J. Phys. Chem. 1995,99, 8050-8057
8050
Spectroscopy of Formaldehyde. 1. Ab Znitio Studies on Singlet Valence and Rydberg States of Planar H&O, with Emphasis on l(.r#) and l(a#) Michel R. J. Hachey, Pablo J. Bruna, and Friedrich Grein* Department of Chemistry, University of New Brunswick, Bag Service #45222, Fredericton, New Brunswick, Canada E3B 6E2 Received: November 11, 1994; In Final Form: February 23, 1995@
CO stretching potentials were obtained by ab initio multireference CI calculations for singlet valence and Rydberg states of H2CO in CzVsymmetry. Within the Franck-Condon region, the valence states 'Bl(o,n*) and 'Al(n,n*) cross all members of the n Ryd series as well as 'Bl(n,3s). The structures of the absorption bands are therefore extensively altered by vibronic mixing, intensity borrowing, and predissociative interactions. This explains why the n Ryd bands are observed to be vibrationally more complex and of higher intensity than expected. Since lA~(n,n*)becomes the ground state at large R(CO),n,n*is capable of coupling all 'AI Rydberg states with the ground state, which dissociates to CH2 0 fragments at 7.64 eV. Thus, the observed absorption continuum above 7.5 eV is attributable to predissociating interactions. In the vertical region, the 'Al(n,n*) valence state lies at 9.6 eV and exhibits a heavy mixing with the no,n*2configuration. The reported "n,3d" band at 8.88 eV is reassigned to the 0-0 band of the 3'A1 %'Al transition, where the minimum of 3'Al results from an avoided crossing between n,n*and n,3p,. This explains the apparent large quantum defect and other anomalies reported for the so-called "n,3d" band.
-
-
+
-
-
I. Introduction The electronic spectrum of formaldehyde, HzCO, has been the subject of numerous e~perimentall-~and theoretical4-I2 studies. The vacuum-ultraviolet ( V W ) absorption region from approximately 7 to 11 eV (recorded by both ~ p t i c a l ' ~ -and '~ electron impact technique^^^-^') has been interpreted as consisting exclusively of n Ryd transitions converging to the ground state of H2COf (A2B2,n 03, with a vertical ionization potential (IP) of 10.88 eV).22-24 Excited valence states, also expected to lie in this area, have not been found. The highest Rydberg states, observed up to 10.78 eV, correspond to 7s, 12p, 12d, and 12f. Other series converging to electronically excited H2COf have been observed lying up to 20 eV above the HzCO ground Despite the prediction of high intensity, the JC 3s ('B1) transition does not appear in the spectrum; the reason behind this behavior is unknown.23 The wide range of energies scanned experimentally might give the false impression that the electronic spectrum of H2CO is currently well understood. In fact, the rather weak dipoleforbidden transition 1'A2(n,n*) A' AI constitutes the only system for which the rovibronic structure is known in great detail.'-3~25-29The 1IA2 state (T, = 3.50 eV) has been especially well studied because of its role in the photochemical decomposition of H2CO into H2 CO and H HC0.2330 One area of contention is the assignment of Rydberg states. So-called "experimental" Rydberg assignments3 usually correspond to numerical fittings of measured absorption energies according to the formula T = IP - R/(n - d)2. While this fitting procedure is capable of differentiating between the s, p, or d series, it does not allow to distinguish per se between the ( x , y . z ) components of p and the (x2,y2, ..., y z ) components of d. On the basis of experimental quantum defects,I5 two 0-0 absorption peaks at 7.97 eV (medium intensity) and 8.11 eV (high intensity) are assigned to the n,3p states. These belong
--
-
+-
+
~
~
~
~
~~
* Corresponding author. E-mail: @
+
~~
FRITZ@UNB. CA. Abstract published in Advance ACS Abstracts, April 15, 1995.
-
to either n 3p, ('B2) or n 3p, (IAl). Calculations carried out in 1971 by Peyerimhoff et aL5 placed 'AI below 'Bz (8.11 vs 8.39 eV). A few years later, two theoretical studies found a reverse ordering, with 'B2 lying below 'AI (8.12 and 8.15 eV by Yeager and McKoy6 in 1974 and 8.08 and 8.09 eV by Harding and Goddard7in 1977). Corroborating the reordering, the latter papers predicted oscillator strengths in which the energetically higher peak had the higher absorption intensity, in good agreement with experiments. In spite of these theoretical developments, the experimental literature continues to place 3p, below 3p,, as proposed in 1971 by Mental1 et a1.I5 solely on the basis of Peyerimhoff et al.'s predictions. Currently, another poorly understood aspect of the electronic spectrum is the anomalous band profile of the n Ryd series.I7 The recorded vibrational structure differs from state to state and from that of its ionization spectrum g2B2 XIA1. These experimental features are at variance with the simple model commonly used in molecular spectro~copy,~' that near equilibrium, Rydberg surfaces are expected to be topologically similar to those of their ionic cores. In the case of HzCO, each n Ryd system should hypothetically consist of only one absorption band because all n Ryd excitations are of type nonbonding nonbonding. This simplified model, however, only holds as long as the Rydberg states involved do not mix with valence states. Since the Rydberg bands in the gas phase spectrum of H2CO are vibrationally structured, it has to be assumed that the Rydberg states mix with valence states, and the anomalous Rydberg profiles are clear indications of perturbing, close-lying states of valence character. We interpret other unusual features in the spectrum as resulting from Rydberg-valence interactions: (a) high absorption intensity of the Rydberg bands (remaining strong up to 0.10 eV below ionization), (b) relatively large quantum defects 6 (that is, Rydberg states lie lower than expected) which are particularly notorious for the d series (with 6 = 0.4 vs standard 6 x 0.131,32),and (c) blue shift of Rydberg bands under absorption in Ar-dense media.33 As all (gas phase) absorption bands above 7 eV are apparently
-
+-
-
-
+
0022-3654/95/2099-8050$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 20, 1995 8051
Valence and Rydberg States of H2CO
-
-
of Rydberg character, the location of the singlet valence states exponents were estimated for this work. From A to D, the total number of contracted Gaussians is 65,85,96, and 95 (6 and 10 generated by the excitations u n* ('BI), n n* ( AI), and Cartesian components were generated for d and f AOs, n a* (lB2) is one of the most intriguing puzzles in the respectively). Potential curves were studied with basis sets A spectrum of H2CO. Excitations to n* are expected to be and B, whereas the vertical spectrum up to 10.6 eV was associated with large changes in R(C0) and should therefore investigated with basis sets C and D. have long vz(C0) progressions. Their absence has been explained by unfavorable Franck-Condon factors. However, The CI calculations were performed with the multireference the recent detection via electron impact2' of a long vz(C0) configuration interaction method (MRD-CI) developed by progression for 13A1(n,n*) X1A1 speaks against such an Buenker, Peyerimhoff, and c o - w o r k e r ~ . ~Estimated ~,~ full-CI argument. Another explanation for the absence of the llA1energies resulting from a generalized Langhoff-Davidson (n,n*) %A1 system is that the upper state a ~ t o i o n i z e s . ' ~ ~ ~correction ~~ formula45will be used throughout. The '(n,n*) SCF Indeed, numerous theoretical studies place lA~(n,n*)rather close MOs were employed for the CI expansions, unless specified to H2CO'. otherwise. In all cases, the frozen-core approximation has been Rydberg-valence interactions could be tested if the excited used (no excitations from the lowest two a1 MOs), and the state hypersurfaces were known. Unfortunately, most prior ab complementary virtual MOs were discarded. The number of initio works have focused only on the vertical transitions, reference configurations varied from 40 to 60, depending on providing no information on possible perturbations from n,n* the symmetry species under consideration. The total CI spaces and a,n* which lie vertically above the n = 3 Rydberg manifold. generated have an average dimension close to 3 x lo6, with According to previous ab initio studies, the vertical excitation finally selected CI spaces lying in the 20 000-32 000 range. energy of '(n,n*) ranges from 9 to 11.7 eV$-8,10-12with an In the calculations with basis B, the six lowest singlet states of average of 10.6 eV. It is estimated that about 40 singlet Rydberg each symmetry species were selected by using a selection states (n = 3 , 4 , 5) lie below 10.6 eV, about a dozen belonging threshold T of 10phartrees. With basis A, only a small number to the 'A1 species alone. The only theoretical study reporting of roots was selected, taking T = 5 phartrees. R(C0) potential curves was carried out with a valence-only basis The standard CzVorientation is used, with the molecule lying set of DZ q ~ a l i t y . ~Obviously, there is a need to study the in the yz plane. The CO stretch curves were studied by keeping behavior of the valence and Rydberg potential surfaces of H2the geometry of the CH2 group frozen at its experimental value CO over a wide range of configurations. in the H2CO ground state (R(CH) = 2.0796 bohrs and LHCH A current project of our laboratory which focuses on the = 116.3'&). The vibrational frequencies vz(C0) were calculated electronic spectrum of a series of isovalent H2AB molecules, by assuming the R(C0) curves to correspond to hypothetical such as H2CS34 and H z S ~ Shas , ~ ~therefore been extended to potentials of diatomic NO. In the text, R generally stands for include H2CO. In this work, the R(C0) stretching potentials R(C0). of this prototype carbonyl compound have been calculated by The ground state configuration ...5a1~1b1~2b2~ is commonly multireference CI methods for several electronic states in both written as ...a2n2n2 (or as ...n2 for short). Two lone pairs planar and pyramidal geometries. The spectroscopic relevance localized on 0 correspond to a (2p,,) and n (2py0; in-plane). of a double minimum on the S 2 surface revealed by these The z MO is slightly polarized toward 0, whereas n* is calculations has already been discussed in our previous paper.36 polarized toward C.5,i,'2,47-48The MO labeled d corresponds The present report gives the results for the singlet states of planar to lb2(CH2). H2CO. Due to the large amount of material, part of the The ground state XIAl, as well as the l'Bl(u,n*) and l'A2comparison between theoretical and experimental data is (n,n*) states, dissociate to CH2(X3B1) O(3Pg) which are published ~ e p a r a t e l y . ~ Singlet ~ states of nonplanar H F O , as experimentally determined to lie 7.64 eV (thermodynamic data well as the properties of triplet and quintet states, will be at 0 K) above the ground state minimum.49 reported elsewhere.38
-
-
-
+
111. CO Stretch Potential Curves for Valence States. Basis Set A The 1Os6p/5s4p Huzinaga-Dunning A 0 basis ~ e t sare ~ ~ , ~ ~ Potential curves for valence states of H2CO were obtained used for carbon and oxygen. These contracted sets have been by performing MRD-CI calculations with the valence-only basis expanded by d-polarization functions, with exponents of 0.75 set A. Later, these results will be supplemented by the adiabatic for C40 and of 0.74 and 1.52 (uncontracted) for the 0 atoms4] potentials calculated with basis B (3spd). The potential curves In addition, one bond s-function (a,= 1.15) has been placed of singlet valence and estimated Rydberg states, the latter in the middle of the CO bond.42 The hydrogen basis consists obtained by shifting the g2B2 curve of H2CO+ by the experiof a 5 ~ 1 3 sset,39expanded by a p-polarization function with ap mental term value, are shown in Figure 1. Throughout section = 1.0. This valence-only basis, called basis A, is of slightly 111, valence-only states will be indicated with the ordering better than TZP quality. number in parentheses. For example, the second 'AI valence Rydberg states with principal quantum number n = 3 are state is labeled (2)'Al. described by diffuse AOs of s-, p-, and d-character added to 111.1. 'A1 States. Three IAI valence potentials were both C and 0 centers. In the same order, the orbital exponents calculated. The repulsive portion of (2)'Al crosses all Rydberg are 0.023, 0.021, and 0.015 for carbon and 0.032, 0.028, and states, whereas (3)'Al crosses the upper Rydberg states at larger 0.015 for oxygen.4O This basis B is also called 3spd basis. R. Basis sets C and D are obtained by expanding basis A with The nature of the interactions between the first three 'A1 states extra Rydberg functions centered on carbon. In basis C (bpdf), becomes transparent by looking at the configurational changes the additional AOs have exponents of 0.023 (3s), 0.0055 (4s), in the wave functions. Tab!e 1 summarizes the results at three 0.0013 (5s), 0.021 (3p), 0.0049 (4p), 0.015 (3d), 0.0032 (4d), different R(C0) distances. XI AI changes gradually from closedand 0.002 (4f).40 On the other hand, basis D (5spd) is derived shell ...n2 near equilibrium to an equal admixture of n2 and n,x* from C by replacing the 4f A 0 by 5p and 5d functions (with at 3.0 bohrs to n,n*(65%) character at 4.0 bohrs. At larger R, exponents of 0.0011 and 0.0007, respectively). The 4f and 5 s 11. Technical Details
8052 J. Phys. Chem., Vol. 99, No. 20, 1995
Hachey et al. to (3)'Al. Near its minimum at 2.55 bohrs and 10.25 eV, (3)'Al is described mainly by the double excitations no,n*2and dn,n*2, each contributing about 45%. At this point, the following picture emerges for the contribution of n,n*along the CO distance. Below 2.2 bohrs, n,n* lies above X2B2 (H2CO+). At R = 2.3 bohrs, n,n*contributes to the %, (2), and (3)'Al states with about 20, 45, and 30%, respectively. At 2.5 bohrs, n,n*resides mainly in % and (2)'Al (31 and 56%). As R(C0) increases, n,n*stabilizes further, becoming the dominant configuration of the ground state. At R = 4.0 bohrs, the n,n*configuration (%'AI) lies at 6.30 eV, 1.34 eV below the products CH2 0. This predicted low energy for singlet n,n*is supported by AE = 6.8 eV for triplet n,n*(13A1) at the same R.38 Summing up, the n,n*diabatic state is unique in the sense that, along the CO distance, it crosses all states of H2CO lying below g2B2 (H2CO+). As the n,n*potential is effectively repulsive within the Franck-Condon region, it is capable of predissociating the whole manifold of n Ryd states. 111.2. 'BI States. The (1)'BI potential shows a minimum near 2.6 bohrs and 8.26 eV. Up to R = 3.8 bohrs, (1)'BI arises from the u,n* configuration. At larger R, it acquires repulsive n,u*co character, due to an avoided crossing with (2)'Bl (section IV.2). Vertically, (l)'Bl(u,n*) lies at 9.25 eV, only 0.35 eV below (2)'Al. As seen in Figure 1, the u,n* potential behaves similar to that of n,n*. Below 2.3 bohrs, both potentials lie above H2CO+ but stabilize significantly at larger R. As the (1)'BI and (2)'Al curves remain energetically close, their mixing in the out-of-plane bending mode is quite strong,36an interaction which certainly does not help either u,n* or n,n*to develop regular vz(C0) progressions in the gaseous VUV spectrum. 111.3. 'Bz States. The minimum of (l)'B2 near 2.3 bohrs and 8.25 eV, shown in Figure 1, results from a crossing of n,u*CH2 with a diffuse state, the latter being composed of the more diffuse orbitals of the valence basis set. The repulsive potential n,u*co is only encountered beyond the maximum at about 2.9 bohrs. Thus, contrary to assumptions in the literat ~ r e , the ~ ' valence state n,u*co does not interact with the lowestlying 'B2 Rydberg states within the Franck-Condon region.36 111.4. 'A2 States. As seen in Figure 1, both 'A2 states lie below %*B2(H2COf). The low-lying (1)'Az (n,n*) state, whose properties are well knowr~,'-~.*~ does not perturb the Rydberg manifold. In contrast, the (2)IAz minimum (R 2.55 bohrs and 9.6 eV) lies within the Rydberg region. At R = 2.3 bohrs, this valence state has contributions from d,n*(55%) dn,x**(21%) and nn,n*2 (lo%), with d being lb2. The double excitations dominate at larger CO distances, with 35% dn,n**and 45% nn,n*2 at R = 3.4 bohrs. The (2)'A2 minimum lies close to that of (3) I A1 (no,n*2).
+
-.
2.5
2 2.0
2.5
3.5
3.0
R(C-0) [bohrl Figure 1. R(C0) stretching potential curves-of diabatic valence states of planar H K O , including the ground state X2B2 of H2CO'. MRD-CI
-
results obtained with basis A (valence-only basis). The curves labeled Ryd, estimated by 3s, 3p, and 3d are diabatic potentials of type n combining experimental term values with the H2CO+(X2B2)curve. The 13Al(n,n*)potential is given to show its proximity to X'Aj(n,n*ln2) for R(C0) > 3.0 bohrs.
TABLE 1: Electronic Structure of the First Three 'A1 Valence States of Planar HXO as a Function of R(C0)" RICO) state
2.3 bohrs
3.0 bohrs
4.0 bohrs
(1)'Al
70% n2 15% n,n* 8% n2 45% n,n* 25% no,n*2 10% n,u*CH2 3 0 8 n,n* 30% no,n*2 15% n,u*CH2 15% dn,n**
45% n2 45% n,n* 40% n2 45% n,n*
10% n2 65% n,n* 50% n2 10% n,n* 30% Q,U*CO
(2)'AI
(31l.41
45% no,n*2 45% d n , n * 2
Results obtained with basis A (valence-only AOs).
%'AI becomes a four open-shell system as it dissociates into CH2(X3Bl) O(3Pg). The (2)'A, potential shows a feature which has far-reaching spectroscopic consequences: (2)IAl has an avoided crossing with (3)'Al at short and with %'AI at large R. The avoided crossing near R = 2.3 bohrs occurs within a dense Rydberg region, justifying the complex structure and high intensity of the 9.5-10.5 eV region of the spectrum. The (2)IAl state has predominant n,n*character within the narrow interval from 2.3 to 2.7 bohrs. Near its minimum at R 3.0 bohrs and -8.05 eV, n,n*is strongly mixed with the (ground state) n2 configuration, giving rise to the predissociated character of all W V absorption bands, due to the predissociating property of n,n*. Below 2.2 bohrs, (2)'Al changes from singly-excited n,n*to doubly-excited n0,n**, after an avoided crossing with (3)'A1. In this region the n,n*configuration lies well above H2COf (g2B2), contributing to higher 'AI states of H2CO. The vertical excitation energy of (3)'Al is 10.60 eV. At the vertical geometry, n,x* and no,n*2 are the main contributors
+
-
-
IV. CO Stretch Potential Curves for Valence and Rydberg States. Basis Set B In this section, the R(C0) potential curves for singlet states of planar H2CO obtained from MRD-CI calculations with basis B (valence plus n = 3 Rydberg AOs) will be discussed. Spectroscopic data are summarized in Table 2. IV.1. 'A1 States. Potential curves for 'A1 states are shown in Figure 2. The minimum of %'A1 is found at R = 2.279 bohrs, with v2(CO) = 1714 cm-I, in fairly good agreement with experimental results. When compared with R = 2.132 bohrs and oe= 2170 cm-' of diatomic C0,50the CO bond in H2CO is seen to be weaker, with a formal change from triple-bond (in CO) to double-bond character (in H2CO). Along the R(C0)
Valence and Rydberg States of H2CO
J. Phys. Chem., Vol. 99, No. 20, 1995 8053
TABLE 2: Adiabatic Excitation Energies (eV), Equilibrium R ( C 0 ) Distances (bohrs), and v ~ ( C 0Frequencies ) (cm-') of Low-Lying Singlet States of Planar HzCO" state
configuration near equilibrium
...02n2n2 n,3p, (left) n,n*ln2 (right)
n,3p,/n,n* n,3d,,ln,n* u,n* n,3dxJa,n* n,3s n,3s n,3p, n,3d,2 n,3dX2-,2 n,n* n,3px n,3dxz ...d n 2 n (n,m)
10.0
T,
R,(CO)
0.00"
2.279 2.274 2.266 2.299 2.161 2.914 2.907 2.160 2.748 2.504 2.361 2.680 2.813 2.797 2.345 -[2.52] 2.302 2.138 2.123 2.298 2.162 2.144 2.285 2.300 2.522 2.312 2.359 2.272 2.275 2.264 2.813
0.00 1.98 7.97 9.68 7.95 7.99 8.61 8.60 8.61 9.18 8.27 7.99 8.19 9.30 [10.12] 7.09 8.40 1.70 1.94 9.19 8.33 9.06 9.12 3.64 4.40 4.35 8.15 9.17 10.65 10.97
v ~ ( C 0 ) rep 1714 1750 1650 1689 770 -835 818 -2100 1074 893 -2250 1704 1862 1676 1831 1630 1600 1180 1645 1188 1710 1659 1510
TW 3
9.0
Tw 10 11 TW 10 11 12 TW TW TW 11 12 TW TW TW 11 12
8.0
