Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers.

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data.

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH2, Ac-Ala-NH2, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.

Structural and Vibrational Properties of Amino Acids from Composite Schemes and Double-Hybrid DFT: Hydrogen Bonding in Serine as a Test Case.

The structures, relative stabilities, and vibrational wavenumbers of the two most stable conformers of serine, stabilized by the O-H···N, O-H···O═C and N-H···O-H intramolecular hydrogen bonds, have been evaluated by means of state-of-the-art composite schemes based on coupled-cluster (CC) theory. The so-called "cheap" composite approach (CCSD(T)/(CBS+CV)MP2) allowed determination of accurate equilibrium structures and harmonic vibrational wavenumbers, also pointing out significant corrections beyond the CCSD(T)/cc-pVTZ level. These accurate results stand as a reference for benchmarking selected hybrid and double-hybrid, dispersion-corrected DFT functionals. B2PLYP-D3 and DSDPBEP86 in conjunction with a triple-ζ basis set have been confirmed as effective methodologies for structural and spectroscopic studies of medium-sized flexible biomolecules, also showing intramolecular hydrogen bonding. These best performing double-hybrid functionals have been employed to simulate IR spectra by means of vibrational perturbation theory, also considering hybrid CC/DFT schemes. The best overall agreement with experiment, with mean absolute error of 8 cm-1, has been obtained by combining CCSD(T)/(CBS+CV)MP2 harmonic wavenumbers with B2PLYP-D3/maug-cc-pVTZ anharmonic corrections. Finally, a composite scheme entirely based on CCSD(T) calculations (CCSD(T)/CBS+CV) has been employed for energetics, further confirming that serine II is the most stable conformer, also when zero-point vibrational energy corrections are included.

The role of dispersion and anharmonic corrections in conformational analysis of flexible molecules: the allyl group rotamerization of matrix isolated safrole.

Conformational changes of the monomeric safrole (5-(2-propenyl)-1,3-benzodioxole) isolated in low temperature xenon matrices were induced thermally or using narrow-band UV radiation. The rotation of the allyl group taking place in the studied matrices was followed by FTIR spectroscopy. Safrole represents a challenging example of a flexible molecule highlighting the importance of dispersion interactions and anharmonic effects in the structural, spectroscopic and energetic analysis. Structures of the safrole conformers, their energetics and infrared spectra have been calculated using various computational methods ranging from density functional theory (DFT) to coupled cluster (CC). The best theoretical results were obtained by integrating CCSD(T) energies including complete basis set extrapolation and core-valence corrections with B2PLYP-D3 equilibrium structures and hybrid B2PLYP-D3/B3LYP-D3 anharmonic computations for IR spectra and thermodynamics.

Conformational Equilibria and Molecular Structures of Model Sulfur-Sulfur Bridge Systems: Diisopropyl Disulfide.

The conformations and molecular structures of diisopropyl disulfide have been studied by high-resolution microwave spectroscopy and quantum chemical calculations. Three conformers, G'GG', G'GT, and GGG', have been observed in the jet expansion. The global minimum, G'GG', adopts a configuration with the G' orientation of H-C-S-S and S-S-C-H and the G orientation of C-S-S-C showing the C2 symmetry. The rotational spectra of monosubstituted 13C and 34S isotopologues have also been recorded for G'GG', leading to an accurate structural determination of this conformer. Two additional 34S isotopologues have also been measured for G'GT. The relative energies of three observed conformers calculated at the MP2/6-311++(d,p) level of theory are within 2 kJ mol-1, while the relative intensity measurements suggested their population ratio to be NG'GG'/NG'GT/NGGG' ≈ 5:3:2.

Absorption-emission symmetry breaking and the different origins of vibrational structures of the 1Qy and 1Qx electronic transitions of pheophytin a.

The vibrational structure of the optical absorption and fluorescence spectra of the two lowest-energy singlet electronic states (Qy and Qx) of pheophytin a were carefully studied by combining low-resolution and high-resolution spectroscopy with quantum chemical analysis and spectral modeling. Large asymmetry was revealed between the vibrational structures of the Qy absorption and fluorescence spectra, integrally characterized by the total Huang-Rhys factor and reorganization energy in absorption of Svib A = 0.43 ± 0.06, λA = 395 cm-1 and in emission of Svib E = 0.35 ± 0.06, λE = 317 cm-1. Time-dependent density-functional theory using the CAM-B3LYP, ωB97XD, and MN15 functionals could predict and interpret this asymmetry, with the exception of one vibrational mode per model, which was badly misrepresented in predicted absorption spectra; for CAM-B3LYP and ωB97XD, this mode was a Kekulé-type mode depicting aromaticity. Other computational methods were also considered but performed very poorly. The Qx absorption spectrum is broad and could not be interpreted in terms of a single set of Huang-Rhys factors depicting Franck-Condon allowed absorption, with Herzberg-Teller contributions to the intensity being critical. For it, CAM-B3LYP calculations predict that Svib A (for modes >100 cm-1) = 0.87 and λA = 780 cm-1, with effective x and y polarized Herzberg-Teller reorganization energies of 460 cm-1 and 210 cm-1, respectively, delivering 15% y-polarized intensity. However, no method was found to quantitatively determine the observed y-polarized contribution, with contributions of up to 50% being feasible.

Accurate geometries for "Mountain pass" regions of the Ramachandran plot using quantum chemical calculations.

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly-peptide molecular models can predict accurate geometries for any well-defined backbone Ramachandran orientation. For conformations along transition regions-ϕ from -60 to 60°-a very good agreement with representative high-resolution experimental X-ray (≤1.5 Å) protein structures is obtained for both backbone C-1 -N-Cα angle and the nonbonded O-1 …C distance, while "standard geometry" leads to the "clashing" of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high-energy or unusual regions.

Theoretical studies of atmospheric molecular complexes interacting with NIR to UV light.

The interaction of weakly bonded complexes of atmospheric constituents with the electromagnetic spectrum available in Earth's atmosphere can induce direct excitation to electronic excited states as well as the excitation of higher vibrational states (overtones) of the electronic ground state. A better understanding of these phenomena requires improved theoretical support by including the anharmonic and vibro-electronic effects on both the band positions and transition intensities. In this work, generalized second-order vibrational perturbation and time-independent Franck-Condon and Herzberg-Teller computations are exploited together with a density functional theory (DFT)/coupled cluster (CC) scheme and its extension to the excited electronic states. Structural and spectroscopic properties are calculated for isolated formaldehyde and its complexes with H2O, CO, SO2 and H2O2, focusing on how small molecules may affect the interactions with NIR to UV irradiation.

Hydrogen detachment driven by a repulsive 1πσ* state - an electron localization function study of 3-amino-1,2,4-triazole.

Electron localization function analysis reveals the details of a charge induced hydrogen detachment mechanism of 3-amino-1,2,4-triazole, identified recently to be responsible for phototautomerization of the molecule. In this process vertical excitation to the 1πσ* state is followed by the barrier-less migration of a H atom along the N-H bond toward the conical intersection with the S0 ground state. The most striking feature revealed for the 1πσ* state is partial ejection of σ* electrons outside the molecule, even beyond the NH group, at the Franck-Condon point. Further gradual spatial localization of the electron around the proton moving along the N-H stretching coordinate gives a plausible explanation for the repulsive character of the 1πσ* potential energy surface with the proton wading through the region of space where some negative charge is accumulated ('a virtual acceptor'), dragging some electron density. This mechanism resembles the one postulated for the hydrogen transfer from a donor molecule (D-H) to an acceptor one (A) in a class of vertically excited molecules with a preexisting inter- or intramolecular D-HA motif, even though the acceptor molecule is absent. The present analysis demonstrates also that the bond evolution and changes in the electron density along the excited state reaction path can be effectively studied with the use of an electron localization function.

Challenges facing an understanding of the nature of low-energy excited states in photosynthesis.

While the majority of the photochemical states and pathways related to the biological capture of solar energy are now well understood and provide paradigms for artificial device design, additional low-energy states have been discovered in many systems with obscure origins and significance. However, as low-energy states are naively expected to be critical to function, these observations pose important challenges. A review of known properties of low energy states covering eight photochemical systems, and options for their interpretation, are presented. A concerted experimental and theoretical research strategy is suggested and outlined, this being aimed at providing a fully comprehensive understanding.

Structural and Vibrational Properties of Iodopentafluorobenzene: A Combined Raman and Infrared Spectral and Theoretical Study.

A combined study of the vibrational spectroscopy of iodopentafluorobenzene by new Raman and Fourier transform infrared (FTIR) spectroscopies, over the spectral range 300 to 3200 cm-1 (Raman) and 50 to 3400 cm-1 (FTIR), with a state-of-the-art theoretical investigation is reported. This has enabled reliable identification of numerous fundamental, overtone, and combination band transitions in unprecedented detail. The theoretical analysis, beyond the double-harmonic approximation, is based on generalized second-order vibrational perturbation theory (GVPT2) with a hybrid coupled cluster/density functional theory (CC/DFT) approach. Anharmonic contributions to structural parameters, rotational constants, vibrational frequencies, and spectral intensities are incorporated. The procedures, of general applicability, enable rigorous comparison of theoretical methods with experimental results in vibrational spectroscopy.

Accurate Vibrational-Rotational Parameters and Infrared Intensities of 1-Bromo-1-fluoroethene: A Joint Experimental Analysis and Ab Initio Study.

The medium-resolution gas-phase infrared (IR) spectra of 1-bromo-1-fluoroethene (BrFC═CH2, 1,1-C2H2BrF) were investigated in the range 300-6500 cm-1, and the vibrational analysis led to the assignment of all fundamentals as well as many overtone and combination bands up to three quanta, thus giving an accurate description of its vibrational structure. Integrated band intensity data were determined with high precision from the measurements of their corresponding absorption cross sections. The vibrational analysis was supported by high-level ab initio investigations. CCSD(T) computations accounting for extrapolation to the complete basis set and core correlation effects were employed to accurately determine the molecular structure and harmonic force field. The latter was then coupled to B2PLYP and MP2 computations in order to account for mechanical and electrical anharmonicities. Second-order perturbative vibrational theory was then applied to the thus obtained hybrid force fields to support the experimental assignment of the IR spectra.

Accurate spectroscopic characterization of the HOC(O)O radical: A route toward its experimental identification.

A set of accurate spectroscopic parameters for the detection of the atmospherically important HOC(O)O radical has been obtained by means of state-of-the-art ab initio computations. These include advanced coupled cluster treatments, involving both standard and explicitly correlated approaches, to correctly account for basis set incompleteness and core-valence effects. Geometric parameters for the X̃2A' and Ã2A'' states and, for the ground state only, vibrationally corrected rotational constants including quartic and sextic centrifugal distortion terms are reported. The infrared spectrum of the X̃2A' state has been simulated in the 4000-400 cm-1 wavenumber interval with an approach based on second order vibrational perturbation theory that allows accounting for anharmonic effects in both energies and intensities. Finally, the vibronic spectrum for the à ← X̃ transition has been calculated at three different temperatures in the 9000-3000 cm-1 energy range with a time-independent technique based on the Franck-Condon approximation.

A combined theoretical and experimental study of the valence and Rydberg states of iodopentafluorobenzene.

A new ultraviolet (UV) and vacuum ultraviolet (VUV) spectrum for iodopentafluorobenzene (C6F5I) using synchrotron radiation is reported. The measurements have been combined with those from a recent high-resolution photoelectron spectroscopic study. A major theoretical study, which includes both Franck-Condon (FC) and Herzberg-Teller (HT) analyses, leads to conclusions, which are compatible with both experimental studies. Our observation that the VUV multiplet at 7.926 eV in the VUV spectrum is a Rydberg state rather than a valence state leads to a fundamental reassignment of the VUV Rydberg spectrum over previous studies and removes an anomaly where some previously assigned Rydberg states were to optically forbidden states. Adiabatic excitation energies (AEEs) were determined from equations-of-motion coupled cluster with singles and doubles excitation; these were combined with time dependent density functional theoretical methods. Frequencies from these two methods are very similar, and this enabled the evaluation of both FC and HT contributions in the lower valence states. Multi-reference multi-root configuration interaction gave a satisfactory account of the principal UV+VUV spectral profile of C6F5I, with vertical band positions and intensities. The UV spectral onset consists of two very weak transitions assigned to 11B1 (πσ*) and 11B2 (σσ*) symmetries. The lowest unoccupied molecular orbital of a σ*(a1) symmetry has a significant C-I* antibonding character. This results in considerable lengthening of the C-I bond for both these excited states. The vibrational intensity of the lowest 11B1 state is dominated by HT contributions; the 11B2 state contains both HT and FC contributions; the third band, which contains three states, two ππ*(11A1, 21B2) and one πσ*(21B1), is dominated by FC contributions in the 1A1 state. In this 1A1 state, and the spectrally dominant bands near 6.7 (1A1) and 7.3 eV (1A1 + 1B2), the C-I bond length is in the normal range, and FC components dominate.

A combined theoretical and experimental study of the ionic states of iodopentafluorobenzene.

A new synchrotron radiation photoelectron spectral (PES) study of iodopentafluorobenzene, together with a theoretical analysis of the spectrum, where Franck-Condon factors are discussed, gives detailed insight into the ionization processes, and this exposes the need for a reinvestigation of the vacuum ultraviolet spectral (VUV) assignments. We have calculated adiabatic ionization energies (AIEs) for several ionic states, using the equation-of-motion coupled cluster method for ionic states combined with multi-configuration self-consistent field calculation study. The AIE sequence is: X2B1 < A2A2 < B2B2 < C22B1 < D2A1 < E32B1. This symmetry sequence has a major impact on previous VUV spectral assignments, which now appear to be to optically forbidden states. Changes in the equilibrium structures for these ionic states are relatively small, but a significant decrease and increase in the C-I bond length relative to the X1A1 structure occurs for the X2B1 and C2B1 states, respectively. The PES shows major vibrational overlaps between pairs of ionic states, X with A, and A with B. The result of these overlaps is the loss of vibrational structure and considerable broadening of the higher energy PES state. Although the baseline is nearly re-established between the A and B states, where the two bands are nearly separate, the B state is also broadened by the A state. Only the C ionic state, which shows the most highly developed vibrational structure, can be regarded as free from vibrational coupling to a neighbor state. The Franck-Condon analysis of the PES bands X, A, B, and C is described in detail; the apparent simplicity of some of these bands is illusory, since almost all the observed peaks arise from super-position of several calculated vibrational states. The experimental AIE of the A state, which is submerged under the X state envelope, has been determined by the subtraction of the calculated X state envelope from the observed PES spectrum. The overlap of these PES bands and the apparent closeness of the potential energy curves describing them have been investigated, using the state-averaged, complete active space self-consistent field method. We have identified two structures, one where the potential energy curves for the X and A states cross and another for the A and B states. At these two conical intersections (ConInts), there is zero-energy difference within each pair of states. Although similar in energy, the ConInt for the crossing of the X with A states, and that for the A with B states, shows that the open-shell occupancies correspond to the 4 lowest AIE states, and all four states that are quite different from each other.

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations.

A new synchrotron-based study of the photoelectron spectrum (PES) of difluoromethane is interpreted by an ab initio analysis of the ionic states, which includes Franck-Condon (FC) factors. Double differentiation of the spectrum leads to significant spectral sharpening; the vibrational structure observed is now measured with greater accuracy than in previous studies. Several electronic structure methods are used, including equation of motion coupled cluster calculations with single and double excitations (EOM-CCSD), its ionization potential variant EOM-IP-CCSD, 4th order Møller-Plesset perturbation theory (MP4SDQ) configuration interaction (CI), and complete active space self-consistent-field (CASSCF) methods. The adiabatic ionization energies (AIEs) confirm the assignments as band I, one state 12B1 (12.671 eV); band II, three states, 12B2 (14.259) < 12A1 (15.030) < 12A2 (15.478 eV); and band III, three states, 22B2 (18.055) < 22A1 (18.257) < 22B1 (18.808 eV). The three ionizations in each of the bands II and III lead to selective line broadening of the PES structure, which is attributed to vibronic overlap. The apparent lack of a vibrational structure attributable to both the 12A1 and 22A1 states in the PES arises from line broadening with the preceding states 12B2 and 22B2, respectively. Although these 2A1 states clearly overlap with their adjacent higher IE, some vibrational structure is observed on the higher IE. The effects of vibronic coupling are evident since the observed structure does not fit closely with the calculated Born-Oppenheimer FC profiles. Correlation of the lowest group of four AIEs in the PES of other members of the CH2X2 group, where X = F, Cl, Br, and I, clearly indicate these effects are more general.

Quantum Chemistry Meets Spectroscopy for Astrochemistry: Increasing Complexity toward Prebiotic Molecules.

For many years, scientists suspected that the interstellar medium was too hostile for organic species and that only a few simple molecules could be formed under such extreme conditions. However, the detection of approximately 180 molecules in interstellar or circumstellar environments in recent decades has changed this view dramatically. A rich chemistry has emerged, and relatively complex molecules such as C60 and C70 are formed. Recently, researchers have also detected complex organic and potentially prebiotic molecules, such as amino acids, in meteorites and in other space environments. Those discoveries have further stimulated the debate on the origin of the building blocks of life in the universe. Many efforts continue to focus on the physical, chemical, and astrophysical processes by which prebiotic molecules can be formed in the interstellar dust and dispersed to Earth or to other planets.Spectroscopic techniques, which are widely used to infer information about molecular structure and dynamics, play a crucial role in the investigation of planetary atmosphere and the interstellar medium. Increasingly these astrochemical investigations are assisted by quantum-mechanical calculations of structures as well as spectroscopic and thermodynamic properties, such as transition frequencies and reaction enthalpies, to guide and support observations, line assignments, and data analysis in these new and chemically complicated situations. However, it has proved challenging to extend accurate quantum-chemical computational approaches to larger systems because of the unfavorable scaling with the number of degrees of freedom (both electronic and nuclear).In this Account, we show that it is now possible to compute physicochemical properties of building blocks of biomolecules with an accuracy rivaling that of the most sophisticated experimental techniques, and we summarize specific contributions from our groups. As a test case, we present the underlying computational machinery through the investigation of oxirane. We describe how we determine the molecular structure and then how we characterize the rotational and IR spectra, the most important issues for a correct theoretical description and a proper comparison with experiment. Next, we analyze the spectroscopic properties of representative building blocks of DNA bases (uracil and pyrimidine) and of proteins (glycine and glycine dipeptide analogue).Solvation, surface chemistry (dust fraction, adsorption, desorption), and inter- and intramolecular interactions, such as self-organization and self-interaction, are important molecular processes for understanding astrochemistry. Using the specific cases of uracil dimers and glycine adsorbed on silicon grains, we also illustrate approaches in which we treat different regions, interactions, or effects at different levels of sophistication.

Reliable vibrational wavenumbers for C=O and N-H stretchings of isolated and hydrogen-bonded nucleic acid bases.

The accurate prediction of vibrational wavenumbers for functional groups involved in hydrogen-bonded bridges remains an important challenge for computational spectroscopy. For the specific case of the C=O and N-H stretching modes of nucleobases and their oligomers, the paucity of experimental reference values needs to be compensated by reliable computational data, which require the use of approaches going beyond the standard harmonic oscillator model. Test computations performed for model systems (formamide, acetamide and their cyclic homodimers) in the framework of the second order vibrational perturbation theory (VPT2) confirmed that anharmonic corrections can be safely computed by global hybrid (GHF) or double hybrid (DHF) functionals, whereas the harmonic part is particularly challenging. As a matter of fact, GHFs perform quite poorly and even DHFs, while fully satisfactory for C=O stretchings, face unexpected difficulties when dealing with N-H stretchings. On these grounds, a linear regression for N-H stretchings has been obtained and validated for the heterodimers formed by 4-aminopyrimidine with 6-methyl-4-pyrimidinone (4APM-M4PMN) and by uracil with water. In view of the good performance of this computational model, we have built a training set of B2PLYP-D3/maug-cc-pVTZ harmonic wavenumbers (including linear regression scaling for N-H) for six-different uracil dimers and a validation set including 4APM-M4PMN, one of the most stable hydrogen-bonded adenine homodimers, as well as the adenine-uracil, adenine-thymine, guanine-cytosine and adenine-4-thiouracil heterodimers. Because of the unfavourable scaling of DHF harmonic wavenumbers with the dimensions of the investigated systems, we have optimized a linear regression of B3LYP-D3/N07D harmonic wavenumbers for the training set, which has been next checked against the validation set. This relatively cheap model, which shows very good agreement with experimental data (average errors of about 10 cm(-1)), paves the route toward a reliable analysis of spectroscopic signatures for larger polynucleotides.

Combined theoretical and experimental study of the valence, Rydberg and ionic states of fluorobenzene.

New photoelectron spectra (PES) and ultra violet (UV) and vacuum UV (VUV) absorption spectra of fluorobenzene recorded at higher resolution than previously, have been combined with mass-resolved (2 + 1) and (3 + 1) resonance enhanced multiphoton ionization (REMPI) spectra; this has led to the identification of numerous Rydberg states. The PES have been compared with earlier mass-analyzed threshold ionization and photoinduced Rydberg ionization (PIRI) spectra to give an overall picture of the ionic state sequence. The analysis of these spectra using both equations of motion with coupled cluster singles and doubles (EOM-CCSD) configuration interaction and time dependent density functional theory (TDDFT) calculations have been combined with vibrational analysis of both the hot and cold bands of the spectra, in considerable detail. The results extend several earlier studies on the vibronic coupling leading to conical intersections between the X(2)B1 and A(2)A2 states, and a further trio (B, C, and D) of states. The conical intersection of the X and A states has been explicitly identified, and its structure and energetics evaluated. The energy sequence of the last group is only acceptable to the present study if given as B(2)B2