stretching coordinates arc the corresponding elements of the inverse of the Wilson G matrix and are 4.3633 and 15.9949 amu. respectively. In none of these cases is the adiabatic correction significant for usual chemical problems. (To get the dimuonium adiabatic corrections from the Ii1 valuesone needs only to apply mass correction.) The adiabatic correction to the ring puckering potential of oxctanc WIS caluclatcd using the 4-2 IG
p II)
I:’ ( clll-1
-0.8
6.6 1 3.46 2.63 2.13
-0.6 - o..t -0.2 (I.11
0.2 (1.4 0.6
1.77 1.72 1.x5 1.91
)
Volume
108. number
Table 5 Tbc adiabatic osef~nc
CHEMICAL
4
PHYSICS
LETTERS
13 July
1984
Acknowledgement correcrion
for the ring puckering
T a)
E (cm-’
0.00 0.32 0.73
0.994 0.995 0.980
mode
of
The author thanks Professor J.E. Boggs and the University of Texas at Austin Computation Center for providing the computer time for these calculations. The author also thanks Louisiana Tech University for paying the phone bill.
1
a) 7 is half the sum of the four ring torsions.
References basis (=$X$
at values
of the
1pi, where
ring
{pi}
puckering is
coordinate,
the set of oxetane
5 ring
dihedral angles) of 0.0.32, and 0.72 radians. The other 3N - 7 = 23 vibrational coordinates were fully
relaxed at these values of 7 [I 3]_ To obtain accurate density matrix derivatives we executed SCF calculations using positive and negative deviations in T of 0.02 rad about
the central values. The associated mass of the ring puckering vibration is a function of the puckering coordinate
[I] [2 ] [3] 141 IS) [6]
and has the values (obtained
from the inverse of the Wilson G matrix) of 3.3417. 3.4053, and 3.6887 amu A2/rad2 for r = 0.0.32. and 0.72 rad, respectively.
Table 5 gives the adiabatic correction to the ring puckering potential of oxetane. It is seen that the adiabatic correction contributes essentially nothing to the ring puckering potential. Since the ring puckering vibration of oxetane is a very slow vibration, it is hyghly unlikely that diabatic effects are important. It is reasonable to conclude that the case of oxetane repfesents a failure of the Hartree-Fock method. Pulay has given the explanation that the Hartree-Fock method overestimates the ring strain energy in oxetane [ 181. Hence, a good quality CI calculation should bring theory and experiment
into agreement.
17 ]
S.I. Chnn. J. Zinn. J. Fernnndez nnd W-D. Gwinn, 1. Chem. Phys. 33 (1960) 1643. S.1. Ghan. J. Zinn and W. D. Gwinn, J. Chem. Phys. 33 (1960) 295. S.I. Cban, J. Zinn and W-D. Gwinn. J. Chcm. Phys. 34 (1961) !319. S.I. Chm, T.R. Borgcrs, J.W. Russell, H.L. Srrauss and \\‘.D. Cwinn. J. Chcm. Phys. 44 (1966) 1103. II. Wicscr. .?I. Danyluk and R.A. Kpdd. J. Mol. Spectr?.. 43 (1972) 382. I. Foltynowicz. J. Konarski and hl. Kreglelvski. J. Mol. Spcct*. 67 (1981‘) 19. G. Banhcghyi, P. Pulay and C. Fograsi. Spectrochinl.
Acta 39 (1983) 76 1. 181 R.A. Crcswcll and LRI. Mills. J. Mol. Spcctry. [9] [IO] [ 111 [ 121 [ 131
51 ( 1974) 392. P.D. Blakkinson and A.G. Robiettc. J. bloL Spectry_ 51 (1974) 413. R.A. CrcsweU. Mol. Pbys. 30 ( 1975) 217. J. Jokisaari and J. Kauppinen, J. Chrm. Pbyr 59 (1973) 2260. R.A. Kydd. II. Wicser and W_ Kiefer. Spcctrochim. Acta 39 (1983) 173. P. Puiuy, C. Banhegyi. T. Jonvik and J.E. Boggs. Paper TX14.9th Austin Symposium on hIoiccuku Structure
(1982). [ 141 P.N. Skanckc.
C. Foogarasi and J.E. Bogs, J. Mol. Structure 62 (1980) 259. [ 151 11.Sellers and P. Pulay, Chem. Phys Letters 103 (19%) 463. [ 161 H. Sellers. Paper Th16. 10111 Austin Symposium on hlolccular Structure (I 984). [ 171 P. I’ulay, G. Fogarasi, F. Pang and J.E. Bogs. J. Ant. Chem. SW. 101 (1979) 2150. [ 181 P. May, private communication (February 1984).
341