2034 (3) W. McFariane, 0. Rev.. Chem. Soc.,23, 187 (1969). (4) J. A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys., 43, S129 (1965); J. A. Pople and G. A. Segal, bid., 43, 5136 (1965); 44, 3289 (1966). (5) J. A. Pople and D. L. Beveridge, “Approximate Molecular Orbital Theory”, McGraw-Hill, New York, N.Y., 1970. (6) J. A. Pople, D. L. Beveridge, and P. A. Dobosh, J. Chem. Phys., 47, 2026 (1967). (7) (a) J. A. Pople, J. W. Mclver, Jr., and N. S. Ostlund, J. Chem. Phys., 49, 2965 (1968): (b) L. Salem and P. Lobe, ibid.. 43, 3402 (1965). (8)G. Binsch. J. B. Lambert, B. W. Roberts, and J. D. Roberts, J. Am. Chem. Soc., 86, 5564 (1964); A. J. R. Bourn and E. W. Randall, Mol. Phys., 8,567 (1964). (9) A. Rauk, J. D. Andose. W. G. Frick, R. Tang, and K. Mislow. J. Am. Chem. SOC.,93, 6507 (1971). (10) P. E. Stevenson and D. L. Burkey, J. Am. Chem. SOC.,96,3061 (1974). (11) J. W. Moskowitz and M. C. Harrison, J. Chem. Phys., 43, 3550 (1965). (12) R. E. Kari and I. G. Csizmada, J. Chem. Phys., 58, 4337 (1972).
(13) The data of Table Ill, ref 12, are fit to a third -ree polynomial In the outof-plane angle. (14) G. Herzberg. “Infrared and Raman Spectra”, Van Nostrand, Toronto, 1945. (15) J. D. Swalen and J. A. Ibers, J. Chem. Phys., 36, 1914 (1962). (16) Calculations employ computer programs CNINDO. by P. A. Dobosh. Quantum Chemistry Program Exchange (Indiana University), Program 141, which was modified for use in this study, and ATCOOR,by J. E. Nordlander. (17) Reference 7a, Table II. (18) (a) R. Wasylishen and T. Schaffer, Can. J. Chem., 50, 2989 (1972); (b) hid., 51, 3087 (1973). (19) Reference 9, p 6508. (20) (a) M. Hollander and D. A. Wolfe, “Nonparametric Statistical Methods”, Wiley, New York, 1973; (b) W. H.Kruskal and W. A. Wallis, J. Am. Stat. Assoc., 47, 583 (1952); (c) 0. J. Dunn. Technometrics, 6, 241 (1964). (21) M. S. Gordon and H. Fischer, J. Am. Chem. SOC.,90, 2471 (1968); ref 9 and 10.
The Electronic Structure of Pyrazine. A Valence Bond Model for Lone Pair Interactions Willard R. Wadt’ and William A. Goddard III* Contribution No. 4970 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91 109. Received September 23, 1974
Abstract: A valence bond (VB) model is developed to describe the interaction of the lone pair excitations in pyrazine. Extensive a b initio minimal basis set (MBS) configuration interaction (CI) calculations show that the description of the n cations and nr* states of pyrazine afforded by the VB model is more accurate than that afforded by the molecular orbital ( M O ) model proffered by Hoffmann. The VB picture of the n cations and nr* states involves the interaction (resonance) of two equivalenr, localized excitations. The resultant splitting is large (1 to 2 eV) because of a slight delocalization of the n orbitals induced by the Pauli principle. (The n orbitals remain 90% localized on the nitrogens.) The splitting of the nr* states is comparable to that of the n cations because the T* orbital is delocalized, even though the excitation process is localized on one nitrogen. The MBS CI calculations indicate that the lowest ionization potential of pyrazine corresponds to the 2A,(n) state. Calculations on the lowest Rydberg states indicate that they involve excitations out of an n orbital rather than a r orbital, in opposition to earlier spectroscopic assignments. Finally, the calculations show that the forbidden 1 ‘B2,(nr*) state is 1 eV higher than the allowed l’B3,(nr*) state, so that the perturbations observed in the absorption spectrum must be ascribed to another source.
I. Introduction The nature of the.excited states of pyrazine has generated great interest among spectroscopists and theoreticians for many years.2 In addition to the R R* transitions, analogous to those of benzene, one expects new n R* transitions involving the nonbonding (or lone pair) orbitals on the nitrogen. Since there are two nitrogens in pyrazine, the question arises as to how the states involving excitations from the two different nitrogens interact with one another. With the advent of photoelectron s p e c t r o ~ c o p y the , ~ question has been extended to the interaction of the two possible n cations. Two models for the interaction of the lone pairs have been previously developed, namely, the exciton model of ElSayed and Robinson4 and the molecular orbital ( M O ) model of H ~ f f m a n nThe . ~ M O model has had good success in elucidating the photoelectron spectra (vide infra). In this paper we present a n alternative model based on valence bond (VB) ideas. A b initio minimal basis set (MBS) calculations have been carried out to test the usefulness of the VB model. In these calculations, emphasis has been placed on describing the na* excited states and the n cations.
-
-
n
n i m N
N a n ,
U
U
lb
la
and lb.6 The nonbonding orbitals are represented by
Q and the electrons by dots. In the VB model the lone pairs (nl and n,) are localized and equivalent, so that the ground state wave function is
where @‘core represents the remaining electrons. Now consider ionization of one of the lone pair electrons. One can remove the electron from either the left or right lone pair. These equivalent ion states are combined (resonance) to form two n cation states, *A, and 2Blu
n
L
The wave functions in this approximation are7
11. Qualitative VB Model (A) n Cations. To begin with, the VB view of the lone pairs in the ground state of pyrazine is represented by l a
Journal o f t h e American Chemical Society
n
N
N
/ 97:8 / April 16. 1975
*(‘A,) = *(2Bi u ) =
(QL (QL
+
q R ) / h ( 1+ S )
- qkR)/ml?)
2035 where8
*,
.~ 3 0 1 ~[(~,,,,,)n12n,cup... opal
= a[(+,,,,)n,2nlcrfi..
(3 1
=
(4)
andg
s
=
(*L
~
I
(51
qR)= -(nl n,)
The energy separation between these n-cation states is given by A E = E?A,)
trons can be symmetrically coupled or "paired up". As a result, electrons become partitioned into singlet (symmetric) pairs, e.g., CC, CH, and CN u bonds, T bonds, 1s pairs, and lone pairs. The interaction between the singlet-coupled pairs is repulsive, so that the orbitals in different pairs tend to become orthogonal to one another. In the case of the nonbonding orbitals (singly or doubly occupied) nodal planes are expected to develop as shown in 3 in order to make the n orbital orthogonal (Pauli principle) to the ucc and u c ~ bonding pairs. Note that the nodal patterns of the n orbitals
- E(~B,,)
3
A E = 2(9L13C/*R) - ~ S ( * L / ~ C / * L + ) dS2)
(6)
Since is taken to be the same in \ k and ~ \kR,' we need only consider the nonbonding orbitals nl and n, in evaluating (6). Moreover, the one-electron terms dominate the two-electron terms'O so that (6) becomes [using S = 4 1 , from ( 5 ) ] AE
2(*Llhl*d = 2[-S,r(h11
+
2S1,('kL~h/3J
+ hrr) - hi,.] + 2~,,(2h,, +
s,, h1r
h11)
favor a negative overlap. Thus, the effect of the Pauli-induced orthogonalization is to decrease Sir (algebraically) and it could make SI, negative. In fact, we find that the overlap is 0.0156 prior to orthogonalization and -0.106 after orthogonalization. Using (8), the Pauli orthogonalization reverses the predicted state ordering, leading to the 2A, state below the *BI,,. (B) n?r* States. Now we turn to the nx* states. In 4 we show the ground state of pyrazine again except that the x electrons are included (represented by circles, indicating 2p orbitals perpendicular to the plane of the paper) and are shown coupled into the two VB Kekul6 structures. The tie
Qa
co
4
-
lines indicate a pair of orbitals singlet coupled into a x bond. The simplest VB model for the n x* excitation involves promotion of an electron from a nonbonding orbital to the pn orbital on the same nitrogen. In this manner electroneutrality of all the atoms is maintained. There are three ways to pair the A orbitals into bonds in this case. Note that
= (nJn,) =
(n1
I h 1 nr)
hll = (nl/hlnl)
1 1
hrr = (nr h nr).
5b
5a
Equation 7 has the same form as the one-electron exchange energy for the H2 molecule, which is dominated by Slrtr,, where t represents the kinetic energy operator." Since t , , is positive A E a Si, (8) Thus, we arrive a t the very simple and intuitively reasonable result that the splitting energy is proportional to the overlap of the nonbonding orbitals. Since the nitrogens are well separated (2.79 A), one would .expect the overlap of the atomic hybrid nonbonding orbitals to be quite small and positive; hence, considering only the n orbitals one would expect AE to be quite small and positive (that is, 2Blu lower). However, the effects on the atomic n orbitals of the other u and x electrons present in pyrazine must be taken into account. Toward this end, we solve for the optimal wave functions [designated generalized valence bond (GVB)] of the form given in (1) and (2). Some rehybridization and scaling of n orbitals is expected, but the most important effect is induced by the Pauli principle. Because of the Pauli principle, no more than two elec-
5c
-
although the electron promotion (n x ) is assumed to be localized on one nitrogen, the resulting unpaired x orbital is on either the ortho carbons or on the para nitrogen. Exciting a lone pair electron from the right nitrogen leads to a comparable set of nx* configurations which must be combined (resonance) with those in 5 to get states of the correct total symmetry. Using the same arguments as be-
&
6
fore, the splitting of the nx* states is expected to be proporWadt, Goddard
/
Electronic Structure of Pyrazine
2036 tional to the product of the lone pair and laps.
orbital over-
A*
AE = E(B~,)- E(B,,) = Snln,S,l*rr+
(9)
The A* orbitals are quite delocalized, so that the splitting energy of the n r * states is expected to be only slightly smaller than that of the n cations. Determining the sign of Snpn,*and, hence, AE requires examination of the three couplings of the a orbitals. In 7 we show the approximate position of the nodal planes that will be induced by the Pauli principle to make the P* orbital orthogonal to three pairs of P electrons. (The u structure is suppressed). Making the phases of the three structures con- , b .
where SI, = (rill n,). The separation of the orbital energies, A€, for n+ and n- is A€ =
c(n,) - c(n,) = ( n , ( x ( n , )
- (n-/xlnJ =
or by arguments similar to those used before A € a -Si,
The splitting of the orbital energies is proportional to minus the overlap of the lone pairs. Since for localized n orbitals SI, is small and positive, we have 7a 7b 7c sistent, we see that the A* orbital will have the form
/,-, /
,
\
(-$\
‘ # .- ,
.-/‘
8
so that the overlap, SnpAr*, will be positive and A E = E(B3,)
-
E(B2,)
~' Our n-r CI excitation energies are in reaOur calculations (vertical excitation energies) show only sonable agreement with experiment, being high by 0.1-0.3 one state proximate to the IB3,. namely the 3 B ~ U ( a a *state ) eV, while the POL CI's lead to excitation energies that are (calculated separation 0.16 eV). Although the adiabatic entoo low by 0.1-0.3 eV. The singlet-triplet splitting is overergy of the 3Bl,, is known to be 0.5 eV lower than the adiaestimated by 0.2 eV. batic energy of the IB3,, state,42 our calculations indicate (C) Comparison with Previous Theoretical Calculations. that 3Blu and 'B3, potential surfaces cross (or are very close The only previous a b initio study of the excited states of pyrazine was that of Hackmeyer and' Whitten (HW).36 to each other) for configurations near the ground state geometry (at energies near 4 eV). Although the interaction of They employed a basis set comparable to our MBS the states is spin forbidden, a strong spin-orbit interaction D Z ( r ) and with the same geometry except that the C H Table IX Vertical Ionization Potentials (in eV)
n POL (2) C1
r
--
+
+
Journal of the American Chemical Society
1 97.9 1 April
16, 1975
2043 Table XI.
CI Results (eV)
State
HF CI
s CI
GVB CI
n POL(2) CI
n POL(3) CI
0.oa
4.64 5.47 5.17 6.64 6.62 6.76 7.75 8.68 6.02 5.46 9.55 9.73
0.oa 3.96 4.94 4.02 5.83 5.79 5.79 7.09 6.49 5.47 4.62 8.24 8.23
10.53 11.19
9.98 10.90
7.45 13.55 13.55
6.92 13.18 12.70
9.69
9.48
10.05
7.94
0.00 3.45 4.23 4.14 4.70 5.34 5.37 5.38 5.41 5.59 5.58 6.68 6.83 6.97 7.33 7.80 7.88 8.33 8.47 9.20 9.04 9.04 9.44 9.87 9.64 10.93
0.00 3.25 4.07 4.08 4.56 5.10 5.12 5.30 5.34 5.46 5.49 6.51 6.65 7.03 7.41 7.80 7.85 8.27 8.42 8.72 9.04 9.01 9.42 9.41 9.65 10.52
0.00 3.10 3.9 1 4.07 4.41 4.88 4.90 5.12 5.26 5.36 5.41 6.27 6.41 6.54 6.93 7.67 7.73 7.93 8.09 8.62 8.85 8.90 9.11 9.31 9.34 10.36
1'Ag(GS) 1'B,,(nn*) l'B,,(nn*) 1 3 ~ , ~ ( ~ ~ * ) 13B,g(nn*) 13Au(nn*) 1'A,(nn*) 1'Bzg(nn*) l'B,,,(nn*) 13BzU(nn*) 2 3 ~ , ~ ( ~ ~ * ) l3BIg(nn*) 1'BIg(nn*) 2 'Ag(nn*)d 33B,,(nn*)d 1' A g ( n n * ) 13BJg(nn*) 23~,~(~~*) 2'BZg(nn*) 2 3 ~ , ~ ( ~ ~ * ) 3 'Ag(nn*) 1'B3g(nn*) 23~,~(~~*) 1'BIu(nn*) 2'B,,(nn*) 2'BZU(nn*)
nw
Exptlb
0.0a 3.56 4.22 4.11 4.99 5.14 5.22 5.65 5.29 5.39 5.41 6.89 7.04 7.33 7.73 7.64 7.79 8.31 8.47 8.38
3.2-3.3 3.8-3.9 3.4-33
4.8-4.9
6.5-6.6
9.10
7.6 -7.7
9.95
aThe ground state energies (au) from left to right are -261.95270, -261.95270, -262.04408 (-262.04180), -262.05674 (-262.05421), -262.05872 (-262.05613), -262.3579. The CI energies in which only the n space was used are listed parenthetically. bReferences 2 and 47. CReference 42 (adiabatic excitation energy). dDominant configurations involve a double excitation, n --* n*,n --t n*. Table XII.
Singlet Rydberg Adiabatic Excitation Energies (eV) State
'Ag n+(ag) -+ 3s
3Py 'B3U 3Px ' B , U --* 3Pz 'Ag 3dyzC %g 3dyz 'Bzg 3dxz 'B1g 3dxy 'Ag + 3 d Z 8 'Big n(blg) 3s 'B3U 3Py lB,u --* 3Px 'A, 3Pz 'B,g 3d,zC 'Bzg 3dyz 'Ag 3dxy 'B3g 342 'Big -+ 3dZxC 'Bzu
+
-+
-+
-+
-+
+
+
-+
-+
-+
-+ -+
-+
'A, core
'n core
6.60 7.23 7.32 7.38 7.72 7.93 8.06 8.08 8.17 7.27 7.87 8.13 8.30 8.39 8.76 8.82 8.92 9.15
6.58 7.13 7.33 7.41 7.74 7.92 8.11 8.06 8.23
'B,, core
Exptla
fcalcdb
6.84
7.33 x 10-3 1.98 x 9.22 x l o 4
6.75
7.39 7.88 8.24 8.31 8.46 8.75 8.84 8.95 9.18
5.52 x 10-3 7.57 x 10-3
a Reference 54. bfcalcd is the (dipole) oscillator strength calculated using IVO's obtained with the 'Ag core. CThe 3d,,z 3dxz-yz orbitals are not properly described since the diffuse functions were partitioned into u and TI sets.
is expected between the two states.52 Therefore, in the advent of near degeneracy of the lBju and 3 B ~ potential u surfaces, the 3 B l , state is a plausible origin of the perturbations observed in the 1B3ubands. (D) Rydberg States. (1) Excitation Energies. In the previous section, we ruled out the possibility of another In=* or IT=* state being in the vicinity of the IB3, state. However, there is a possibility that the lowest Rydberg singlet state, namely the lA,(n 3s) state, is near the 'B3,, state. At first, this sounds preposterous in light of the vacuum uv work of Parkin and Innes (PI)53and Scheps, Florida, and Rice (SFR)54 who observed the lowest allowed Rydberg singlet (presumably n 3p) a t 6.75 eV. However, in water the ' B l ( a 3s) Rydberg state is 2.5 eV lower than the ' B ~ ( T 3p,) state. The large separation arises from the fact that the OH bonds in water are strongly polarized toward the oxygen so that the electron in the 3s orbital
-
-
- x ~ - y and ~
"sees" the protons; the 3s orbital tightens and lowers the energy.I6.l7 Therefore, we calculated the energies of the lowest Rydberg states in pyrazine using the IVO method,I6 which has been successfully applied to ~ a t e r . Singlet ~ ~ . ~ ~ excitation energies were calculated for the lowest Rydberg states arising from excitation of an electron from either a nonbonding orbital or the most loosely bound ?r orbital. The 1VO calculation yields directly the stability (ionization potential) of the excited (Rydberg) orbitals; to obtain excitation energies, we subtract the stability of the Rydberg orbital from the experimental adiabatic ionization potentiali6 (9.28 eV for n and 10.11 for T ) . This ~ procedure assumes that the potential surfaces of the Rydberg state and appropriate cation are similar, so that the differences in the adiabatic and vertical excitation energies are the same. The results of the IVO calculations are given in Table XII. Two sets of calculations were made, one using a Wadt, Goddard
/ Electronic Structure of Pyrazine
2044
'c-c "
the 3u Rydberg orbitals of pyrozine
N\
'c-
c, -c the 3 7 Rydberg orbitals of pyrazine
/
N,
I
c'
excitafim from Iblq (nl
exifation from 6oq (nJ
--l 13s
3s
!
I
1
L X = l bohr
1
i
7
X = l Dohr
I_
i Y
4
i
Y
.........
i Y
,, ,
,
,
...
....... .
I
.IS
