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Multiplet splittings in the photoelectron spectra of organic radicals: Trimethylenemethane
Volume 35, number
CHEMICAL
3
PilYSICS LETTERS
15
SeDtember 1
MULTELET SPLkmNGS i.N THE PHOTOELECTRON SPECTRA OF ORGANIC RADICALS: TRIMETHYLENEMETWANB David R. YARKONY and Henry F. SCHAEFER III Depariment of Cimnir~ Received
and Lrwrmce Berkeley Laborctmy,
University of CaiifGmia, B&xZey. Cdijiomia94720, USI
30 June 1975
Open shell seIf-consistent-field theory has been applied to systems arising from the photalozization of organic radics Specifically, the multiplet splittings of the . . lajle”’ electron configuration of C(CHa): h ~vc been invest&ted both BI ically and numerically. These exchange splittings arc found to be quite large and should dcftitely be considered in tie i
pietntion of the photoelectron
spectra of organic radic&.
In recent years photoelectron come an increasingly important the study of the electronic
spectroscopy has beexperimental taol in structure of molecules. Pres-
ent experimental techniques [1,2] are capable of measuring the ionization potential (IP) of both core and valence electrons and this has stimulated considerable thecxetical effort in an attempt to accurately determine these IPs [3,4]. Of late expcrimentai methods have been developed
which permit
the range of photo-
electron spectra (PES) to be extended from stable, closed shell 151 molecules to the more evanescent c&s of organic radicals [6] _ An important feature of the PES of these radicals should be the multiplet or exchange splittings arising from the open shell electron occupancies characteristic of these species. In fact this type of multiplet splitting has been observed in the core levels of a number of molecules, including some as large as di-t-butylnitroxide 17j _ tiowever valence level exchange splittings have yet to be identified in the PES of organic radicals. In this communication we report the results of a theoretical treatment of ihe trimet3ylenemethane radical (1)
0)
wl-tich demonstrate that valence level multiplet spli tings can be substantial, and must be considered in interpretation of the PES of organic radicals. Trim ylenemethane has been of particular interest since when Moffitr and Coulson [8] showed that its ten atom has the greatest x bond order attainable by a bon atom. The relevance of C(CH,)j to the questit of exchange splittings comes from the fact that the PES of two related organic compounds have been I termined. Dewar and Worley [9] have reported eig ionization potentials for the iron carbonyl comple: C(CH,)J-Fe(C0)3 and Koenig [lo] has studied 2 propylidene cyclopent-I ,3 diyl
ctw,
CH
i(
I H2C
12
I CH,
Dewar and Worley attributed their second measurec (at 9.15 eV) to trirnethylenemethane and estimate that this I? would faI! to 8.63 eV in the absence of Fe(W), part of the complex. They. a!so identify !! IP 2: 4 1.07 eV with C(CH& and not& excelIent a~ ment tith their calculated serni-empkic~ 77orbital ergy. Dewar and Morley do not merition ‘rhe possil
Voidme 35, nun@Yer3
I5 Seplcmber 1975
CHEMKAL PHYSICS LETl-ERS
of multiple: splittings in the PES. Koenig’s rsearch, althaugh not Gut complete, yielded a pair of peaks, centered ai, 8.6 eV and split by 0.4 eV. Preliminm in* dications are that these two peaks should be attributed to the doubly degenerate *E” state (in Djh symmetry), which has been perturbed by an unsymmetric environ-
TabIc 1 ‘Theoretical predictions of the positions of tf:c electroflic states ofC(CH:);. Encr&s are @en in ev relative to the triplet ground state of the neutral rzdi&l
I;rozen orbital Electron con&uuiation
State
approximation
Dir& SCI: calculations
ment: The theoretical approach followed here is anaio~ous to that used in our earlier study [l I] of the 3A; ground state of the neEtra1 radical. The ground electron coniigurat:on for C(CH2)3 is
... lag4e’4
la;’
le”
..* lai24cr4 la: 1er7
8.74
2EGs
10.15
2A:’ 2 E”
15.47
t 9.77
15.08
L3.85 14.62
18.24
2Aj:
1a;21e’42a~3a;‘Ze’44a;23e’4
!aF4er4 laizle”2
5.03
4A:
(3)
8.99
and the lowest I;WOorbital occ~pancjes for the positive ion are ._. la’2&‘4 la”21cr’ 2 2 2nd .. . 1a’&‘4 2
1a; lp,“2
(3
The ground state of the ion, resulting from (4) is a 2E” state, but the situation with respect to (5) is more complicated, wit!~ four different electronic states arising.
The single configuration
wavefunctions
for these
open-shell states may be written ;A’; : la~&lc!&leJff,
AE(zE” --f 2A;‘) = 2(X,
- Cx,) ,
(12)
where ,3c, =K{la’;, le”), %2 =K(Te_E, Iei> and the gs are the appropriate exchange integrals. Since K(i, i) > 0 [S J eqs. (9)-(ll) S!IOWthat the lA;l is the lowest lying state in the multiplet and that
(6)
E(4A.;) c: E(2E”) < E(2A;). 2A;’ : (2/61/2)la~81e~crle~cr
Reference
to table 1 shows our theoretic&
Sowever the exact location of the 2A;’ state relative to the 7 E” and 2A; states requires the numerical values of the above exchange integrals. Further as 3i 1 z q2 (see below) the ordering of the 2E” and 2A’; states is a delicate matter which cannot be Anally resolved until
esti-
mates of the lowest IP of trime~hy~enemethanc are in good agreement with the available experimental values [9,10] for related moIecules. It is worth noting that simple arguments f12] suggest electron correlation shoutd be Perhaps 1 eV greater for C(CH& than for its positive ion. However of particular interest here an the spltttings between the four elec:ronir: states tising from electron configura&o~ (5). -4ssuming ezch state described by a single configuration wavefunction 1121 coastmcted from a common set of I-@oiecufnr orb&, une can readily obtain analytical ex-
the effects ‘cf electron correlation [ 121 zre explicitly included in the wavefunctions As our common set of orbitals we selected those orbitaIs corresponding to the 3A; ground state of the C(CI-$ jS radical’:. The values of ‘%I and 312 which are 0.0652 and 0.0581 hartree, respectively, are seen to be sizeable and of comparal?le msgnitude, as mentioned earlier. We have &o carried out direct SCF cal-
cuf@ons on the five states arising from the electron occupancies (4) and (5). The restits from both these methods,
the direct SCF and frozen orbit& approti-
is gdequately
pressions for the multiplet splitting: 292
‘.
..
* However, similar results were obtakd using orbirais Wiationally determined for e&her the 2 E” or 4A” St&es oi the positive ion.
mation, are summarized in table 1. Note that the ordering of the 2A; and 7_E” states corresponding to eqs. (6) and (8) has been reversed by aliowing the orbit& to relax. Also note
1.5 September
CHEMICALPHYSICSLETTERS
Volume 35, number 3
that in neither
method
is the second
2E” state a rigorous upper bound to the true 2 E” state, since in each case the wavefunctions corresponding to the second “E” state is connected to the lower 2E” wavefunctiog through the hamiltotian.
This research was supported by the Energy Research and Development .4dministration and by the National Science Foundation, Grant G?4 1509X. Computations were performed on the Datacraft 602414 minicomputer, supported by the National Science Foundation, Grant GP-393 17
References [ 11 K. Siegbahn, C. Nordling, G. Johansson, J. Hcdmsn, P.F. Hedc’n, K. Iiamrin, U. Gclius,T. Bergmark, L.O.
Wcrme.
R b¶anno
and Y- Bze_r, ESCA applied
molecules (North-Holland,
i21 D,W, ?urn~r, C. Baker.
Amsterdam,
A.D. B&er
197.5
to free
1963).
and C.R. Brun”lc,
photoeiemon s~cctroscop~ Ilntersciencc, New York, 1970). [31 P.S. Bagus, in: Proceedings of the Symposium onX-~-’ Spectra and Electronic Structure of Matter, eds. A. bIolecu1~
FXZSSIC~
2nd G. Witch
(Univeisity
of Munich
P~CSS,
hkmich) p. 256. (11 Xf.E. Sch:vartz, Ken:klodern theoretical chemistry, cd. H.F. Schzet-cr (Plenum Rcss, New York. !975). ijl C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [61 T. Koenig, T. Balk and W. SneU, I. hm. Chem. Sot. 97 (197.5) 662. [71 D.W. Davis, R.L hktin, MS. BNUU and D.A. Shk!ey, J. Chcm.
Phys. 59 (1953)
4235.
181 C.X. Coulson, J. Chim. Fnys. Physiochim. Biol. 45 (1918) 243. f91 M.J.S. Dcwar and SD. Worley, J. Chem. Phys. 51 (1969 1672. [lOI T. Koenig, unpublished. 11’1 H-F. Schaefer, The clcctronic structure of stems and molecules: a survey of rigoroils quantum mechakl results (Addison-Wesley, Rrxding, 1972). [19-j D.R. Yxkony and M.F. Schaefer, J. Am. Chem. Eoc. U6 (1374) 37.54.
21
CHEMICAL
3
PilYSICS LETTERS
15
SeDtember 1
MULTELET SPLkmNGS i.N THE PHOTOELECTRON SPECTRA OF ORGANIC RADICALS: TRIMETHYLENEMETWANB David R. YARKONY and Henry F. SCHAEFER III Depariment of Cimnir~ Received
and Lrwrmce Berkeley Laborctmy,
University of CaiifGmia, B&xZey. Cdijiomia94720, USI
30 June 1975
Open shell seIf-consistent-field theory has been applied to systems arising from the photalozization of organic radics Specifically, the multiplet splittings of the . . lajle”’ electron configuration of C(CHa): h ~vc been invest&ted both BI ically and numerically. These exchange splittings arc found to be quite large and should dcftitely be considered in tie i
pietntion of the photoelectron
spectra of organic radic&.
In recent years photoelectron come an increasingly important the study of the electronic
spectroscopy has beexperimental taol in structure of molecules. Pres-
ent experimental techniques [1,2] are capable of measuring the ionization potential (IP) of both core and valence electrons and this has stimulated considerable thecxetical effort in an attempt to accurately determine these IPs [3,4]. Of late expcrimentai methods have been developed
which permit
the range of photo-
electron spectra (PES) to be extended from stable, closed shell 151 molecules to the more evanescent c&s of organic radicals [6] _ An important feature of the PES of these radicals should be the multiplet or exchange splittings arising from the open shell electron occupancies characteristic of these species. In fact this type of multiplet splitting has been observed in the core levels of a number of molecules, including some as large as di-t-butylnitroxide 17j _ tiowever valence level exchange splittings have yet to be identified in the PES of organic radicals. In this communication we report the results of a theoretical treatment of ihe trimet3ylenemethane radical (1)
0)
wl-tich demonstrate that valence level multiplet spli tings can be substantial, and must be considered in interpretation of the PES of organic radicals. Trim ylenemethane has been of particular interest since when Moffitr and Coulson [8] showed that its ten atom has the greatest x bond order attainable by a bon atom. The relevance of C(CH,)j to the questit of exchange splittings comes from the fact that the PES of two related organic compounds have been I termined. Dewar and Worley [9] have reported eig ionization potentials for the iron carbonyl comple: C(CH,)J-Fe(C0)3 and Koenig [lo] has studied 2 propylidene cyclopent-I ,3 diyl
ctw,
CH
i(
I H2C
12
I CH,
Dewar and Worley attributed their second measurec (at 9.15 eV) to trirnethylenemethane and estimate that this I? would faI! to 8.63 eV in the absence of Fe(W), part of the complex. They. a!so identify !! IP 2: 4 1.07 eV with C(CH& and not& excelIent a~ ment tith their calculated serni-empkic~ 77orbital ergy. Dewar and Morley do not merition ‘rhe possil
Voidme 35, nun@Yer3
I5 Seplcmber 1975
CHEMKAL PHYSICS LETl-ERS
of multiple: splittings in the PES. Koenig’s rsearch, althaugh not Gut complete, yielded a pair of peaks, centered ai, 8.6 eV and split by 0.4 eV. Preliminm in* dications are that these two peaks should be attributed to the doubly degenerate *E” state (in Djh symmetry), which has been perturbed by an unsymmetric environ-
TabIc 1 ‘Theoretical predictions of the positions of tf:c electroflic states ofC(CH:);. Encr&s are @en in ev relative to the triplet ground state of the neutral rzdi&l
I;rozen orbital Electron con&uuiation
State
approximation
Dir& SCI: calculations
ment: The theoretical approach followed here is anaio~ous to that used in our earlier study [l I] of the 3A; ground state of the neEtra1 radical. The ground electron coniigurat:on for C(CH2)3 is
... lag4e’4
la;’
le”
..* lai24cr4 la: 1er7
8.74
2EGs
10.15
2A:’ 2 E”
15.47
t 9.77
15.08
L3.85 14.62
18.24
2Aj:
1a;21e’42a~3a;‘Ze’44a;23e’4
!aF4er4 laizle”2
5.03
4A:
(3)
8.99
and the lowest I;WOorbital occ~pancjes for the positive ion are ._. la’2&‘4 la”21cr’ 2 2 2nd .. . 1a’&‘4 2
1a; lp,“2
(3
The ground state of the ion, resulting from (4) is a 2E” state, but the situation with respect to (5) is more complicated, wit!~ four different electronic states arising.
The single configuration
wavefunctions
for these
open-shell states may be written ;A’; : la~&lc!&leJff,
AE(zE” --f 2A;‘) = 2(X,
- Cx,) ,
(12)
where ,3c, =K{la’;, le”), %2 =K(Te_E, Iei> and the gs are the appropriate exchange integrals. Since K(i, i) > 0 [S J eqs. (9)-(ll) S!IOWthat the lA;l is the lowest lying state in the multiplet and that
(6)
E(4A.;) c: E(2E”) < E(2A;). 2A;’ : (2/61/2)la~81e~crle~cr
Reference
to table 1 shows our theoretic&
Sowever the exact location of the 2A;’ state relative to the 7 E” and 2A; states requires the numerical values of the above exchange integrals. Further as 3i 1 z q2 (see below) the ordering of the 2E” and 2A’; states is a delicate matter which cannot be Anally resolved until
esti-
mates of the lowest IP of trime~hy~enemethanc are in good agreement with the available experimental values [9,10] for related moIecules. It is worth noting that simple arguments f12] suggest electron correlation shoutd be Perhaps 1 eV greater for C(CH& than for its positive ion. However of particular interest here an the spltttings between the four elec:ronir: states tising from electron configura&o~ (5). -4ssuming ezch state described by a single configuration wavefunction 1121 coastmcted from a common set of I-@oiecufnr orb&, une can readily obtain analytical ex-
the effects ‘cf electron correlation [ 121 zre explicitly included in the wavefunctions As our common set of orbitals we selected those orbitaIs corresponding to the 3A; ground state of the C(CI-$ jS radical’:. The values of ‘%I and 312 which are 0.0652 and 0.0581 hartree, respectively, are seen to be sizeable and of comparal?le msgnitude, as mentioned earlier. We have &o carried out direct SCF cal-
cuf@ons on the five states arising from the electron occupancies (4) and (5). The restits from both these methods,
the direct SCF and frozen orbit& approti-
is gdequately
pressions for the multiplet splitting: 292
‘.
..
* However, similar results were obtakd using orbirais Wiationally determined for e&her the 2 E” or 4A” St&es oi the positive ion.
mation, are summarized in table 1. Note that the ordering of the 2A; and 7_E” states corresponding to eqs. (6) and (8) has been reversed by aliowing the orbit& to relax. Also note
1.5 September
CHEMICALPHYSICSLETTERS
Volume 35, number 3
that in neither
method
is the second
2E” state a rigorous upper bound to the true 2 E” state, since in each case the wavefunctions corresponding to the second “E” state is connected to the lower 2E” wavefunctiog through the hamiltotian.
This research was supported by the Energy Research and Development .4dministration and by the National Science Foundation, Grant G?4 1509X. Computations were performed on the Datacraft 602414 minicomputer, supported by the National Science Foundation, Grant GP-393 17
References [ 11 K. Siegbahn, C. Nordling, G. Johansson, J. Hcdmsn, P.F. Hedc’n, K. Iiamrin, U. Gclius,T. Bergmark, L.O.
Wcrme.
R b¶anno
and Y- Bze_r, ESCA applied
molecules (North-Holland,
i21 D,W, ?urn~r, C. Baker.
Amsterdam,
A.D. B&er
197.5
to free
1963).
and C.R. Brun”lc,
photoeiemon s~cctroscop~ Ilntersciencc, New York, 1970). [31 P.S. Bagus, in: Proceedings of the Symposium onX-~-’ Spectra and Electronic Structure of Matter, eds. A. bIolecu1~
FXZSSIC~
2nd G. Witch
(Univeisity
of Munich
P~CSS,
hkmich) p. 256. (11 Xf.E. Sch:vartz, Ken:klodern theoretical chemistry, cd. H.F. Schzet-cr (Plenum Rcss, New York. !975). ijl C.C.J. Roothaan, Rev. Mod. Phys. 23 (1951) 69. [61 T. Koenig, T. Balk and W. SneU, I. hm. Chem. Sot. 97 (197.5) 662. [71 D.W. Davis, R.L hktin, MS. BNUU and D.A. Shk!ey, J. Chcm.
Phys. 59 (1953)
4235.
181 C.X. Coulson, J. Chim. Fnys. Physiochim. Biol. 45 (1918) 243. f91 M.J.S. Dcwar and SD. Worley, J. Chem. Phys. 51 (1969 1672. [lOI T. Koenig, unpublished. 11’1 H-F. Schaefer, The clcctronic structure of stems and molecules: a survey of rigoroils quantum mechakl results (Addison-Wesley, Rrxding, 1972). [19-j D.R. Yxkony and M.F. Schaefer, J. Am. Chem. Eoc. U6 (1374) 37.54.
21