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Effect of higher excited configurations on the charge density distributions in the ground and excited states of acrolein
‘.
tiMICAL
~‘~Vohne11,numbqI
PHYSICi LFT+2
15 Septembq
., ‘._
:
.‘. :. .: ,
.’ ; ..
.’ .. ”
‘,.
1..
:.
”
N. TYUTYLTWCOVand G. HIEBAUM BuZg~
.’
.’
,a_‘..
Ei’iECT Oi? HIGHEhk!Il’ED CONi+GtiRii’IONSVdV ‘.. THE CHARGE’DENSITY DlISTRlBUTIONS-IN THE .’ GROUND AiVD l&CITED STATES QF~ACRiWZN
‘:.
‘.
:
,.;
i??l
Acacl’emy
ofSciencts,
Institute
of’Urgmrie
Chehistly.
Sofm 13, &&a&
Received 18 June 1971
: :
.,‘. Usingthe ecrolein ~oiecuie as an example, the importana3 of doubly and high&excited confyuations in ob2 correct c-e density distributions in the ground stats and particulariy in the excited statesof molecuies is
7%: effect of the width of configuration iriteraction, in&rding higher excited configurations, on the energetic spectrum of moiecules calculated by semi-empirical ” methods, has been studied by a number of authors [ 11. However, similar studies on 4he effect of the confguration interaction width on the moleculti characteristics which am dependent on the wavefunctions, and in particular studies on charge den@ distributions, are absent. The o.dy exceptions are the papers in which the effect of singly excited configurations has been investigated [2J, as weU as the paper 131 w-here the ground state of the benzyi radical was examined i the radical however being an open-shell system. The‘kF and configuration interaction methods including sQly excited con&rations may in a number .of cases give an accurate picture of the charge density&stribr@ion, hot+ in the ground and excited states’of tke nioiecule; Thus for non-alternant hydracarbons 141, the various methods have revealed a qualitatively similar charge density distribution, not only for the ground state, but also for the fluorescen& and phosphorescerke states. In soma cases of excited mole&_&u states, however, the various modir%ations of these methods have sometimes given results for the electronic density distribution in a molecule which are both quantitatively.and qua+tiveIy different. This is illustrated by fig. I, where the charge densities are shown for the ground and three exCited singlet states calculated by the
86
:
Fig. 1. Charge
densities in ground state (q”), first &.z’). second calculated by. @‘7 and.tifiird(4”‘) excited states oiacroleine,
the HMO (-
), SCF MO (.....), HME) CI (-), SCF CI (-.-.-) and by the MIM (T.--.-) methods.
Hiickel MO (HMO), SCF.MO, configuration interac-. ti’on (SCF CI and Hh50 CI) including only singly excited confllrations,and by’the MU1 method (a method of configuration interaction where the mo!ecular, orbitali of the fragment C=C and C=O are used as basis functiHis). & seen from fig. I, quantitatively different values are obtained for the electronic charges of the atoms in the ground state, yet qualitatively all _
Votime 11, number 1
Table 1 Excitation energiesand n-electron components of the dipole moments calculated by different methods. (The number of stars shows the configurations which are included in the configuration interaction: *-monoexcited; l*-monp and biexcited, etc.) Method HMO HMO CI
MIM SCF SCF a* SW a** SCF a***
SCF CI****
fuza) (eV) 6.06 5.78 5.98 5.87 5.74 5.66 5.73
15 September 1971
CHEMICALPHYSICSLJZ-R-ERS
PO@)
PlOX
4.11 0.41 1.04 1.51 1.51 0.79 0.76
6.10
0.71
2.10 5.05 2.53 5.93 0.86 0.76 0.72
a)Eexp=6.11 eV [lo]. these methods give the same results for the charge density distribution. The results for the excited states, however, differ both quantitatively and qualitatively. The substantial difference in the values for the charges leads to quantitatively and qualitatively different values for the intramolecular charge transfer from the ethylene bond to the c.arbonyl group, as well as for the values of the dipole moments (table 1). The strong dependence of the charge density distribution on the MO basis displays the necessity of including higher excited configurations - since, according to the Lijwdin theorem [5], if the configuration interaction comprises all possible configurations (with the appropriate parameters) the results should be independent of the type of the MO basis. The purpose of this paper is to show, using acrolein as an example, the importance of the higher excited configurations in obtaining correct (within the framework of the Pariser-Parr-Pople treatment of n-systems) results for the chargedensitydistributions withparticularreference to the distributions in the excited states. The parameters and geometry of the molecule were the same as described elsewhere. 161. The resonance integrals between the carbon atoms were calculated as K$F = -2.3 18 X S/So eV (where So is the overIap integral at R = 1.397 A).For the resonance integral @$ the value -2.67 eV was taken; the same value was used in investigating a number of carbonyl compounds [7]. The difference between the ionization potentials I0 - 1, = 4.00 eV was also taken, from ref. 171. The penetration integrals were neglected.
TEble 2 C.I~arge lensit& for ground and excited states
1 2 3 4
0.9640 1.0020 0.8390 1.1950
0 0 0 0
0.0263
0.0244
-0.OOL7 0.0011 0.0532 0.0588 -0.0777 -p.p42
0.0256
0.0@08 0.0642 -0.0907
Fksstexcite-d singlet state ****
Atom @SW
Aq*
Aq**
&p**
W
f
-0.1253 -0.0334
-0.2796 -0.1791
-0.0995 0.0277
-0.0942 0.0303
-0.0954 0.0331
3 4
0.1639 -0.0052
0.3081 -Cl506
0.2415 -0.1698
0.2337 -0.1703
0.2436 -0.1819
The electron repulsion integrals were calculated using the Mataga-Nishimoto approximation [8] and oneo = 14.51866 and & = 10.84262 centre mtegrals rcrr eV. The Cl matrix elements between the doubly excited configurations were calculated using the &ek formulas [9]. The inclusion of the doubly excitpd configurations results in lowering the ground state energy: AE = -1.44 eV; the energy of excitation to the fist singlet state was not changed appreciably, due to lowering of the first sing& state as well (table 1). The triply and higher excited configurations have no practical effect on the ground state energy. The corrections for the electronic charges obtained at different configuration interaction widths (SCF MO’s as basis) are given in table 2, and the r-electronic components of the dipole moments in the ground and first excited states are given in table 1. As seen from the tables.the chargedensities, as wellas the dipole moments in the ground and excited states, are affected substantially ordy by the doubIy excited configurations.
The results should not be used to conclude that the inclusion of doubly excited states is sufficient in all cases for obtaining quaIitativeIy and quantitatively accurate values for the charge densiv
distribution.
In
order to obtain a criterion
which could b-e used as a basis for evaluating the required sufficient number of configurations it is necessary to study a greater number of motecu~es: 87
-W~iwne11, number 1.
CHEMICAL PHYSICSLEMERS
., The resulis tibt&net so’& indicate that the incluof higher excited con.tigur&ions, in sor& cases, is s&&cant for,obtWg correct results about the charge density djstribtitioti in the excited states, which ” was the purpose of the pii%Cllt WO+g.
sion
R&&c&
--,.
: [l] T.Anno and-A.&do,
3:&m.
Phys. 39 (1963) 2293;
W.E.Donath. 3. Chem. whys. 40 (19643 77; J.N.Muxrel and EL.McEwen, 1. Chem. Phys. 25 (1956) ,’ 1143; .,
R:G.Parr, D.P.Craig and J.G.Ross, J. Clwn. Fhys. 1s 11950) 1561; N.L.Allinger and J.C.Tai,‘J. Am. Chem. Sod. 87 (1965)
2081; J.Kouteck$, J.efieG, J.Dubsky and K.Hiavaty, Theoret.
:
._ :
‘.
:
‘.j :
$2,.
“_ 15 September
chim. Acta 2 (1964) 462;. ‘:‘:” JCS?kaploto and YJ.I’Haya, Theoret. C+II, Acta 13 -.. : .(1969)225. : ,121 N.Tyutyulkov and F.F;atev, Theo&.-m. A+8 ... .: (1%7) 62. (31 Y.A.Krbglyak and E.Mozdor, Theoret Chim. Acta 15 (1969) 374. !4] ~.‘T&tyulkov,~F.Fratev and M.Ivaoova, Theoret Chin Acta 20 (1971) 385; [S] P.-O.L~wdin, Phys. Rev. 97 (1955) 1474. [6 ] Ta@Ies of interatomic distances axd configuration in
molecules and ions (The Chem. Sot., London; 1958). (7 1 G. Hiebaum. N. Tyutyulkov and hf. Ivanova, Zh. Tear. i * Ekqerim. Khim. (USSR) 6 (1970) 595. [ 81 N.Mataga and K.Nishimoto, Z. Phy.$k. C&em. (Frankftlrt) 13 (1957) 140. 191 J.i%ek, ‘Iheoret. Chk Ati 6 (1966) 292. [lo] R.L.FIury,E.W.Stoutand J.J.Rell; Theoret Chim. Acta 8 (1967) 203.
tiMICAL
~‘~Vohne11,numbqI
PHYSICi LFT+2
15 Septembq
., ‘._
:
.‘. :. .: ,
.’ ; ..
.’ .. ”
‘,.
1..
:.
”
N. TYUTYLTWCOVand G. HIEBAUM BuZg~
.’
.’
,a_‘..
Ei’iECT Oi? HIGHEhk!Il’ED CONi+GtiRii’IONSVdV ‘.. THE CHARGE’DENSITY DlISTRlBUTIONS-IN THE .’ GROUND AiVD l&CITED STATES QF~ACRiWZN
‘:.
‘.
:
,.;
i??l
Acacl’emy
ofSciencts,
Institute
of’Urgmrie
Chehistly.
Sofm 13, &&a&
Received 18 June 1971
: :
.,‘. Usingthe ecrolein ~oiecuie as an example, the importana3 of doubly and high&excited confyuations in ob2 correct c-e density distributions in the ground stats and particulariy in the excited statesof molecuies is
7%: effect of the width of configuration iriteraction, in&rding higher excited configurations, on the energetic spectrum of moiecules calculated by semi-empirical ” methods, has been studied by a number of authors [ 11. However, similar studies on 4he effect of the confguration interaction width on the moleculti characteristics which am dependent on the wavefunctions, and in particular studies on charge den@ distributions, are absent. The o.dy exceptions are the papers in which the effect of singly excited configurations has been investigated [2J, as weU as the paper 131 w-here the ground state of the benzyi radical was examined i the radical however being an open-shell system. The‘kF and configuration interaction methods including sQly excited con&rations may in a number .of cases give an accurate picture of the charge density&stribr@ion, hot+ in the ground and excited states’of tke nioiecule; Thus for non-alternant hydracarbons 141, the various methods have revealed a qualitatively similar charge density distribution, not only for the ground state, but also for the fluorescen& and phosphorescerke states. In soma cases of excited mole&_&u states, however, the various modir%ations of these methods have sometimes given results for the electronic density distribution in a molecule which are both quantitatively.and qua+tiveIy different. This is illustrated by fig. I, where the charge densities are shown for the ground and three exCited singlet states calculated by the
86
:
Fig. 1. Charge
densities in ground state (q”), first &.z’). second calculated by. @‘7 and.tifiird(4”‘) excited states oiacroleine,
the HMO (-
), SCF MO (.....), HME) CI (-), SCF CI (-.-.-) and by the MIM (T.--.-) methods.
Hiickel MO (HMO), SCF.MO, configuration interac-. ti’on (SCF CI and Hh50 CI) including only singly excited confllrations,and by’the MU1 method (a method of configuration interaction where the mo!ecular, orbitali of the fragment C=C and C=O are used as basis functiHis). & seen from fig. I, quantitatively different values are obtained for the electronic charges of the atoms in the ground state, yet qualitatively all _
Votime 11, number 1
Table 1 Excitation energiesand n-electron components of the dipole moments calculated by different methods. (The number of stars shows the configurations which are included in the configuration interaction: *-monoexcited; l*-monp and biexcited, etc.) Method HMO HMO CI
MIM SCF SCF a* SW a** SCF a***
SCF CI****
fuza) (eV) 6.06 5.78 5.98 5.87 5.74 5.66 5.73
15 September 1971
CHEMICALPHYSICSLJZ-R-ERS
PO@)
PlOX
4.11 0.41 1.04 1.51 1.51 0.79 0.76
6.10
0.71
2.10 5.05 2.53 5.93 0.86 0.76 0.72
a)Eexp=6.11 eV [lo]. these methods give the same results for the charge density distribution. The results for the excited states, however, differ both quantitatively and qualitatively. The substantial difference in the values for the charges leads to quantitatively and qualitatively different values for the intramolecular charge transfer from the ethylene bond to the c.arbonyl group, as well as for the values of the dipole moments (table 1). The strong dependence of the charge density distribution on the MO basis displays the necessity of including higher excited configurations - since, according to the Lijwdin theorem [5], if the configuration interaction comprises all possible configurations (with the appropriate parameters) the results should be independent of the type of the MO basis. The purpose of this paper is to show, using acrolein as an example, the importance of the higher excited configurations in obtaining correct (within the framework of the Pariser-Parr-Pople treatment of n-systems) results for the chargedensitydistributions withparticularreference to the distributions in the excited states. The parameters and geometry of the molecule were the same as described elsewhere. 161. The resonance integrals between the carbon atoms were calculated as K$F = -2.3 18 X S/So eV (where So is the overIap integral at R = 1.397 A).For the resonance integral @$ the value -2.67 eV was taken; the same value was used in investigating a number of carbonyl compounds [7]. The difference between the ionization potentials I0 - 1, = 4.00 eV was also taken, from ref. 171. The penetration integrals were neglected.
TEble 2 C.I~arge lensit& for ground and excited states
1 2 3 4
0.9640 1.0020 0.8390 1.1950
0 0 0 0
0.0263
0.0244
-0.OOL7 0.0011 0.0532 0.0588 -0.0777 -p.p42
0.0256
0.0@08 0.0642 -0.0907
Fksstexcite-d singlet state ****
Atom @SW
Aq*
Aq**
&p**
W
f
-0.1253 -0.0334
-0.2796 -0.1791
-0.0995 0.0277
-0.0942 0.0303
-0.0954 0.0331
3 4
0.1639 -0.0052
0.3081 -Cl506
0.2415 -0.1698
0.2337 -0.1703
0.2436 -0.1819
The electron repulsion integrals were calculated using the Mataga-Nishimoto approximation [8] and oneo = 14.51866 and & = 10.84262 centre mtegrals rcrr eV. The Cl matrix elements between the doubly excited configurations were calculated using the &ek formulas [9]. The inclusion of the doubly excitpd configurations results in lowering the ground state energy: AE = -1.44 eV; the energy of excitation to the fist singlet state was not changed appreciably, due to lowering of the first sing& state as well (table 1). The triply and higher excited configurations have no practical effect on the ground state energy. The corrections for the electronic charges obtained at different configuration interaction widths (SCF MO’s as basis) are given in table 2, and the r-electronic components of the dipole moments in the ground and first excited states are given in table 1. As seen from the tables.the chargedensities, as wellas the dipole moments in the ground and excited states, are affected substantially ordy by the doubIy excited configurations.
The results should not be used to conclude that the inclusion of doubly excited states is sufficient in all cases for obtaining quaIitativeIy and quantitatively accurate values for the charge densiv
distribution.
In
order to obtain a criterion
which could b-e used as a basis for evaluating the required sufficient number of configurations it is necessary to study a greater number of motecu~es: 87
-W~iwne11, number 1.
CHEMICAL PHYSICSLEMERS
., The resulis tibt&net so’& indicate that the incluof higher excited con.tigur&ions, in sor& cases, is s&&cant for,obtWg correct results about the charge density djstribtitioti in the excited states, which ” was the purpose of the pii%Cllt WO+g.
sion
R&&c&
--,.
: [l] T.Anno and-A.&do,
3:&m.
Phys. 39 (1963) 2293;
W.E.Donath. 3. Chem. whys. 40 (19643 77; J.N.Muxrel and EL.McEwen, 1. Chem. Phys. 25 (1956) ,’ 1143; .,
R:G.Parr, D.P.Craig and J.G.Ross, J. Clwn. Fhys. 1s 11950) 1561; N.L.Allinger and J.C.Tai,‘J. Am. Chem. Sod. 87 (1965)
2081; J.Kouteck$, J.efieG, J.Dubsky and K.Hiavaty, Theoret.
:
._ :
‘.
:
‘.j :
$2,.
“_ 15 September
chim. Acta 2 (1964) 462;. ‘:‘:” JCS?kaploto and YJ.I’Haya, Theoret. C+II, Acta 13 -.. : .(1969)225. : ,121 N.Tyutyulkov and F.F;atev, Theo&.-m. A+8 ... .: (1%7) 62. (31 Y.A.Krbglyak and E.Mozdor, Theoret Chim. Acta 15 (1969) 374. !4] ~.‘T&tyulkov,~F.Fratev and M.Ivaoova, Theoret Chin Acta 20 (1971) 385; [S] P.-O.L~wdin, Phys. Rev. 97 (1955) 1474. [6 ] Ta@Ies of interatomic distances axd configuration in
molecules and ions (The Chem. Sot., London; 1958). (7 1 G. Hiebaum. N. Tyutyulkov and hf. Ivanova, Zh. Tear. i * Ekqerim. Khim. (USSR) 6 (1970) 595. [ 81 N.Mataga and K.Nishimoto, Z. Phy.$k. C&em. (Frankftlrt) 13 (1957) 140. 191 J.i%ek, ‘Iheoret. Chk Ati 6 (1966) 292. [lo] R.L.FIury,E.W.Stoutand J.J.Rell; Theoret Chim. Acta 8 (1967) 203.