The T,T* State in Formaldehyde and Thioformaldehyde F. GREIN AND M. R. J. HACHEY Department of Chemistry, University of New Brunswick, Bag Service #45222, Fredericton, New Brunswick, Canada E3B 6E2; e-mail (F.G.): [email protected] Received March 26, 1996; revised manuscript received June 11, 1996; accepted lune 13, 1996 ABSTRACT m For formaldehyde, the C - 0 stretch potential of '(T,r*) crosses all 'A, Rydberg otentials, such as n, 3p,, n, 3d,,, etc., thereby transferring the intensity of the unassigned \r, r* + 2 system to these Rydberg states. For thioformaldehyde, the situation is similar but a shift in the potentials allows for direct observation of '(r,T*). In its '(T,T*) state, H,CO is planar, having a low barrier of about 0.2 eV toward the nonplanar '(v, T*>state. For H,CS, the planar conformation of '(T,r*) is a saddle point, with '(v,r*) being the global minimum on the 2'A' surface. The triplet r,r* states of H,CO and H,CS are nonplanar, having inversion barriers of 0.1 and 0.05 eV, respectively. For both H,CO and H,CS, the T,r* configuration also crosses the ground-state configuration, which explains predissociation and radiationless transitions of some Rydberg states. 0 1996 John Wiley & Sons, Inc. For a long time, it was believed that '(r,r*) Introduction had a vertical excitation energy in excess of the first ionization potential (IP) of 10.8887 eV [2] and, therefore, is not observed. For example, Langhoff n the absorption spectrum of formaldehyde, et al. [31 predicted '(r, ?T*) to be near 11.2 eV. I the electric dipole forbidden transition The absorption spectrum in the vacuum ultravi- 1 A,(n, r*)+ glAl is observed and well studied, olet (VW) region of formaldehyde was first stud- whereas the allowed transition '(r, r*)+ XIAl, ied by Price [4]. Currently, all medium and strong despite being predicted to be very intense, has so bands in the VUV spectrum of H,CO are assigned far escaped all attempts at detection. The problem to Rydberg transitions. The latest assignments by of the "missing" '(r,r*) state also plagues many Brint et al. 151 identified n + s, p, d, f-Rydberg other aldehyde and ketones. Consequently, Robin, transitions up to 5s, 12p, 12d, and 9f, converging a prominent reviewer in the field of higher excited to the first IP. However, in many cases, the intensi- states, wrote that "aldehydes and ketones are a ties or quantum defects do not conform to expecta- most perplexing chromophoric group" [ 111. tions for Rydberg transitions. For example, the international Journal of Quantum Chemistry: Quantum Chemistry Symposium 30, 1661 -1671 (1 996) 0 1996 John Wiley & Sons, Inc. CCC 0360-0832 I96 I071661 -1 1 GRElN AND HACHEY intensity of n,4p is higher than that of n,3p, and 60. They were selected such that all symmetry- the quantum defect of n,3d is 0.4, whereas it is adapted functions (SAF) with c2 > 0.001 in the expected to be 5 0.1. Further, for n > 4, the np, final wave function were part of the reference nd, and nf transitions have similar intensities, con- space, for the whole range of geometries covered trary to their normal behavior [l, 51. Although the by the calculations. source of the Rydberg anomalies is usually at- tributed to Rydberg-valence interactions, the na- ture of the perturbing valence state has never been The Role of '( 'TT, 7t* ) in the Absorption positively identified. Spectrum of H, CO In contrast to the missing singlet n- -+ n-* sys- tem, the triplet n- + n-* system of H,CO has been In Figure 1, the 'Al potential curves for the observed by electron impact studies ([6] and refer- C - 0 stretch of H,CO are shown. They are simi- ences therein). It should also be noted that the lar to the ones obtained in [8], but a lower configu- absorption spectrum of thioformaldehyde, whose .ration selection threshold (4 pHartrees) was used. electronic spectrum is expected to be similar to The other geometry parameters were held at ex- that of formaldehyde, shows a progression of perimental ground state (GS) values (RcH = 2.0796 bands, lying between n + 4s and n -+ 4p, that uo and &(HCH) = 116.3" [171). It is seen that dia- were assigned to '(n-, n-* 1. batically the l(~, n-* ) state crosses all Rydberg Obviously, it is of significant interest to investi- potentials, also the higher ones not shown here. gate theoretically the reasons for the strange be- Even the apparent long-distance minimum of havior of the n-, n-* state. In a series of multirefer- 1 (n-, n-*), at 2.914 uo is due to an avoided crossing ence (MR) configuration interaction (CI) studies of T,n-* with the GS configuration n2.At 3 do, the performed over the last few years, potential en- l1A1 wave function contains about 45% n2 and ergy curves for the C - 0 stretch and the out-of- 45% n-,n-*, whereas 21A1 has 40% n2 and 45% plane motion were obtained for H,CO [7-111 and n-,n-* (see Fig. 2). (The percentage contribution H,CS [12-151. Using more extended basis sets and was calculated from c:, where is the coefficient large CI expansions, the vertical excitation energy ci of the respective SAF in the CI wave function. In of the '(n-, n-*) state of H,CO is calculated to be the CI expansion, '(n,n-*) MOs were used. The 9.6 eV [8]. It is important to include the doubly given numbers change slightly, but not greatly, excited configuration no, in the set of refer- T*' with the choice of MOs.) At the largest CO dis- ence configurations. From the calculated potential tance shown in Figure 2,4 do, the eventual dissoci- energies, vibronic energy levels and oscillator ation to CH, 0 is not yet important. Open-shell strengths were evaluated [8, 131. The results, as + configurations to describe the dissociation become they concern the n-, n-* state of H,CO and H,CS, dominant at larger distances than shown. The re- are most interesting and, in our opinion, explain pulsive crossing of '(n-, n-*) with all 'Al Rydberg why '(n-, n-* ) had previously not been assigned in states and the ground state leads to predissociation the absorption spectrum of H,CO. and radiationless transitions. According to Figure 1, the doubly excited 1(no,n-*2) state appears at about 10.2 eV, having a fairly shallow potential, Methods and crossing ?T, rr* at small R and higher Rydberg states at larger R. Ab initio MR-CI calculations were performed Figure 3 shows an enlarged version of the using the MRD-CI programs [161. A (lOs6p/5s4p) C - 0 stretch curves for 2'A1 to 41A1, including basis set for C and 0, (12s9p/5s4p) for S, with vibrational energy levels for each of the minima. It additional polarization functions and s, p, d should be noted that all minima, except for n, 3p, Rydberg functions on C and 0 (C and S for H,CS) and n, 3d,,, are caused by avoided crossings with is used. The hydrogen basis is (5s/3s) with a p n-, T*.These potential wells are bounded by rr, n-* polarization function. Details are given in [8, 10, on the left, and by a Rydberg configuration on the 13,141. In their ground states, H,CO and H,CS are right. A notation such as n-, n-*/n,3py, used here planar, having C,, symmetry. For the out-of-plane to describe such potentials, should be obvious. motion, C, symmetry was observed. The number Assuming that all 'A, states are planar, and that of reference configurations varied between 40 and the C - 0 stretch vibrations can be approximated 1662 QUANTUM CHEMISTRY SYMPOSIUM NO. 30 T,T* STATE IN FORMALDEHYDE AND THIOFORMALDEHYDE by the one-dimensional potentials given in Figure 3, the vibronic oscillator strengths were evaluated for each vibrational level, by first calculating the electric dipole transition moment as a function of R,, and then combining it with the Franck-Con- 11.0- :\ don (FC) factor. In Table I, experimental values for energies and . -- oscillator strengths are compared with calculated vertical values and with vibronic values evaluated for each vibrational level, as described above. For the 0-0 bands of the n + 3s and n + 3p transi- tions, the vertical numbers agree reasonably well with the experimental values. However, for the 0-0 bands of n + 3d,, (8.88 eV), n,4s (9.26 eV), and higher states, the calculated vertical oscillator 8.0 - strengths are too small. Also, the 0-1 and 0-2 < bands of Rydberg states have very low Franck-Condon factors, and the observed bands at 8.32, 9.04, and 9.18 eV could not be explained on the basis of vertical oscillator strengths. In the last three columns of Table I, the calcu- lated vibronic values are given. It is seen that 0.0 vibronic energies can be matched with the energies 1""1""1"",~ of the observed bands to a maximum deviation of 2.0 2.5 3 .O 3.5 0.24 eV, but mostly lying within 0.05 eV. Larger (C4) a, 1 R deviations may be indicative of the need for a FIGURE 1. C - 0 stretch potentials for 'A, states of non-Born-Oppenheimer treatment. H,CO. Except for the three lowest bands, the literature assignments, as given in Table I, had to be changed 1OOO? c2 5o?? o?? 100% 7-_ n2 I 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 R(C0) distance (a,) FIGURE 2.