J. Phys. Chem. 1996, 100, 13487-13491
13487
Ab Initio Calculations of the Excited States of Formamide Jonathan D. Hirst,* David M. Hirst,† and Charles L. Brooks III Department of Molecular Biology, MB-19, The Scripps Research Institute, 10666 North Torrey Pines Road, La Jolla, California 92037 ReceiVed: February 27, 1996; In Final Form: May 23, 1996X
The excited states of formamide in the gas phase have been calculated using multireference configuration interaction methods. The nπ* transition is calculated to be at 5.85 eV, and the ππ* transition is placed at 7.94 eV. The corresponding experimental energies are 5.65 and 7.32 eV, respectively. In addition, a number of states with significant intensity are calculated to occur in the region of the experimental spectrum designated as the V1 band. The experimental ππ* transition dipole moment, 3.71 D, is estimated by assuming that the intensity of the V1 band is due solely to the ππ* transition. The calculated ππ* transition dipole moment is 3.70 D, if only one unoccupied a′′ orbital is included in the active space. If the number of unoccupied a′′ orbitals in the active space is increased, the calculated ππ* transition moment drops to 2.40 D, and another transition, the π3pπ, appears at 7.40 eV, but with only low to moderate intensity. The calculated orientation of the ππ* transition dipole moment agrees with the experimental data, lying along the axis defined by the N and O atoms.
Introduction In this paper, we present ab initio calculations of the electronic absorption spectrum of formamide. Formamide is the simplest model for the peptide chromophore in proteins. As such, a detailed understanding of its electronic excited states is a prerequisite for understanding the electronic spectroscopy of proteins and, in particular, their circular dichroism (CD) spectra. CD spectroscopy is a widely used tool in the study of protein conformation.1-3 The key features of the CD spectra arise from the optical rotation of light around chiral centers. The rotational strength depends on both the electronic transition dipole moment and the magnetic transition dipole moment.4 To calculate CD spectra, one requires knowledge of the electronic transitions of model chromophores like formamide or N-methylacetamide.5 The ground state geometry of formamide has been determined by microwave spectroscopy6,7 and by gas-phase electron diffraction.8 The electronic absorption spectrum has been measured by several groups.9-12 These experimental studies provide the following data by which one may assess the quality of our calculations. The ground state dipole moment, µ00 ) 3.71 ( 0.06 D, is oriented at an angle of 39.6° away from the N-C bond toward the O atom.6 Five bands have been identified in the electronic absorption spectrum:12 a weak transition at 5.65 eV, labeled the W band and identified as the nπ* transition; a Rydberg excitation at 6.7 eV, the R1 band; and an intense ππ* band at 7.32 eV, termed the V1 band; a second Rydberg excitation at 7.8 eV, the R2 band; and the Q band at 9.2 eV. The electronic transition dipole moment of the dominant ππ* excitation is µππ* ) 3.7 D and is oriented along the axis defined by the N and O atoms.9,10,12 The corresponding oscillator strength for this transition is f ) 0.37. The bands in the spectrum are broad, and the assignments and precise locations of the vertical transitions are by no means definitive (see Figure 1). For example, the portion of the spectrum assigned to the V1 and R2 transitions consists of a broad band of width 1 eV extending from 7.0 to 8.0 eV with sharp peaks at 7.7, 7.9, and 8.1 eV. † Department of Chemistry, University of Warwick, Coventry, CV4 7AL, U.K. X Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00597-7 CCC: $12.00
Figure 1. Experimental spectrum, adapted from ref 12 (dashed curve), and the calculated spectra (solid vertical lines are the 9,0;16,6 calculation; dashed vertical lines are the 9,0;13,3 calculation) of formamide. The calculated spectra are line spectra with absolute intensities that have been arbitrarily scaled for the figure, because bandwidths cannot be reliably estimated. The states are labeled according to the 9,0;16,6 calculation. Labels for the low-intensity 4 1 A′′ and 5 1A′′ states, which fall either side of the 5 1A′ state, are omitted for clarity. Both the experimental and calculated intensities of the 1 1 A′′ state are magnified by a factor of 50.
There have been a number of theoretical studies of the excited states of formamide, although only one recently. In an early study, Basch et al.13 performed self-consistent-field (SCF) calculations, using double-zeta Gaussian basis sets, which placed the nπ* transition at 4.08 eV and the ππ* transition at 10.49 eV. The addition of configuration interaction (CI) brought the ππ* transition down in energy of 6.42 eV. They also estimated the ground state dipole moment to be 4.95 D. In another study by Goddard and Harding,14 the nπ* transition was found to be at 5.65 eV and the ground state dipole moment to be 3.8 D. In this study, a generalized valence bond methodology was employed. A description of the ππ* transition was precluded by the inadequacy of the valence basis set. © 1996 American Chemical Society
13488 J. Phys. Chem., Vol. 100, No. 32, 1996 SCF and CI calculations of Stenkamp and Davidson15 placed the nπ* transition at 5.7 eV (in good agreement with experiment) and the ππ* transition at 8.5 eV (1.2 eV higher than experiment) with a predicted oscillator strength of 0.37. The ground state dipole moment was predicted to be 4.1 D. The conclusion of this study was that ordinary SCF theory is not applicable to the ππ* state and that this state is extensively mixed with the states n3s, n3py, π3pπ, and n3pz. Stenkamp and Davidson15 suggested that an accurate treatment of the ππ* state would require a basis set and configuration list which is unbiased in its treatment of these states. To address this, a hybrid orbital basis and a partitioning perturbation theory were developed.16 These calculations gave ππ* transition energies between 6.96 and 8.21 eV. CI calculations using the CIPSI algorithm,17 which combines variational and perturbation techniques, placed the nπ* transition at 5.85 eV and the ππ* transition at 7.56 eV (f ) 0.36), with four intervening Rydberg transitions at 6.09, 6.68, 7.08, and 7.09 eV. Oliveros et al. suggested that the improvement in the ππ* transition energy may have resulted from a larger account of the σπ correlation effects and the underestimation of some ground state correlation effects. The excited state CIPSI calculations used ground state SCF orbitals. The work of Stenkamp and Davidson15 and of Nitzsche and Davidson16 has shown this to be an inadequate starting point for calculations of the ππ* state. More recently Sobolewski,18 in a study of the formamide dimer and the formamide-water complex, reported CASPT2 calculations with a double-zeta plus polarization basis set for formamide and obtained excitation energies of 5.85 and 7.67 eV for the nπ* and ππ* transitions. However, since the basis set does not include Rydberg functions, it is not capable of giving an accurate description of the excited states of formamide. Furthermore, the active space in this calculation only included the 11a′ and the 3a′′ orbitals beyond those occupied in the ground state and would seem to be inadequate for a description of the observed excited states. Finally, we note that the geometries of some of the excited states of formamide have been optimized19 using CI singles20 and a 6-31g* basis set. Additionally, in a study of the electrostatic properties of N-acetylalanine-N′-methylamide, Price et al.21 calculated the dipole moment of formamide for a series of basis sets and obtained values in the range 4.39-4.57 D in SCF calculations and 3.89-4.11 D in MP2 calculations. The limitations of the earlier calculations have demonstrated several features that must be taken into account in the calculation of excited states of amides. First, it is necessary to use an adequate basis set. The calculations of Basch et al.12 used double-zeta basis sets with the addition of either diffuse s or diffuse p functions, but not both. Diffuse functions were not included in either the calculations of Harding and Goddard14 or those of Sobolewski,18 and therefore these papers were not able to describe Rydberg states. The work of Davidson and co-workers15,16 employed double-zeta polarization Gaussian lobe basis sets with diffuse s and p functions on the carbon atom only. The basis set used by Oliveros et al.17 was a double-zeta basis set with diffuse s and p functions on each heavy atom, but did not include polarization functions. The calculations reported here employ much more extensive basis sets than those used in any of the previous calculations on this system. The second requirement for a realistic description of the excited states is the use of molecular orbitals suitable for each of the excited states and which are not biased in favor of one particular state. The work of Stenkamp and Davidson15 and of Nitzsche and Davidson16 highlighted the problems associated
Hirst et al. with the 1A′(ππ*) state. We have used the CASSCF/MCSCF method in which state averaging was performed over the excited states of interest. Finally, electron correlation needs to be properly accounted for, and we have done this by using the multireference configuration interaction (MRCI) method, in which the set of reference configurations includes all of the important configurations in the CASSCF calculation. Our aim is to perform calculations on formamide within a consistent framework, in which no particular state requires special treatment, to provide a basis for investigating other amides. Computational Details We have performed excited state calculations for formamide with the MOLPRO suite of programs.22 The ground state and excited state energies, permanent dipole moments, and transition dipole moments were computed using the internally contracted MRCI procedure.23,24 As in excited state calculations for the CN+ ion,25 these MRCI calculations used the MCSCF orbitals from state-averaged CASSCF calculations.26,27 The molecular orbitals obtained in this procedure are not biased toward any particular electronic state and should be a good starting point for MRCI calculations of excited states. The reference configurations for the MRCI calculations were chosen by selecting those configurations which had a norm g0.05 for any state in the CASSCF wave function. The geometry used in these calculations was taken from a geometry optimization at the MP2 (second-order Møller-Plesset perturbation theory28) level using the 6-31+g** basis set. The bond lengths and angles used are as follows: rCN ) 1.362 Å (1.368 Å); rCO ) 1.2287 Å (1.212 Å); rNH1 ) 1.0075 Å (1.027 Å); rNH2 ) 1.0053 Å (1.027 Å); rCH ) 1.0991 Å (1.125 Å); ∠NCO ) 124.5481° (125.0°); ∠CNH1 ) 119.2950° (118.7°); ∠CNH2 ) 121.3087° (119.7°); ∠NCH ) 112.7905° (112.7°). The experimental data8 are shown in parentheses. This calculation, which utilized the package Gaussian94,29 led to a geometry that essentially reproduced the experimental geometry. In the complete active space SCF (CASSCF) method,30,31 three sets of orbitals are defined. The lowest orbitals, known as the inactive or closed orbitals, are doubly occupied in all configurations. The highest orbitals, the virtual orbitals, are unoccupied in all configurations. The active orbitals lie between the closed orbitals and the orbitals that are unoccupied in all configurations. In a CASSCF calculation, the configurations of appropriate symmetry and spin are generated from all possible arrangements of the active electrons (electrons not in the doubly occupied closed orbitals) among the active orbitals. If one is interested in several electronic states, molecular orbitals can be derived by a state-averaged procedure in which all of the states of interest are treated simultaneously. The ground state of formamide has the electronic configuration (1a′)2...(10a′)2(1a′′)2(2a′′)2. A number of different active spaces were explored in our calculations. These ranged from two a′ orbitals (10a′-11a′) and three a′′ orbitals (1a′′-3a′′) to seven a′ orbitals (10a′-16a′) and six a′′ orbitals (1a′′-6a′′) with some orbitals restricted to single occupancy. Nine a′ orbitals were treated as closed. The orbitals 1a′-3a′ are 1s orbitals on the O, N, and C atoms and 4a′ and 5a′ are essentially 2s orbitals on O and N. To consider just five closed a′ orbitals was computationally prohibitive. The four a′ orbitals lying above these core orbitals are all involved in σ-bonding, and their energies were sufficiently close to one another that inclusion of only some of them in the active space resulted in convergence problems in the MCSCF. Thus, the choice of nine closed a′ orbitals was obvious.
Excited States of Formamide
J. Phys. Chem., Vol. 100, No. 32, 1996 13489
TABLE 1: Exponents of the Diffuse Functions type
atom
s p s s s p p p
TABLE 3: Calculated Transition Energies and Dipole Momentsa
exponents
H H C N O C N O
transition transition dipole moment (D) oscillator strength assignt µy µz state energy (eV) µx
0.036 00 0.036 00 0.017 52 0.021 00 0.024 00 0.015 75 0.018 75 0.021 00
0.043 70 0.053 20 0.060 80 0.039 90 0.047 50 0.053 20
TABLE 2: Permanent Moments of the Statesa state
µx (D)
µy (D)
state
µx (D)
µy (D)
1A′
-4.37 3.36 0.57 -2.16 -2.22 4.49
-1.21 0.11 1.42 -1.46 -2.20 -1.47
1A′
0.41 -2.00 4.05 0.14 -4.92 5.00
-0.03 -0.39 -0.06 -0.68 0.57 -0.34
1 2 1A′ 3 1A′ 4 1A′ 5 1A′ 6 1A′
7 1 1A′′ 2 1A′′ 3 1A′′ 4 1A′′ 5 1A′′
a The active space used was 9,0;13,3; the basis set is 6-31+g**, in which the diffuse functions have exponents appropriate for Rydberg states.
Several split-valence basis sets with polarization functions were explored:32 6-31+g**, 6-31++g**, and 6-311++g**. Calculations were also done using the valence double- and triplezeta correlation consistent basis sets.33-35 The results of the calculations were fairly insensitive to basis set (as discussed later), and we report calculations for the 6-31+g** basis set, i.e., 6-31g** with two diffuse s-functions and two diffuse p-functions centered on each of the heavy atoms with exponents appropriate for Rydberg states36 and one diffuse s-function on each H atom. (The exponents of the diffuse functions are given in Table 1.) An important feature in the basis sets employed here was the use of exponents for the diffuse functions appropriate for Rydberg states,36 which are different from those described by Hehre et al.32 which were optimized for anions. Results Although many of the variations in active space and basis set had very little quantitative effect on the calculated spectrum, the number of unoccupied a′′ orbitals in the active space did give rise to some qualitative differences. We present data from two calculations: one in which the active space contained one unoccupied a′′ orbital and one which contained four unoccupied a′′ orbitals. The first calculation was performed using an active space of 9,0;13,3, i.e., four a′ orbitals (10a′-13a′) and three a′′ orbitals (1a′′-3a′′). In this active space notation, a,b;c,d, a is the number of closed orbitals of a′ symmetry, b is the number of closed orbitals of a′′ symmetry, c is the number of closed and active a′ orbitals, and d is the number of closed and active a′′ orbitals. The transition energies and transition dipole moments were taken from a MRCI calculation, with the same active space as the CASSCF calculation. The first nine a′ orbitals were treated as core orbitals in the MRCI calculation. The initial orbitals for this calculation were obtained in a state-averaged MCSCF calculation for 10 A′ states and seven A′′ states (with approximately 250 configurations for each state). In the MRCI calculation, seven A′ states and five A′′ states were calculated using the projection procedure of Knowles and Werner.37 For each A′ state, approximately 67 000 contracted configurations were included, and around 105 000 contracted configurations were included for the A′′states. The permanent moments of the states are given in Table 2. The transition energies and transition dipole moments are presented in Table 3.
2 1A′ 3 1A′ 4 1A′ 5 1A′ 6 1A′ 7 1A′ 1 1A′′ 2 1A′′ 3 1A′′ 4 1A′′ 5 1A′′
6.51 7.22 7.54 7.90 12.08 13.12 5.85 6.09 6.96 7.43 9.61
0.09 -0.70 -0.27 3.65 -0.05 -0.15 0.00 0.00 0.00 0.00 0.00
0.01 -1.22 -0.93 -0.30 -0.21 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.12 -0.94 -0.13 -0.37 -1.05
0.0002 0.0541 0.0268 0.4009 0.0021 0.0011 0.0003 0.0204 0.0004 0.0038 0.0401
n3s n3py n3px ππ* nπ* π3s π3py n3pπ
a The active space used was 9,0;13,3; the basis set is 6-31+g**, in which the diffuse functions have exponents appropriate for Rydberg states. Assignments are based on analyses of the natural orbitals and of the CI configurations. No assignments have been made for the highenergy states. The energies are relative to a ground state energy of -169.046 69 hartrees.
TABLE 4: Permament Moments of the Statesa state
µx (D)
µy (D)
state
µx (D)
µy (D)
1 1A′ 2 1A′ 3 1A′ 4 1A′ 5 1A′ 6 1A′
-4.39 3.35 -0.96 -2.70 -1.62 -2.72
-1.24 0.15 2.56 -2.28 -0.21 3.12
7 1A′ 1 1A′′ 2 1A′′ 3 1A′′ 4 1A′′ 5 1A′′
-0.83 -1.98 4.00 0.19 -4.32 -0.11
0.12 -0.05 -0.40 -0.64 0.32 1.40
a The active space used was 9,0;16,6; the basis set is 6-31+g**, in which the diffuse functions have exponents appropriate for Rydberg states.
In the second calculation that we present, the active space was increased to 9,0;16,6. Other active spaces were also explored, but the results of the calculations were qualitatively similar to either the 9,0;13,3 calculation (if the number of a′′ orbitals in the active space was three) or the 9,0;16,6 calculation (if the number of a′′ orbitals in the active space was greater than three). The initial orbitals for this calculation were obtained in a state-averaged MCSCF calculation for nine A′ states and six A′′ states; otherwise, the second calculation was performed in a similar fashion to the first. The number of configurations for each state in the MCSCF calculation was approximately 13 000; in the MRCI calculation 159 000 contracted configurations were included for the A′ states and 640 000 for the A′′ states. The permanent moments of the states, from this calculation, are given in Table 4, and the transition energies and transition dipole moments are presented in Table 5. The experimental spectrum (from Basch et al.12) and the calculated vertical electronic spectra are shown in Figure 1. The calculated states were assigned by analysis of the natural orbitals and the principal configurations in the CI calculation. The assignments of the Rydberg states in the calculated spectrum were complicated by the significant mixing of these states. Further, the Rydberg orbitals centered on the oxygen and nitrogen atoms often made significant contributions to the wave functions. The use of a single set of Rydberg orbitals has been used previously in calculations on formaldehyde38 and on formamide;15 however, we found that this gave qualitatively worse energies for formamide (data not shown). The calculated 1 1A′′ state is the nπ* transition and corresponds to the W band in the experimental spectrum. The 2 1A′′ state corresponds to the π3s transition seen experimentally as the R1 band. The other A′′ states do not feature significantly in the spectrum. The 2 1A′ state has negligible intensity. The 3 1A′ and 5 1A′ states are n3p states and occur in the V1 band.
13490 J. Phys. Chem., Vol. 100, No. 32, 1996
Hirst et al.
TABLE 5: Calculated Transition Energies and Dipole Momentsa
TABLE 6: Sensitivity of the Calculated Spectrum with Respect to Active Space and Basis Seta
transition transition dipole moment (D) oscillator strength assignt µy µz state energy (eV) µx 2 1A′ 3 1A′ 4 1A′ 5 1A′ 6 1A′ 7 1A′ 1 1A′′ 2 1A′′ 3 1A′′ 4 1A′′ 5 1A′′
6.49 7.16 7.40 7.50 7.94 8.33 5.86 6.14 7.01 7.47 7.57
0.12 -0.93 2.07 -0.95 -2.21 -0.08 0.00 0.00 0.00 0.00 0.00
0.01 -1.16 -0.75 -0.73 0.27 0.15 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 -0.11 -0.98 -0.14 0.40 -0.40
0.0004 0.0599 0.1358 0.0408 0.1491 0.0009 0.0003 0.0223 0.0005 0.0045 0.0046
n3s n3py π3pπ n3px ππ* nπ* π3s π3py n3pπ π3px
a The active space used was 9,0;16,6; the basis set is 6-31+g**, in which the diffuse functions have exponents appropriate for Rydberg states. Assignments are based on analyses of the natural orbitals and of the CI configurations. The energies are relative to a ground state energy of -169.049 61 hartrees.
The 4 1A′ and 6 1A′ states both involve transitions from the highest occupied π orbital. The 4 1A′ state is the π3pπ transition, and the 6 1A′ state is the ππ* transition. The 4 1A′ state is located in the V1 band and the 6 1A′ state is in the region labeled R2 by Basch et al.12 In the larger active space calculation the appearance of the π3pπ transition reduces the total intensity of the calculated spectrum. In the smaller active space calculation, the intensity of the ππ* transition is close to the estimate from the area under the V1 band in the experimental spectrum. While increasing the number of a′ orbitals in the active space did not significantly alter the transition energies or dipole moments, it did have an effect on the CI wave functions. The final CI wave functions for some states did include a number of significant configurations (having a coefficient g0.05) which were not in the set of reference configurations. As the number of active a′ orbitals was increased, the number of these configurations dropped substantially. With an active space of 9,0;16,6, only the 6 1A′ state contained significant contributions not in the reference set. Extensions of the 6-31+g** basis set, such as the inclusion of diffuse d orbitals, greater flexibility in the s and p diffuse functions or the inclusion of an extra set of valence functions, did not yield any significant changes. The similar results obtained with the correlation consistent valence double- and triple-zeta basis sets indicate that there is no obvious deficiency with the 6-31+g** basis set provided that the exponents for the diffuse functions are appropriate for Rydberg states. The sensitivity of the calculated spectrum with respect to changes in active space and basis set is summarized in Table 6. Conclusions State of the art ab initio methods have been applied to calculate the excited states of formamide. The calculated electronic absorption spectrum exhibits many of the features of the experimental spectrum. The calculated nπ* and π3s states correspond well with the W and R1 bands, respectively. Three moderately intense transitions are calculated to lie in the V1 band. The calculated ππ* transition energy is a little high, falling in the R2 region. The broad nature of the experimental spectrum suggests that there is significant vibrational structure. These features hamper the experimental assignment of the precise locations of the vertical transitions. Our calculations do not probe the vibrational structure, and the computation of the required vibrational wave functions is currently difficult for molecules of the size of formamide. The appearance of the
state
∆E (eV)
|µ| (D)
state
∆E (eV)
|µ| (D)
2 1A′ 3 1A′ 4 1A′ 5 1A′ 6 1A′ 7 1A′
6.46 (0.02) 7.14 (0.02) 7.37 (0.02) 7.48 (0.02) 7.90 (0.08) 8.49 (0.10)
0.07 (0.02) 1.53 (0.05) 2.13 (0.09) 1.09 (0.12) 2.23 (0.17) 0.28 (0.09)b
1 1A′′ 2 1A′′ 3 1A′′ 4 1A′′ 5 1A′′
5.82 (0.04) 6.10 (0.01) 6.97 (0.02) 7.43 (0.04) 7.53 (0.02)
0.12 (0.04) 1.00 (0.02) 0.15 (0.01) 0.43 (0.01) 0.44 (0.03)
a The mean transition energies (in eV) and the mean magnitudes of the transition dipole moments (in D) are given with standard deviations in parentheses. These values were computed from the results of the following 10 calculations: correlation consistent valence double-zeta basis set with active spaces of (i) 9,0;13,6, (ii) 9.0;14,6, and (iii) 9,0;15,6; (iv) correlation consistent valence triple-zeta basis set with an active space of 9,0;13,6; 6-31+g** basis set (with two sets of diffuse functions as described in the Methods section) with active spaces of (v) 9,0;13,6, (vi) 9,0;14,6, and (vii) 9,0;15,6; (viii) 6-31+g** basis set with one set of diffuse functions and an active space of 9,0;13,6; (ix) 6-31+g** basis set with three sets of diffuse functions and an active space of 9,0;14,6; (x) 6-31+g** basis set with two sets of diffuse functions plus diffuse d functions and an active space of 9,0;13,6. The results of the calculations presented in Tables 1-4 are not included in this table. b Properties of the 7 1A′ state were not computed for the correlation consistent basis sets.
π3pπ transition in the larger active space calculations is interesting. This suggests that there may be borrowing of intensity from the higher energy ππ* transition; however, further exploration of this is beyond the scope of these calculations. Two earlier studies have reported ππ* energies that are closer to the peak of the V1 band in the experimental spectrum. CIPSI calculations17 gave the ππ* transition energy as 7.56 eV. Oliveros et al. remarked that this agreement was perhaps surprising and arose, in part, from the underestimation of some ground state correlation effects. In order to understand the more recent results of Sobolewski,18 we have performed MCSCF and MRCI calculations using the same basis set as Sobolewski. A two-state MCSCF calculation (i.e., state-averaging over two states) followed by MRCI gave a ππ* transition energy of 8.33 eV. However, Sobolewski optimized each state separately. When we optimized each state separately in our MCSCF and MRCI calculations, the difference between the ground state and the ππ* energies gave a transition energy of 7.83 eV. The agreement with experiment is better, but one has used different orbitals for the two states. Treating each state separately is unbalanced, and one obtains a worse energy for the ground state, but does better for the excited state. The difference between our calculated ππ* transition energy and the location of the peak in the V1 band of the measured spectrum may, in principle, be due to a number of factors, including the choice of basis set or the CI treatment. The MRCI method we have used accounts for a significant amount of correlation, but obviously it is not necessarily an optimal treatment. Very preliminary calculations, that we have performed, suggest that including the 6a′, 7a′, 8a′, and 9a′ orbitals in the CI treatment may give a better ground state dipole moment, but there has been no indication of an improvement in the ππ* transition energy. Explorations of extensions to our basis set have also not shown any change in the computed ππ* transition energy. Another possible influence on the computed ππ* transition energy could be artificial mixing between the Rydberg states and the ππ* state. Roos and co-workers39 have suggested that basis sets that do not contain good representations of Rydberg orbitals can lead to artificial mixing between Rydberg and valence statessthis occurs, for example, in the case of ethylene.40,41 We are currently investigating the relevance of this possibility in our calculations.
Excited States of Formamide Our calculations on formamide are done within a consistent framework, in which no particular state requires special treatment, and thus they serve as a basis to investigate other amides. However, the extension to N-methylacetamide may not be trivial. Earlier calculations42 suggest that there are a large number of intervening states before the ππ* state. The formamide calculations suggest that the number of a′′ states in the active space and the use of appropriate diffusion functions are of importance. Acknowledgment. We thank the Pittsburgh Supercomputing Center for access to substantial computational resources which made this initial study possible, J.D.H. thanks the Human Frontiers Science Program for a long-term fellowship. The EPSRC and the NIH (GM 48807, GM 37554) also provided financial support. References and Notes (1) Yang, J. T.; Wu, C.-S. C.; Martinez, H. M. Methods Enzymol. 1986, 130, 208-269. (2) Tinoco, I. AdV. Chem. Phys. 1962, 4, 113-160. (3) Woody, R. W.; Tinoco, I. J. Chem. Phys. 1967, 46, 4927-4945. (4) Charney, E. The Molecular Basis of Optical ActiVity; John Wiley: New York, 1979. (5) Manning, M. C.; Woody, R. W. Biopolymers 1991, 31, 569-586. (6) Kurland, R. J.; Wilson, E. B. J. Chem. Phys. 1957, 27, 585-590. (7) Costain, C. C.; Dowling, J. M. J. Chem. Phys. 1960, 32, 158165. (8) Kitano, M.; Kuchitso, K. Bull. Chem. Soc. Jpn. 1974, 47, 67-72. (9) Hunt, H. D.; Simpson, W. T. J. Am. Chem. Soc. 1953, 75, 45404543. (10) Peterson, D. L.; Simpson, W. T. J. Am. Chem. Soc. 1957, 79, 23752382. (11) Kaya, K.; Nagakura, S. Theor. Chim. Acta 1967, 7, 117-123. (12) Basch, H.; Robin, M. B.; Kuebler, N. A. J. Chem. Phys. 1968, 49, 5007-5018. (13) Basch, H.; Robin, M. B.; Kuebler, N. A. J. Chem. Phys. 1967, 47, 1201-1210. (14) Harding, L. B.; Goddard, W. A. J. Am. Chem. Soc. 1975, 97, 63006305. (15) Stenkamp, L. Z.; Davidson, E. R. Theor. Chim. Acta 1977, 44, 405-419. (16) Nitzsche, L. E.; Davidson, E. R. J. Chem. Phys. 1978, 68, 31033109. (17) Oliveros, E.; Riviere, M.; Teichteil, C.; Malrieu, P. Chem. Phys. Lett. 1978, 57, 220-223. (18) Sobolewski, A. L. J. Photochem. Photobiol. 1995, 89, 89. (19) Li, Y.; Garrell, R. L.; Houk, K. N. J. Am. Chem. Soc. 1991, 113, 5895-5896.
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