5642
J. Phys. Chem. 1996, 100, 5642-5648
Low-Lying Electronically Excited States of CH3Cl: Comparison of Theory and Experiment Dana Nachtigallova, Daniel E. Love, and Kenneth D. Jordan* Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260 ReceiVed: October 17, 1995; In Final Form: January 23, 1996X
Electron energy loss spectroscopy is used to determine the energies of the low-lying singlet and triplet states of methyl chloride. The experimental results are interpreted with the aid of ab initio calculations. The triplet n f σ*(C-Cl) state is found to lie about 0.4 eV below the singlet n f σ*(C-Cl) state. Both the electron energy loss measurements and the calculations indicate that it is possible to distinguish singlet and triplet states derived from the n f 4s and n f 4p excitations.
1. Introduction The problem of Rydberg/valence mixing is of considerable importance in the interpretation of optical and electron-impact spectra of molecules.1,2 Although simple MO theory leads one to expect valence excited states in molecules such as CH3F, (CH3)2O, and (CH3)3N, there is little or no evidence of such states in the singlet manifolds of these molecules.2 In the words of Robin,2 the expected valence states have “dissolved in the Rydberg sea”. In contrast, CH3Cl, (CH3)2S, and (CH3)3P all display valence transitions in their optical spectra. This can be understood in terms of the longer C-X (X ) heteroatom) bonds in these molecules as compared to their first-row counterparts, leading to lower lying σ* orbitals.3 This, in turn, causes the lowest valence transitions in the singlet manifold to drop below the Rydberg states. In this work we focus on the CH3Cl molecule, presenting the results of electron energy loss measurements as well as electronic structure calculations using the single-excitation configuration interaction4 (CIS), complete-active-space selfconsistent-field (CASSCF), and multireference MP2 (CASPT2)5 methods. Although CH3Cl has been studied previously, by means of both optical spectroscopy6-10 and trapped-electron spectroscopy,11,12 uncertainties exist in the assignments of some of the Rydberg states, evidence for the triplet σ(C-Cl) f σ*(C-Cl) valence state is lacking, and only indirect evidence exists for the singlet σ(C-Cl) f σ*(C-Cl) state.2 In addition, surprisingly little theoretical work has been done on the excited states of methyl chloride. The coupling scheme appropriate for describing the low-lying Rydberg states of CH3Cl is not immediately clear. The two limiting cases are the (Ωc,ω) and Russell-Saunders L-S coupling schemes.13 Most analyses of the low-lying Rydberg states seen in optical absorption spectra of CH3Cl have made use of the (Ωc,ω) coupling scheme, in which the Rydberg electron is viewed as being very weakly coupled to the 2E ground cationic state, formed by removal of an electron from a lone-pair (n) orbital. In this limit, it would not be possible to distinguish between singlet and triplet Rydberg states and the n f n′s, n f n′p, and n f n′d transitions, where n′ ) 4, 5, ... is the principal quantum number, would each give rise to a doublet, with the splitting being due to the spin-orbit coupling in the cationic core. The introduction of spin-orbit interactions between the Rydberg electron and the appropriate core levels could then result in additional splittings. In the L-S coupling scheme, all electrons are treated on an equal footing and are coupled to give singlet and triplet states. X
Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-5642$12.00/0
The spin-orbit interactions are then considered as a secondary perturbation. The L-S coupling scheme is most useful when the interaction of the Rydberg electron with the core electrons is greater than the spin-orbit interaction in the cation core. Interestingly, although most analyses of the low-lying Rydberg states of CH3Cl have assumed that the (Ωc,ω) coupling scheme is appropriate, experimental studies of HCl14,15 show that the low-lying n f 4s and n f 4p Rydberg states of this species are predominantly singlet or triplet in character. To the extent that the couplings are comparable in CH3Cl and HCl, the n f 4s and n f 4p states of CH3Cl should also be fairly well described in the L-S coupling scheme and would thus be either predominantly triplet or singlet in character. Consequently, there would be significant differences between electron energy loss spectra obtained with low and high residual electron energies, with spectra obtained with low residual energies favoring the predominantly triplet states and spectra obtained with high residual energies favoring the predominantly singlet states. 2. Methodology 2.1. Experiment. The electron energy loss spectrometer (EELS) used in this study has been described elsewhere,16,17 and only a brief description is given here. The EELS system consists of a single-stage trochoidal analyzer18 to select the energy of the incident electrons, which are passed through a static cell where scattering with the target gas takes place, and a dual-stage trochoidal analyzer to energy analyze the scattered electrons. The electrons are counted at a dual microchannel plate detector. This spectrometer typically attains a resolution of 60-80 meV.17,19 However, obtaining adequate signal was problematical for CH3Cl due to its interactions with the hot filament and electrodes, and somewhat poorer resolution was employed in order to enhance the signal intensity. In spite of this, the energies determined for the various electronic transitions were reproducible to 50 meV from spectrum to spectrum. Calibration was achieved by fixing the energy loss scale in the spectrum obtained with a residual energy of 20 eV to the sharp feature at 9.20 eV in the optical spectrum.9 2.2. Theory. The calculations of the energies of the excited states were carried out neglecting spin-orbit interactions. The CIS procedure uses molecular orbitals (MOs) determined from a Hartree-Fock (HF) calculation on the ground state and describes the excited states as linear combinations of configurations that are singly excited with respect to the HF ground state. This approach allows for the configuration mixing essential for describing the zeroth-order wave functions when there are orbital degeneracies. However, because it does not describe dynamical © 1996 American Chemical Society
Excited States of CH3Cl correlation effects, it may not correctly order valence and Rydberg states. The CIS calculations were carried out using the Gaussian 92 program.20 The more computationally demanding CASPT2 method5 treats both dynamical and nondynamical correlation effects. In this method, for each root of interest, a CASSCF calculation is carried out in an appropriate active orbital space, and the resulting orbitals are used to carry out a multireference MP2 calculation allowing for excitations from all valence orbitals and using all configurations from the CASSCF calculation as references. The CASSCF and CASPT2 calculations were carried out using the MOLCAS-3 program.21 The major challenge in the CASPT2 calculations is the selection of suitable active spaces. Our original goal was to treat all electronically excited states of CH3Cl derived from n f σ*(C-Cl), σ(C-Cl) f σ*(C-Cl), n f 4s, n f 4p, and n f 4d single excitations. Hereafter, the σ(C-Cl) and σ*(CCl) orbitals will be denoted as σ and σ*, respectively. In C3V symmetry, the lone-pair orbitals are of e symmetry, the valence σ, σ*, and 4s Rydberg orbitals are of a1 symmetry, the 4p Rydberg orbitals give rise to e and a1 orbitals, and the 4d Rydberg orbitals give rise to an a1 and two e orbitals. Combining these occupied and virtual orbitals gives a total of four e and five a1 orbitals for inclusion in the active space. In C1 symmetry, in which the calculations are actually performed in order to avoid problems due to symmetry breaking, these result in a total of 13 orbitals, which comprise the active space for the CASSCF calculations. A total of 14 electronic statessseven E, four A1, and three A2 states (of both singlet and triplet multiplicity)sare obtained from the σ f σ*, n f σ*, n f 4s, n f 4p, and n f 4d single excitations. In C1 symmetry these give rise to 21 states. Difficulty was encountered when trying to converge the CASSCF calculations on the higher-lying excited states. This problem could be partially solved by the use of state averaging, but even then it was necessary to restrict the CASSCF and, hence, also the CASPT2 calculations to either the 10 or 11 lowest states in C1 symmetry. This effectively limits the CASPT2 calculations to the states derived from the n f σ*, n f 4s, n f 4p, and σ f σ* excitations. The CASPT2 calculations of the excitation energies of the n f σ* and n f 4s states were based on CASSCF wave functions in which these two states were state-averaged with equal weights. The CASPT2 calculations on the higher-lying states were based on CASSCF wave functions in which either the 10 or 11 lowest energy excited states were state-averaged (again with equal weights). The energies of the n f σ* and n f 4s states obtained from the latter calculations are similar (differing at most by 0.2 eV) to those obtained from the calculations with only two states state-averaged. The nondiagonal zeroth-order Hamiltonians were used for the CASPT2 calculations.5 CASPT2 calculations were also carried out on the ground state, using the same active spaces as were used in the excited state calculations. The excitation energies were calculated from the differences between the excited state and ground state energies. The CASPT2 method was also used to calculate the energy for removal of an electron from the lone-pair orbital. The error in this ionization energy must be small if the CASPT2 method is to accurately predict the energies of the Rydberg transitions. With the ANO′ basis set, described below, the CASPT2 calculations gave a vertical ionization potential of 11.14 eV, in excellent agreement with experimental values of 11.17 (2E3/2) and 11.25 eV (2E1/2).22 The CIS calculations were performed using the 6-31+G contracted Gaussian basis set23 as well as with a 6-31+G*+2s2pd
J. Phys. Chem., Vol. 100, No. 14, 1996 5643
Figure 1. Electron energy loss spectra of CH3Cl obtained with constant residual energy values of 0.05, 0.25, 0.65, and 20.05 eV.
basis set, formed by adding to the 6-31+G basis set diffuse s (two), p (two), and d (one) primitive Gaussian-type functions centered on the Cl atom. The exponents of the supplemental diffuse functions were obtained by optimizing the low-lying virtual orbitals from Hartree-Fock calculations on the ground state cation of CH3Cl. The CASSCF and CASPT2 calculations were performed by using an atomic natural orbital (ANO) Gaussian basis set, contracted to (5s4p2d), (4s3p2d), and (3s2p) on the Cl, C, and H atoms, respectively,24 as well as an augmented ANO basis set, designated ANO′, formed by adding to the ANO basis set diffuse s and p “orbitals” located on the C-Cl axis at the center of charge. These diffuse “orbitals” were formed from eight primitive s and eight primitive p functions contracted to single s and p functions, using a procedure of Roos et al.25 In both the CIS and CASPT2 calculations, excitations were excluded from the nonvalence core orbitals. All calculations were carried out at the MP2/6-31G* optimized geometry of the electronic ground state which is in good agreement with the experimental geometry. 3. Results 3.1. Experimental Results. The electron energy loss spectra, displayed in Figure 1, were obtained with fixed residual energy (Eres) values of 0.05, 0.25, 0.65, and 20.05 eV. (Hereafter, when referring to the last spectrum, we will quote the residual energy simply as 20 eV.) The spectra obtained with low (i.e., e0.25 eV) residual energies are expected to be dominated by excitation of triplet states, and that obtained with Eres ) 20 eV should be dominated by dipole-allowed singlet states. (Here we are assuming that the states can be labeled according to multiplicity.) Dipole-forbidden singlet states are expected to appear in the Eres ) 0.65 eV spectrum. Tables 1-3 compare the excitation energies obtained in this study with those from previous experimental studies and from the CIS and CASPT2 calculations, carried out with the 6-31+G*+2s2pd and ANO′ basis sets, respectively. A detailed discussion of the theoretical results is presented in section 3.2. Except for the lower resolution, the Eres ) 20 eV electron impact spectrum closely resembles the optical absorption spectra.
5644 J. Phys. Chem., Vol. 100, No. 14, 1996
Nachtigallova et al.
TABLE 1: Calculated and Experimental Excitation Energies (eV) of the Low-Lying Singlet States of CH3Cl state
CASPT2
CISa
11E (n f σ*) 21E (n f 4s) 21A1 (n f 4px, 4py) 31E (n f 4px, 4py) 11A2 (n f 4px, 4py) 41E (n f 4pz) 51E (n f 5s) (6,7,81E, 3,41A1, 2,31A2) (n f 4d) 51A1 (n f 5px, 5py) 91E (n f 5px, 5py) 41A2 (n f 4px, 5py) 101E (n f 5pz)
7.61 7.69 8.79 8.92 8.98 9.13
7.58 7.94 8.90 8.88 8.95 9.35 9.53 9.82-9.93 10.09 10.08 10.10 10.24
present previousb experiment experiment 7.14 7.84 8.85
7.21c 7.76, 7.88d 8.81, 8.89e
9.20 9.39 9.82
9.20e 9.32,c,e 9.39 9.82, 9.89d
10.18
10.12, 10.20d 10.10d
All CIS transition energies have been reduced by 0.8 eV. b In reporting results from previous experimental studies, the assignments from these studies have been retained and pairs of features attributed to the spin-orbit coupling in the core, are grouped together. c From ref 6. d From ref 7. e From ref 9. a
TABLE 2: Calculated and Experimental Excitation Energies (eV) of the Low-Lying Triplet States of CH3Cl state
CASPT2
CISa
13E (n f σ*) 23E (n f 4s) 13A1 (n f 4px, 4py) 33E (n f 4px, 4py) 13A2 (n f 4px, 4py) 43E (n f 4pz) 23A1 (σ f σ*) 53E (n f 5s) (6,7,83E, 3,43A1, 2,33A2) (n f 4d) 53A1 (n f 5px, 5py) 3 9 E (n f 5px, 5py) 43A2 (n f 5px, 5py) 103E (n f 5pz)
6.70 7.68 8.70 8.81 8.90 8.85 9.15
6.66 7.71 8.60 8.80 8.95 9.14 9.19 9.47 9.64-9.88 9.97 10.03 10.10 10.12
present previous experiment experiment 6.74 7.70
6.80b
8.79 8.99 9.12 ∼9c 9.34 9.76 10.14
a With the exception of the triplet (σ f σ*) state, all CIS energies have been reduced by 0.8 eV. b From ref 11. c The triplet (σ f σ*) transition underlies the Rydberg transitions.
The low-energy, broad structure centered at 7.14 eV is due to the singlet n f σ* transition. This transition is followed by several narrower features due to Rydberg states. The lowest in energy of these, at 7.84 eV, is due to the n f 4s Rydberg transition. We assign the two pronounced peaks at 8.85 and 9.20 eV to n f 4p transitions. In the vacuum-UV spectra, the n f 4p Rydberg states display fine structure due to vibrational progressions and possible spin-orbit splittings.6-9 The Eres ) 20 eV spectrum also displays weak features near 9.39 and 9.82 eV and a more pronounced feature near 10.18 eV. All of these features have counterparts in the vacuum-UV spectrum. The 9.39 eV feature is tentatively assigned to the n f 5s transition, the 9.85 eV feature to the n f 4d transitions, and the 10.18 eV feature to the n f 5p transitions. The bases for the assignments are discussed below, as is the question of the parentage (in terms of multiplicity) of the observed features. The Eres ) 0.05 eV spectrum displays a pronounced peak centered at 7.25 eV, with a shoulder near 7.65 eV. This is followed at higher energy by a series of sharp peaks starting near 8.8 eV. The Eres ) 0.05 and 0.25 eV spectra are qualitatively similar in appearance at energies above about 8.5 eV, but they differ appreciably at lower energies. In particular, the broad low-energy peak (located at 7.25 eV in the Eres ) 0.05 eV spectrum) moves to lower energy and diminishes in intensity as the residual energy is increased. The dependence of this peak position on the incident electron energy indicates that part of the structure in this energy region is due to a core-
excited anion state which decays to the 11E and 13E n f σ* excited states. The anion state in question is almost certainly the n-1(4s)2 Feshbach resonance, which has been observed centered at 7.5 eV in an electron transmission spectrum.26 As is customary for Feshbach resonances,27,28 it lies energetically a few tenths of an electronvolt below its parent n f 4s state. Due to the pronounced structure associated with the n-1(4s)2 Feshbach resonance, it is not possible to determine a reliable energy for the triplet n f σ* state from the Eres ) 0.05 and 0.25 eV spectra. However, from examination of the Eres ) 0.65 eV spectrum, in which interference due to the Feshbach resonance is greatly reduced, the energy of the triplet n f σ* state is determined to be 6.74 eV, about 0.4 eV below its singlet counterpart. The triplet n f σ* state has been observed previously at 6.8 eV in trapped-electron spectra.11,12 The peak due to the n f 4s transition occurs at 7.70 eV in the Eres ) 0.05 and 0.25 eV spectra as compared to 7.84 eV in the Eres ) 20 eV spectrum. The optical absorption spectrum displays a series of peaks around this energy: the first two and most intense of which appear at 7.76 and 7.88 eV and have been associated in several prior studies6,7,10 with the spin-orbit splitting in the cation core. It appears that these two features in the optical absorption spectrum coalesce into the single peak near 7.84 eV in the Eres ) 20 eV electron impact spectrum. This is a result of the lower resolution in the electron impact measurements. The appearance of a still lower energy feature near 7.70 eV in the electron impact spectra obtained with low residual energies is inconsistent with the interpretation that the 7.76 and 7.88 eV features in the optical absorption spectrum primarily reflect the spin-orbit splitting between 2E3/2 and 2E1/2 cation states. Another problem with this interpretation is that the splitting between the 7.76 and 7.88 eV peaks is appreciably larger than the spin-orbit splitting between the 2E3/2 and 2E1/2 cation states. Our results suggest an alternative interpretation, namely, that the 7.70 eV feature in the Eres ) 0.05 and 0.25 eV spectra is due to the triplet n f 4s state and that the 7.84 eV feature seen in the Eres ) 20 eV electron impact spectrum (and as the 7.76 and 7.88 eV doublet in the optical absorption spectra) is due to the corresponding singlet state, with the doublet character in the optical spectrum being due to vibronic structure. The optical absorption spectrum of Felps et al.10 displays a very weak shoulder near 7.70 eV which could be due to the triplet n f 4s state. The low residual energy spectra also display structure near 8.79, 8.99, 9.12, 9.34, 9.76, and 10.14 eV. The energy of the first of these features is taken from the Eres ) 0.25 eV spectrum in which it appears more prominantly, and the energies of the higher lying features are taken from the Eres ) 0.05 eV spectrum, in which they appear somewhat more sharply. The structure between 8.79 and 9.12 eV in the low residual energy spectra is attributed to n f 4p transitions. The feature near 9.34 eV in these spectra is probably due both to an electronically excited state of the neutral molecule, with n f 5s being the most likely candidate, and a Feshbach resonance. The electron transmission spectrum reveals that there is a Feshbach resonance near 9.5 eV.26 The peaks at 9.76 and 10.14 eV are attributed to n f 4d and n f 5p transitions, respectively. These features were not reported in the earlier trapped-electron studies.11,12 In addition to the slightly lower energies (by 0.04-0.09 eV) of the features between 8.7 and 10.2 eV in Eres ) 0.05 and 0.25 eV spectra compared to those in the Eres ) 20 eV spectrum, the relative intensities of these features are quite different in the high residual and low residual energy spectra. In particular, the Eres ) 20 eV spectrum is dominated by the two peaks near
Excited States of CH3Cl
J. Phys. Chem., Vol. 100, No. 14, 1996 5645
TABLE 3: Calculated Energies, 〈x2〉, 〈y2〉, and 〈z2〉 Expectation Values, and Oscillator Strengths of the Low Lying Excited States of CH3Cl ∆E (eV) state
CASSCF
CASPT2
CISb
〈x2〉 (au)
〈y2〉 (au)
〈z2〉a (au)
f σ*) 21E (n f 4s) 21A1 (n f 4px, 4py) 31E (n f 4px, 4py) 11A2 (n f 4px, 4py) 41E (n f 4pz) 13E (n f σ*) 23E (n f 4s) 13A1 (n f 4px, 4py) 33E (n f 4px, 4py) 13A2 (n f 4px, 4py) 43E (n f 4pz) 23A1 (σ f σ*)
8.33 8.05 10.52 10.40 10.46 11.47 7.59 8.03 10.33 10.45 10.55 10.31 11.25
7.61 7.69 8.79 8.92 8.98 9.13 6.70 7.68 8.70 8.81 8.90 8.85 9.15
7.58 7.94 8.90 8.88 8.95 9.35 6.66 7.71 8.60 8.80 8.95 9.14 9.19
14.9 21.2 28.8 41.0 41.5 41.5 27.1 15.6 29.7 41.1 41.1 41.1 23.7 15.1
14.9 21.2 28.8 41.0 41.5 41.5 27.1 15.6 28.3 41.0 41.1 41.1 23.7 15.1
13.1 32.6 24.9 23.2 23.4 23.4 44.9 21.6 23.5 22.9 22.9 22.9 39.4 17.3
11A1d 11E (n
osc strengthc 0.006 0.020 0.084 0.004 0.000 0.022
a The 〈x2〉, 〈y2〉, and 〈z2〉 expectation values were calculated from the CASSCF wave functions. b All CIS excitation energies, except that for the triplet (σ f σ*) state, have been reduced by 0.8 eV. c The oscillator strengths (in au) were calculated using the CIS method. d Ground state.
8.85 and 9.20 eV, whereas the Eres ) 0.05 and 0.25 eV spectra have the peak near 9.0 eV as the most prominent. This is consistent with the structure in the low residual energy spectra being due to states that are mainly triplet in character and that in the Eres ) 20 eV spectrum to states that are mainly singlet in character. The features near 9.4 and 10.1 eV, attributed respectively to n f 5s and n f 5p transitions, also appear more pronounced in the Eres ) 0.05 and 0.25 eV spectra than in the Eres ) 20 eV spectrum. The peak positions associated with these features shift by less than 0.05 eV in going from high to low residual energies, and in these cases, the shifts could even be partly instrumental in origin. The 9.76 eV feature in the low residual energy spectra is apparently due to the cluster of n f 4d transitions. This feature occurs 0.06 eV below the corresponding feature in the Eres ) 20 eV spectrum. However, in the latter case the peak is quite weak, and we do not attribute much significance to the shift. The Rydberg states in the 8.75-10.10 eV region of the Eres ) 0.05, 0.25, and 0.65 eV spectra are superimposed on a broad, underlying background. As will be discussed below, we believe that this background is due to the triplet σ f σ* excited state. There is also a broad feature centered near 10.7 eV in the Eres ) 0.05 eV spectrum which drops in intensity and shifts downward in energy (to about 10.4 eV) in the Eres ) 0.25 eV spectrum. It is less pronounced still in the Eres ) 0.65 eV spectrum. The width of this feature and its dependence on the residual electron energy suggest that it is due to a core-excited shape resonance. Possible candidates for an anion state in this energy range include n-1σ*2 and σ-1σ*2. 3.2. Theoretical Results. CASSCF and CASPT2 Calculations. The results of the CASPT2 calculations with the ANO and ANO′ basis sets and of the CIS calculations with the 6-31+G and 6-31+G*+2s2pd basis sets are summarized in Figures 2 and 3. Tables 1 and 2 compare the experimentally determined excitation energies (from both the present and previous studies) with the predictions of the CASPT2/ANO′ and CIS/6-31+G*+2s2pd calculations. Table 3 provides additional results, in particular the 〈x2〉, 〈y2〉, and 〈z2〉 expectation values from the CASSCF calculations and the CIS values of the oscillator strengths for the low-lying transitions. With the exception of the σ f σ* states, the CIS excitation energies reported in Figures 2 and 3 and in the tables have been reduced by 0.80 eV. As is discussed below, this reduction brings the CIS/6-31+G*+2s2pd excitation energies for the n f σ* and Rydberg states into good agreement with the CASPT2/ANO′
Figure 2. Calculated excitation energies of the singlet states of CH3Cl at different levels of theory. The CIS excitation energies have been reduced by 0.8 eV. The n f 4d states are designated by horizontal dashed lines; the other states are designated by horizontal solid lines.
and experimental results. In the ensuing discussion, unless noted otherwise, the CASSCF and CASPT2 results are those obtained with the ANO′ basis set and the CIS results are those obtained with the 6-31+G*+2s2pd basis set. The two lowest energy 1E states derive from the n f σ* and n f 4s configurations. In the CASSCF/ANO′ calculations, there is appreciable mixing between the n f σ* and n f 4s configurations, with the lower 1E state having somewhat more Rydberg character and the upper 1E state somewhat more valence character, as can be seen from examination of the 〈x2〉, 〈y2〉, and 〈z2〉 expectation values. The upper of these 1E states also has a significant contribution from the n f 4pz configuration. The CASPT2 calculations predict the 11E and 21E states to fall at 7.61 and 7.69 eV, respectively, with the 11E state now having more valence character. (Although MOLCAS does not permit calculation of the 〈x2〉, 〈y2〉, and 〈z2〉 expectation values at the CASPT2 level of theory, the nature of the states can still be established by examination of the natural orbitals.) The CASPT2 calculations place the 11E state 0.4-0.5 eV higher in energy than experiment. This disagreement between theory and
5646 J. Phys. Chem., Vol. 100, No. 14, 1996
Figure 3. Correlation diagram of the calculated excitation energies of the triplet states of CH3Cl at different levels of theory. With the exception of the σ f σ* state, all CIS energies have been reduced by 0.8 eV. The n f 4d and σ f σ* states are designated by horizontal dashed and dot-dashed lines, respectively. The remaining states are designated by horizontal solid lines.
experiment may be caused by excessive mixing of the n f 4pz configuration into the CASSCF wave function for the valence state. It is also possible that the “true” vertical excitation energy may be somewhat higher than that deduced from experimental studies, particularly since the n f σ* transition is quite broad, making a precise determination of the peak maximum difficult. The CASPT2 calculations predict that the next four singlet states are due to n f 4p transitions, with the 21A1, 31E, and 11A2 states, arising from n f (4px,4py) excitations, lying close in energy (between 8.79 and 8.98 eV) and the 41E n f 4pz state lying higher in energy (at 9.13 eV). These calculations form the basis of our assignment of the 8.85 eV peak in the Eres ) 20 eV electron energy loss spectrum to the 21A1 and 31E states and the peak observed at 9.2 eV to the 41E n f 4pz state. In the latter case, our assignment agrees with those of Robin2 and Truch et al.,9 which superseded earlier assignments of the 9.2 eV feature to a σ f 4p transition,8 the E1/2 component of the 3 E state, or n f 4d transitions.6,7 The feature that appears at 8.85 eV in the Eres ) 20 eV spectrum appears as an intense doublet (8.81 and 8.89 eV) in the optical absorption spectrum.7,9 The two lines in this doublet are comparable in intensity and are followed at higher energy by a series of weaker lines. This doublet structure has been attributed to a n f (4px,4py) transition, with the splitting being due to that between the 2E1/2 and 2E3/2 levels of the core.7,9 In other words, it has been assumed that the coupling of the Rydberg 4px and 4py electrons to the core is so weak that the spectrum is dominated by the spin-orbit splitting of the core rather than by splittings between the E, A1, and A2 states that would result in the L-S coupling scheme. Interestingly, even studies that adopt this weak coupling model assume that the E state due to n f 4pz transition can be distinguished from the doublet derived from the n f (4px,4py) transitions. Both the calculations and the electron energy loss spectra appear to be at odds with the weak coupling model for the n f (4px,4py) states of CH3Cl. The CASPT2 and CIS calculations predict sizable splittings (up to 0.30 eV) between the A1, A2,
Nachtigallova et al. and E states derived from the n f (4px,4py) excitations, and in the relevant energy region (8.5-9.1 eV), the electron-impact spectra obtained at low residual energies differ significantly from that obtained with a residual energy of 20 eV. These results suggest that the L-S coupling scheme is more appropriate than the (Ωc,ω) scheme for describing that n f 4p states. In the L-S coupling scheme only two of the three n f (4px,4py) singlet states would be expected to be seen in the Eres ) 20 eV electron impact and optical spectra since the 1A2 state would be dipole-forbidden, whereas it should be possible to detect all three of the triplet states in the low residual energy electron impact spectra (assuming that they are sufficiently separated to be resolved). This suggests that the (8.81, 8.89 eV) doublet in the optical absorption spectrum, which appears as a single peak in the Eres ) 20 eV electron energy loss spectrum, derives from the 1A1 and 1E n f (4px,4py) states. The structure seen at 8.79 and 8.99 eV in the low residual energy electron impact spectra would then correspond to triplet n f (4px,4py) states. One possible problem with the above interpretation is that the CIS calculations, discussed below, indicate that transitions to the 1E1 and 1A1 n f (4px,4py) states should have very different intensities, whereas the 8.81 and 8.89 eV features in the optical absorption spectra have similar intensities. However, configurational mixing, and spin-orbit interactions, neglected in the CIS calculations, could cause considerable changes in the intensities. Also, it is possible that these features at 8.81 and 8.89 eV are due to vibronic structure in the 1A1 n f (4px,4py) state and that the 1E n f (4px,4py) state is not seen due to its low oscillator strength. Both the CASSCF and CASPT2 calculations predict the lowest 3E state to be n f σ* in character and to lie about 1 eV below the 23E n f 4s Rydberg state. The 13E n f σ* state is considerably more compact than the 11E n f σ* state as can be seen from comparison of the 〈x2〉, 〈y2〉, and 〈z2〉 expectation values of these two states. The CASPT2 values of the excitation energies of the 13E n f σ* and 23E n f 4s states, 6.70 and 7.68 eV, respectively, agree to within 0.04 eV of the excitation energies obtained from the low residual energy electron impact spectra. The CASPT2 calculations place the 3A1 n f (4px,4py), 3E n f (4px,4py), 3E n f 4pz, and 3A2 n f (4px,4py) states at 8.70, 8.81, 8.85, and 8.90 eV, respectively. The predicted 3E n f 4pz below 3A2 n f (4px,4py) ordering is opposite that obtained from the CIS calculations. It is possible that CASPT2 procedure gives an energy for the 3E n f 4pz state which is too low relative to that of the 3A2 n f (4px,4py) state as a consequence of the use of state averaging in the CASSCF calculations. On the basis of the results of the CASPT2 and CIS calculations and comparison of the electron energy loss spectra obtained at high and low residual energies, we conclude that the features seen at 8.79 and 8.99 eV in the low residual energy spectra are due respectively to the 3E and 3A2 states derived from the n f (4px,4py) excitations and that the 3A1 n f (4px,4py) state is not observed. The 9.12 eV feature in the energy loss spectrum is assigned to the 3E n f 4pz state. CIS Calculations. The CIS/6-31+G*+2s2pd calculations place the n f σ*, n f 4s, and n f 4p states higher in energy (relative to the ground state) than do the CASPT2/ANO′ calculations. The errors in the CIS values of the excitation energies of these states are, to a good approximation, nearly constant, and the average absolute difference between the CIS and CASPT2 values of the excitation energies of the n f σ*, n f 4s, and n f 4p states is only 0.1 eV after the former are reduced by 0.8 eV. This gives us confidence that the CIS
Excited States of CH3Cl method can be used to assign the higher-lying Rydberg features seen in the optical and electron impact spectra. In the following discussion, all CIS excitation energies, except those for the σ f σ* states, have been reduced by 0.80 eV. The CIS results for the n f σ*, n f 4s, and n f 4p states are not considered in detail since the trends are qualitatively similar to those obtained from the CASPT2 calculations. We note, however, that the relative energies between the various states derived from n f 4p excitations differ in the two theoretical methods. In particular, the separation between the (n f 4pz) state and the three n f (4px,4py) states (in both the singlet and triplet manifolds) is appreciably larger in the CIS than in the CASPT2 calculations. This may be the result of errors introduced by state averaging in the CASPT2 calculations. In the singlet manifold, the CIS calculations predict that the group of states derived from the n f 4p excitations are followed, in terms of increasing energy, by the 1E n f 5s state (at 9.53 eV), a cluster of seven states derived from the n f 4d transitions (between 9.82 and 9.93 eV), and the n f 5p states (between 10.09 and 10.24 eV). The Eres ) 20 eV electron impact spectrum displays weak features near 9.39 and 9.82 eV. We have tentatively assigned the former to the n f 5s transition. The 9.8 eV feature, seen previously in optical absorption spectra, was assigned as n f 5s by Truch et al.9 and as n f 4d by Robin.2 Our calculations indicate that the latter assignment is more likely the correct one. The CIS calculations place the three singlet n f (5px,5py) states near 10.0 eV and the singlet n f 5pz state at 10.24 eV. The Eres ) 20 eV electron impact spectrum reveals only a single peak (at 10.18 eV) in the 10.0-10.3 eV energy range, whereas the optical absorption spectrum has peaks at 10.10, 10.12, and 10.20 eV, which are not resolved in our spectrum. Truch et al.9 assigned the 10.10 eV feature in the optical absorption spectrum to the state derived from the (n f 5pz) transition and the 10.12 and 10.20 eV features to a pair of spin-orbit states derived from n f (5px,5py) transitions. Our calculations indicate that the n f 5pz state lies above the n f (5px,5py) states, and we attribute the structure at 10.10 and 10.12 eV in the optical absorption spectrum to the n f (5px,5py) states and the peak at 10.20 eV to the n f 5pz excited state. The CIS calculations predict the singlet σ f σ* transition to fall at 11.82 eV. This is the uncorrected excitation energy, since, as discussed below, the calculations on the corresponding σ f σ* triplet state show that the correction is unnecessary in that case. The 〈x2〉, 〈y2〉, and 〈z2〉 expectation values (38.9, 38.9, and 39.1 au2) for this state, although large for a valence state, are smaller than those expected for the Rydberg states in this energy range. The singlet σ f σ* transition is expected to be quite broad in the vertical excitation region. Evidence for the existence of the singlet σ f σ* state is provided by the appearance of Fano antiresonances in the absorption spectrum above 10.3 eV.2 We now consider the CIS results for the triplet states. As for the singlet manifold, the CIS excitation energies for the n f σ*, n f 4s, and n f 4p triplet states, after reduction by 0.8 eV, are in fairly good agreement with the CASPT2 results, although the splittings between the various n f 4p states differ appreciably between the two sets of calculations. The CIS calculations place the triplet n f 5s state 0.06 eV below its singlet counterpart, the various triplet n f 4d states from 0.05 to 0.18 eV below the corresponding singlet states, and the various triplet n f 5p states up to 0.12 eV below their singlet counterparts. Even allowing for the fact that CIS calculations often give too large a gap between singlet and triplet states derived from a given configuration, it appears that the
J. Phys. Chem., Vol. 100, No. 14, 1996 5647 singlet/triplet gaps for several of these states (assuming the L-S coupling scheme) are comparable to the spin-orbit coupling in the core, which would imply that the coupling is actually intermediate between the (Ωc,ω) and L-S coupling schemes. The 9.34, 9.76, and 10.14 eV features in the Eres ) 0.05 eV electron energy loss spectra which we assign to n f 5s, n f 4d, and n f 5p states, respectively, lie 0.04-0.06 eV below the corresponding features seen in the Eres ) 20 eV spectra. The fact that these states can be distinguished in the electron impact spectra obtained with different residual energies is consistent with the interpretation that the singlet/triplet mixing is not “complete”. The CIS (uncorrected) and CASPT2 calculations place the triplet σ f σ* state near 9.2 eV, about 2.7 eV below the corresponding singlet state. The triplet σ f σ* state is valence in character as its 〈x2〉, 〈y2〉, and 〈z2〉 expectation values are 15.1, 15.1, and 23.8 au2, respectively, and it is likely responsible for the broad background on which the n f 4p, n f 5s, and n f 5p transitions are superimposed. 4. Conclusions The excitation energies of several electronic states of CH3Cl have been determined by means of electron energy loss spectroscopy. The triplet n f σ* and n f 4s states are found to lie energetically 0.40 and 0.14 eV below the corresponding singlet states. The production of the triplet n f σ* state is strongly enhanced near threshold due to intermediate formation of the n-1(4s)2 temporary anion state. Electronic structure calculations indicate that the singlet and triplet n f σ*(C-Cl) states are valence-like, with the singlet species having somewhat more Rydberg character. The vertical transition to the triplet σ(C-Cl) f σ*(C-Cl) state is predicted to occur near 9.2 eV. This state, in spite of its relatively high energy, is predominantly valence in nature. Its singlet counterpart is predicted to lie about 2.6 eV higher in energy and to have considerable Rydberg character. The Rydberg states seen in the optical absorption spectra of CH3Cl have been interpreted in earlier studies in terms of the (Ωc,ω) coupling scheme in which the Rydberg electron is weakly coupled to the core. Our calculations and electron energy loss measurements indicate that this weak coupling interpretation is too simplistic and that it is indeed possible to distinguish between predominantly singlet and predominantly triplet states arising from the n f 4s and n f 4p configurations. In addition, our results indicate that the n f 4d, n f 5s, and n f 5p Rydberg states of CH3Cl should be interpreted as being intermediate between the L-S and (Ωc,ω) coupling limits. Acknowledgment. This research was carried out with support of a grant from the National Science Foundation. We thank Professor B. O. Roos for helpful suggestions about the CASSCF and CASPT2 calculations and Dr. P.-O. Widmark for sending us his routines for generating the Rydberg orbitals for the CASPT2 calculations. References and Notes (1) Mulliken, R. S. J. Am. Chem. Soc. 1964, 86, 3183. (2) Robin, M. R. Higher Excited States of Polyatomic Molecules; Academic Press: New York, 1974; Vol. I Robin, M. R. Higher Excited States of Polyatomic Molecules; Academic Press: New York, 1985; Vol. III and references therein. (3) Burrow, R. D.; Modelli, A.; Chiu, N. S.; Jordan, K. D. J. Chem. Phys. 1982, 77, 2699. (4) Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. J. Phys. Chem. 1992, 96, 135.
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