Markus P. Fülscher

Towards an accurate molecular orbital theory for excited states: the benzene molecule

Abstract A computational scheme is proposed for ab initio calculations of electronic spectra of molecular systems. The scheme is firmly based on the different effects that determine the excitation energies and properties of the excited states. It aims to be accurate to better than 0.5 eV for excitation energies and should provide structural and physical data for the excited states. Applications are possible to rather large molecules (up to 20 atoms) with high-quality basis sets. Extensions of the approach will be possible when direct methods have been implemented. The scheme is based on the CASSCF method, which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, and accounts for all near-degeneracy effects and includes full orbital relaxation. Remaining dynamic electron correlation effects are added using second-order perturbation theory with the CASSCF wavefunction as the reference state. The electronic spectrum of the benzene molecule is used as an illustration. Using a (C, 4s3p2d/H, 3s2p) atomic natural orbital basis set, the following excitation energies are obtained (experimental values in parentheses); 1B2u, 4.70 (4.90); 1B1u, 6.10 (6.20); 1E1u, 7.06 (6.94); 1E2g, 7.77 (7.80) eV. The computed oscillator strength for the 1E1u state is 1.05 as compared to the experimental 1.25. Results of similar accuracy are obtained for the triplet states.

Applications of level shift corrected perturbation theory in electronic spectroscopy

Abstract Multiconfigurational second-order perturbation theory (CASPT2) with a level shift technique used to reduce the effect of intruder states has been tested for applications in electronic spectroscopy. The following molecules have been studied: formamide, adenine, stilbene, Ni(CO) 4 , and a model compound for the active site in the blue copper protein plastocyanin, Cu(Im) 2 (SH)(SH 2 ) + . The results show that the level shift technique can be used to remove the effects of the intruder states in all these molecules. In some cases a drift in the energies as a function of the level shift is observed, which however is small enough that the normal error bar for CASPT2 excitation energies (≈ 0.3 eV ) still holds.

A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol

SummaryThe valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence ππ* state predicted by elementary π-electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm−1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.

A theoretical study of the low-lying excited states of ozone

Abstract A theoretical study has been performed on the five lowest excited states of the ozone molecule using multiconfigurational second-order perturbation theory (CASPT2). The predicted order of states is: 3A2 (T0 = 1.15 eV), 3B2 (T0 = 1.33 eV, 3B1 (T0 = 1.33 eV), 1A2 (T0 = 1.44 eV) and 1B1 (T0 = 1.88 eV). Corresponding experimental data are: 1.18, 1.30, 1.45, 1.58, and 2.05 eV, respectively. Equilibrium geometries, harmonic frequencies of symmetric vibrations, and vertical excitation energies are also reported. The dissociation limit De for the ground state of ozone is found to be 1.08 eV, in agreement with the experimental value (1.13 eV). The calculations make use of a modified Fock operator in the CASPT2 theory. Relative energies of states with a different number of open shells are substantially improved. The modified CASPT2 method was checked by calculating spectroscopic constants of the oxygen molecule.

Theoretical Studies of the Electronic Spectra of Organic Molecules

The complete active space (CAS) SCF method in conjunction with multiconfigurational second-order perturbation theory (CASPT2) has been used to study the electronic spectra of a large number of molecules. The wave functions and the transition properties are computed at the CASSCF level, while dynamic correlation contributions to the excitation energies are obtained through the perturbation treatment. The methods yield energies, which are accurate to at least 0.2 eV, except in a few cases, where the CASSCF reference function does not characterize the electronic state with sufficient accuracy. The applications comprise: the polyenes from ethene to octatetraene (cis- and trans-forms); a number of cyclic pentadienes; norbornadiene; benzene, phenol, phosphabenzene, and the azabenzenes; free base porphin; and the nucleic acid base monomers cytosine, uracil, thymine, and guanine. Finally, the photochemistry of the molecules aminobenzonitrile (ABN) and dimethylaminobenzonitrile (DMABN) has also been studied, in particular the double fluorescence that occurs in DMABN. Taken together these studies comprise large amounts of new spectroscopic data of high accuracy, which either confirm existing assignments of experimental data or lead to new predictions and qualitative as well as quantitative understanding of a large number of electronic spectra. Most studies are restricted to ground state geometries (vertical energies), but in a few cases (octatetraene, ABN, and DMABN) also excited state geometries have been determined, thus yielding 0-0 transition energies and emission spectroscopic data.

SOLVENT EFFECTS ON ELECTRONIC SPECTRA STUDIED BY MULTICONFIGURATIONAL PERTURBATION THEORY

The complete active space CAS self-consistent field SCF method . combined with multiconfigurational second-order perturbation theory CASPT2 and a . self-consistent reaction field SCRF model is used to study the effect of solvation on excited states of different molecules such as acetone, pyrimidine, some aminobenzene derivatives, indole, and imidazole. The present SCRF model, in which the solute molecule is placed into a spherical cavity surrounded by a dielectric continuum, also includes a repulsive potential representing the solute)solvent exchange repulsion and considers the time dependence of the absorption process. In general, we find that our calculations do reproduce the trends observed in experiment but underestimate the solvatochromic shifts. Q 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 167)181, 1997

A theoretical study of the electronic spectrum of thiophene

Abstract The electronic spectrum of thiophene has been studied using multiconfiguration second-order perturbation theory and extended ANO basis sets. The calculations comprise four singlet valence excited states and the 3s3p3rd Rydberg series. The lowest triplet states were included and some n-π* and n-σ* states. The results have been used to assign the experimental spectrum below 8.0 eV, with a maximum deviation of about 0.1 eV for vertical transition energies. The calculations place the 2 1 A 1 valence state at 5.33 eV, below the 1 1 B 2 valence state at 5.72 eV, and the most intense valence transitions at 6.69 eV (3 1 A 1 ) and 7.32 eV (4 1 B 2 ) with oscillator strengths 0.19 and 0.39, respectively.

The electronic spectra of symmetric cyanine dyes: A CASPT2 study

Ab initio quantum mechanical calculations were performed to study the electronic spectra of symmetric all-E configurated streptocyanine dyes, [R2N–(CH–CH)n–CH–NR2]+, R = H and CH3, from n = 0 (monomethine) to n = 4 (nonamethine). Ground state geometries were optimized based on density functional theory. Excitation energies were calculated using multi-configurational second-order perturbation theory (CASPT2). CASPT2 corrected vertical excitation energies for the long wavelength absorptions were within 0.08 eV of the experiment. Also, these calculations reproduced the 100 nm vinylene shift which is characteristic for these dyes. The agreement between calculated and experimental oscillator strengths was satisfactory. The results were compared with calculations based on a single determinant ab initio approach and on density functional linear response theory. These methods systematically overestimated experimental transition energies.

An ab initio quantum chemical study of vertically excited singlet states of pyrimidine

Abstract Ab initio calculations of a number of singlet electronic states of pyrimidine are presented. In addition to the ground 1 A 1 state, ten valence excited states were studied: three 1 A 1 and three 1 B 2 states, which are ππ* excited states, and two 1 B 1 and two 1 A 2 states, which are nπ* excited. Rydberg states were encountered, but since these were irrelevant to the present study, the basis set employed was not designed to describe these states well, and their energy relative to the valence states will be incorrect. Such spurious states may perturb the valence states by accidental near-degeneracy, and care was taken to effectively remove them to prevent such perturbation. The calculation were performed by the CASSCF and MRCI methods, using a modest basis set (C, N: 3s3p1d; H: 2s; 116 basis functions) of ANO type. Energies, dipole and quadrupole moments, transition moments, and oscillator strengths are reported. All calculations were made using the experimental equilibrium geometry, and all excitation data are therefore vertical. The MRCI excitation energies, corrected for unlinked clusters, give results in good agreement with known experimental data. The error in the computed excitation energy is in no case larger than 0.4 eV. In some cases, alternative assignments of experimental energies are indicated.

A theoretical study of the electronic spectra of pyridine and phosphabenzene

The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest π → π* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then → π* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn → π* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.