1300
allowed” S k
-
J . Phys. Chem. 1987, 91, 1300-1302 So radiative transitions.
ConcIusion The results of the present investigation firmly establish the formation of the L- (or butterfly-) shaped triplet excimers in naphthalene and related molecules. The radiative and nonradiative decay rates of the triplet excimers are about three orders of
magnitude greater than those of the corresponding triplet monomers, consistent with the prediction of an earlier study. Acknowledgment. We are very grateful to Professor Steve Scheiner of Southern Illinois University for bringing to our attention the quadrupole moment calculations of naphthalene. This work was supported in part by a grant from the Department of Energy.
Theoretical Study of the Structures and Stabilities of the (CO,),-
Ions
S. H. Fleischmant and K. D. Jordan* Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (Received: December 19, 1986)
Ab initio calculations using flexible basis sets and including the effects of electron correlation are used to examine various possible structures for the (C02),- species. These calculations reveal that the symmetrical DM and the asymmetrical CO,CO, forms of the anion are close in energy, with the former being about 0.2 eV more stable. The two forms of the anion give very different vertical detachment energies, with that calculated for the DU structure being in agreement with the experimental results.
Recently several experimental reports’-3 have appeared dealing with electron attachment to CO, clusters. Of fundamental importance are the questions whether the odd electron is localized or delocalized for a particular (C02), cluster anion and whether there is a change from localized to delocalized behavior for a certain cluster size. Even for the “simplest” such cluster, (CO&, this question has not yet been resolved. The experimental photodetachment studies] by themselves do not provide an answer to this question. Hartree-Fock calculations performed several years ago in our group indicated that the C02.C02-ion-molecule complex was 0.3 eV more stable than the most stable symmetrical structure, with the odd electron delocalized over the two C 0 2 group^.^^^ However, these calculations invoked a number of approximations, in particular, the neglect of electron correlation and the use of relatively small atomic basis sets, which limit their utility for determining the relative stability of these two structures. These approximations were imposed due to CPU time restrictions and to the limitations of the programs used to perform the calculations. With the development of efficient algorithms for evaluating gradients and for including electron correlation and with the increased speed of today’s computers, it is now possible to perform much higher quality calculations on this system. This fact, combined with the growing interest in the (CO,),- clusters, has led us to reexamine the dimer anion. The previous calculations used an extended 6-3 1G basis set generated by augmenting the 6-31G carbon basis set6 with a set of diffuse p functions to allow for the diffuse nature of the LUMO of CO, in bent geometries. In the present study two more flexible basis sets, 6-31+G and 6-31+G*, are considered. These basis sets’ include diffuse s and p functions (denoted by the ”+“), determined specifically for describing anions, on both the C and 0 atoms. The 6-31+G* basis set includes also d polarization functions. (Only the five unique components of the d functions are retained.) The geometries were optimized by using the Hartree-Fock procedure with the 6-3 l+G basis set and analytical gradients.* Electron correlation was included by means of second- and third-order Mdler-Plesset perturbation theory” using the 63 1+G* basis sets and the HF/6-3 l + G geometries. The second+ Present address: Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA 15213.
0022-3654/87/2091-1300.$01.50/0
TABLE I: Normal-Mode Vibrational Frequencies (em-’) of D Z d , DW and C,(COd2-‘‘ D2d
1886 (E) 1886 1348 (A,) 1211 ( B 2 ) 748 (AI) 710 (E) 710 706 ( B 2 ) 224 (A,) 222 (E) 222 66 ( B , )
2310 (A’) 1704 (A’) 1389 (A’) 1339 (A’) 771 (A‘) 656 (A”) 642 (A‘) 232 (A‘) 133 (A‘) 61 (A‘) 55 (A”) 10 (A“)
“The frequencies were obtained with the Hartree-Fock method using the 6-31+G basis set. bThe 49-cm-’ a, mode has an imaginary frequency, indicating that the planar anion is unstable to twisting. ‘The existence of very low frequency modes for the C, structure is consistent with the finding that the energy of this form of the anion varies very little as the “solvent” C 0 2 molecule is twisted out of the plane. and third-order results are referred to as MP2 and MP3, respectively. (1) Coe, J. V.; Snodgrass, J. T.; McHugh, K. M.; Freidhoff, C. B.; Bowen, K. H., preprint. (2) Quitevis, E. L. Ph.D. Dissertation, Harvard University, 1980. (3) Klots. C. E.; ComDton. R. N. J . Chem. Phvs. 1977. 67. 1779. Klots. C. E.;Compton, R. N. Ibid. 1978,69, 1636. Klots,-C. E. Ibid. i979, 71, 4172: Stamatovic, A.; Leiter, K.; Ritter, W.; Stephan, K.; Mark, T. D. Ibid. 1985, 83, 2942. Knapp, M.; Kreisle, D.; Echt, 0.; Sattler, K.; Recknagel, E. Surf. Sci. 1983,156,313. Kondow, T.; Mitsuke, K. J . Chem. Phys. 1985,83,2612. Alexander, M. L.; Johnson, M. A.; Levinger, N. E.; Lineberger, W. C. Phys. Rev. Lett. 1986, 57, 976. (4) Rossi, A. R.; Jordan, K. D. J . Chem. Phys. 1979, 70, 4422. (5) Yoshioka, Y.; Jordan, K. D. J . A m . Chem. SOC.1980, 102, 2621. (6) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2757. Dill, J. D.; Pople, J. A. Ibid. 1975, 62, 2921. Binkley, J. S . ; Pople, J. A. Ibid. 1977+66, 879. (7) Clark, T.; Chandrasekhar, J.; Spitnagel, G. W.; Schleyer, P. v. R. J . Comput. Chem. 1983, 4, 294. (8) Binkley, J. S.;Frisch, M. J.; Raghavachari, K.; DeFrees, D. J.; Schlegel, H. B.; Whiteside, R.; Fluder, E.; Seeger, R.; Pople, J. A,; Yates, J. H.; Sunil, K. K. GAUSSIAN 82, Harris/VOS version; Carnegie-Mellon University; Pittsburgh, PA, 1985.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6, I987
Letters 0
0
1301
TABLE 11: Energies and Stabilities of the Various (CO,),' Structures"
dissociation energy, eV
energy, a u
structure HF MP2 MP3 HF M P 2 M P 3 D2h -375.2295 -376.2043 -376.1737 D2d -375.2343 -376.2084 -376.1791 0.11 0.58 0.51 C,
-375.2426
-376.1970
-376.1712
0.19
0.27
0.30
"The results reported in this table were obtained with 6-31+G* basis set with geometries obtained from HF/6-3 1 +G calculations.
O, 1.167A
the symmetrical structures more than the C, structure, with the Dzd species predicted to be 0.31 and 0.22 eV more stable at the MP2 and MP3 levels of theory, respectively. An estimate of the importance of zero-point vibrational energies can be obtained using the S C F frequencies (reduced by 12%).'O With this correction the DZdstructure is found to be more stable by 0.27 and 0.18 eV at the MP2 and MP3 levels of theory, respectively. At the HF/6-31+G level of treatment the C, species is predicted to be bound (relative to co, COT) by 0.43 eV and the DZd structure by 0.25 eV. In the MP2 and MP3 approximations the DZdspecies is predicted to be bound by 0.58 and 0.52 eV, respectively and the C, species by 0.27 and 0.30 eV, respectively. The relatively small difference between the MP2 and MP3 stabilities suggests that higher order correlation effects may not be very important in determining the energy difference between the DU and C, structures. The adiabatic EA of CO, increases by 0.12 eV in going from the MP2 to the MP3 approximation, but it is essentially unchanged by the inclusion of still higher order correlation effects by means of fourth-order perturbation theory. This provides additional evidence that the MP3 approximation is adequate for the calculations on the dimers. At all levels of theory considered, the (CO,),- species are unstable with respect to 2C0, + e- and, hence, also to the van der Waals (CO,), dimer plus a free electron. The MP3 calculations give an adiabatic EA'] of (CO,), (assuming formation of the DZdanion) of -0.31 e v . For comparison we note that the corresponding MP3 calculations yield an adiabatic EA of -0.76 eV for CO,, consistent with the experimental value12 of -0.6 f 0.2 eV. Thus, the present calculations cast doubt on the 0.8 0.2 eV value for the EA of (C02), deduced by Quitevis., We estimate that the changes in the EA due to the use of larger basis sets and the inclusion of higher order correlation effects is likely to be less than 0.2 eV. Bowen and co-workers' have found that the vertical detachment energy of C02- is 1.40 eV while that for the dimer anion formed under their experimental conditions is greater than 2.3 eV. For C0,- the MP3 calculations give a vertical detachment energy of 1.2 eV, in good agreement with the experimental value.' For the C, and Dad forms of the (cO,),- we obtain vertical detachment energies of 1.7 and 2.8 eV, respectively, leading us to conclude that the experimental photodetachment spectrum derives from the DZdstructure. The present study shows that it is essential to include electron correlation effects when considering the relative stability of the symmetrical and asymmetrical forms of an anion such as (CO,);. Electron correlation is found to stabilize the DZdstructure about 0.4 eV more than the C, structure. This is apparently due to the presence of an additional bond (of order in the symmetrical species. Both the total energies and the comparison of the calculated and measured photodetachment energies lead us to conclude that the D2d form of the dimer anion is more stable than the C, ion-molecule complex. The results of this study also lead us to speculate that (CO,),will have two ion-molecule complex type structures, characterized as C02-.(C02)2and (C2O4).CO2. We further anticipate that the stabilization due to the addition of a second CO, "solvent" molecule to the CO2-CO2-complex will be somewhat greater than that for adding a C 0 2 molecule to the DZd C204-species. I f this is the
+
czo;
/imA
(CS)
0
Figure 1. Geometries of the DZd,D21, and C, forms of (C02),- as determined in the Hartree-Fock approximation using the 6-3 l + G basis set.
The optimizations were done using the 6-31+G rather than the 6-31+G* basis set to exploit the fact that polarization functions and electron correlation often act in opposite directions on geometrical parameters with the result that HartreeFock geometries obtained by using sp basis sets are frequently closer to the experimental geometries than are those determined by using spd basis sets. Complete MP2 or MP3 optimizations of the (CO,),species with the 6-31+G* basis set, which contains 108 contracted functions, would be very CPU time consuming even on a Cray X M P supercomputer. To establish that the inclusion of electron correlation in the geometry optimizations is not likely to alter the main conclusions of this study, calculations were performed for CO, and C02- using both HF/6-31+G and MP2/6-31+G* approaches. The MP2 and MP3 values for the vertical and adiabatic electron affinities (EA'S) of CO, or the vertical detachment energy of COzobtained by using these two sets of geometries are found to be nearly the same. Also, the energies of the D2d and C, forms of (CO,),- were changed by less than 0.01 eV when the CC bond length of the former and the distance between the COzand CO< in the latter were optimized by using the MP2/6-31+G* method. The gradient-optimized HF/6-31 +G geometries given in Figure 1 are very close to those reported previously by Rossi and Jordan? The Hartree-Fock normal-mode vibrational frequencies, summarized in Table I, indicate that both the DZdand C, structures are true minima and that the DZhstructure is a first-order transition state. Presumably the greater stability of the DZdstructure than the DZhstructure is due to the greater repulsion between the oxygen atoms in the latter. The energies of the C,, Du, and Dzhstructures and the stabilities of these species with respect to CO, COT are given in Table 11. From these results it is seen that electron correlation stabilizes
+
(9).Bartlett, R. J.; F'urvis, G . D. Phys. Reu. A 1979, 20, 1313. Pople, J. A.; Krishnan, R.;Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem. 1978, 14, 545. (10) Normal-mode frequencies determined in the Hartree-Fock approximation are generally larger than the experimentally derived quantities. The neglect of electron correlation tends to make potential energy surfaces rise too steeply, causing the calculated frequencies to be too high. Numerous studies have found that an overall reduction of all calculated frequencies by about 12% considerably improves the agreement with experiment. (1 1) In determining the adiabatic EA of (COz)z,we have taken the binding energy of the neutral van der Waals dimer to be 0.06 eV. This value is from: Murthy, C. S.; Singer, K.;McDonald, I. R. Mol. Phys. 1981, 44, 135.
*
(12) Cooper, C. D.; Compton, R. N. J . Chem. Phys. 1973, 59, 3550.
J. Phys. Chem. 1987, 91, 1302-1305
1302
case, then these two forms of the trimer could be nearly isoenergetic. Calculations are under way to examine this possibility. Acknowledgment. This research was carried out with support from the National Science Foundation. The calculations were
carried out on a Harris HlOOO minicomputer funded in part by the N S F and on the Cray XMP supercomputers at the Boeing and the Pittsburgh Supercomputer Centers. We thank Professor K. Bowen for helpful discussions of his work and for comments on the manuscript.
Hole-Burning Spectroscopy of Polar Molecules in Polar Solvents: Solvation Dynamics and Vibrational Relaxation Roger F. Loring, Yi Jing Yan, and Shaul Mukamel*+ Department of Chemistry, University of Rochester, Rochester, New York 14620 (Received: December 29, 1986)
The time- and frequency-resolved hole-burning line shape of polar molecules in a polar solvent is expressed in terms of gas-phase spectroscopic parameters of the solute, vibrational relaxation rates, dielectric properties of the solvent, and the temporal profile of the pump pulse. At short times, a progression of narrow vibronic holes is predicted. As a consequence of solvent relaxation, these holes broaden and undergo a red shift. This behavior has been observed in the measurements of Shank et al. on cresyl violet in ethylene glycol. We propose hole burning as an alternative to fluorescence measurements in probing solvation dynamics.
Hole-burning (saturation spectroscopy) measurements with femtosecond time resolution of cresyl violet in ethylene glycol have recently been reported by Shank and co-workers.' In these experiments, the sample is excited with a 60 femtosecond pump pulse, and the absorption spectrum is measured with a 10 fs probe pulse. If the delay time between pump and probe is short, the absorption spectrum shows a decrease in absorption (hole) at the pump frequency, as is expected for a system with an inhomogeneously broadened absorption spectrum. In addition, two holes of smaller intensity occur 600 cm-I to the red and to the blue of the central hole. Stimulated Raman measurements have shown that the dominant Raman-active vibration in cresyl violet has a frequency of 590 As the delay between pump and probe is increased, the holes undergo substantial broadening and a red shift, and a t a delay of 150 fs, the vibronic structure is lost and the hole width is comparable to the width of the entire absorption spectrum. The temporal evolution of the absorption spectrum is ascribed by Shank et al. to vibrational relaxation in cresyl violet. We have developed a theory of the hole-burning spectroscopy of a polar molecule in a polar solvent that includes both vibrational relaxation of the solute and the reorganization of the solvent about the electronically excited solute. We propose that the broadening and red shift of the vibronic holes in the cresyl violet spectrum may arise from the relaxation of solvent dipoles around the electronically excited dye molecule. We consider a solution composed of solute and solvent molecules. The solute molecules are present in sufficiently low concentration that interactions among them are negligible, and we may treat a single solute in its solvent environment. The differential absorption spectrum, A a ( w 2 ) , is defined to be the difference between the absorption coefficient at w2 in the absence of a pump pulse and the absorption coefficient at w2 measured with a probe pulse that follows a pump pulse. The differential absorption a t w2 is related to E2(w2),the amplitude of the probe field, and PNL(w,), the nonlinear polarization of the medium3 by
A 4 4 = -(4aw,/c)
Im IFNL(w,)/E*(w,)I
(1)
FNL(w2) is the Fourier transform of PNL(7),the nonlinear polarization of the medium at time
7.
'Camille and Henry Dreyfus Teacher-Scholar.
0022-3654/87/2091-1302$01 S O / O
pNL,the nonlinear contribution to the density matrix, is the dif-
ference between the full density matrix and that part of the density matrix that is linear in the radiation-matter interaction. In eq 2b, 1is the transition dipole operator, n is the number density of solute molecules, and Tr denotes the trace. Substitution of the linear part of the density matrix into the right side of eq 2b yields the linear polarization, which, when inserted into the right side of eq 1, yields the absorption spectrum in the absence of a pump pulse. We shall evaluate pNLto third order in the radiation-matter interaction4s5for the following model. The solute is taken to be a polyatomic molecule with two electronic states. The molecular energy levels are shown in Figure 1. The labels a and c denote vibronic states in the manifold of the ground electronic state of the solute, while b and d refer to vibronic states in the excited-state manifold. The influpce of the solvent on Aa is expressed by the solvation coordinate U(t),an operator that represents the difference between the interactions of the solvent with the excited-state solute and with the ground-state solute h
o(lct)= exp(ihet/h)C(Vme - Vmg)exp(-ihet/h) m
(3)
In eq 3, he is the Hamiltonian of the solvent in the presence of the electronically excited solute and Vme( Vmg)is the interaction between the solvent molecule labelled m and the excited-state (ground-state) solute. We adopt a semiclassical approach in which the solute is treated quantum mechanically-but the solvent is treated classically. We replace the operator U(t) by a stochastic variable U(t), with mean ( U ( t ) ) . Prior to the excitation of the (1) (a) Shank, C. V.; Fork, R. L.; Brito Cruz, C. H.; Knox, W. In Ultrafast Phenomena V; Fleming, G . R., Siegman, A. E., Eds.; Springer: Berlin, 1986. (b) Brito Cruz, C. H.; Fork, R. L.; Knox, W. H.; Shank, C. V., to be published. (2) Werncke, W.; Lau, A.; Pfeiffer, M.;Weigmann, H. J.; Hunsalz, G.; Lenz, K. Opt. Commun. 1976, 16, 128. (3) Shen, Y. R. The Principles of Nonlinear Optics; Wiley: New York, 1984; p 216. (4) Loring, R. F.; Yan, Y. J.; Mukamel, S. Chem. Phys. Lett., in press. ( 5 ) Mukamel, S. Phys. Rep. 1982, 93, 1; Adu. Chem. Phys., in press. Sue, J . ; Yan, Y. J.; Mukamel, S. J . Chem. Phys'. 1986, 85, 462.
0 1987 American Chemical Society
