Towards an accurate molecular orbital theory for excited states : Ethene, butadiene, and hexatriene

A newly proposed quantum chemical approach for ab initio calculations of electronic spectra of molecular systems is applied to the molecules ethene, trans‐1,3‐butadiene, and trans‐trans‐1,3,5‐hexatriene. The method has the aim of being accurate to better than 0.5 eV for excitation energies and is expected to provide structural and physical data for the excited states with good reliability. The approach is based on the complete active space (CAS) SCF method, which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation. Remaining dynamic ele…

A theoretical determination of the electronic spectrum of Methylenecyclopropene

The vertical electronic spectrum of methylenecyclopropene, the prototype of the nonalternant hydrocarbons known as fulvenes, has been studied using multiconfigurational second-order perturbation theory. The calculations comprise three valence states and the 3s, 3p, and 3d members of the Rydberg series converging to the first π ionization limit. Vertical excitation energies to three valence states are found at 4.13, 6.12, and 6.82 eV. The second of them corresponds to an excitation from the highest occupied σ orbital to a π* orbital, while the other two are π → π* excitations. The third transition gives rise to the most intense feature in the electronic spectrum. The results are rationalized…

A theoretical determination of the dissociation energy of the nitric oxide dimer

Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N2O2 molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional…

Theoretical Study of the Electronic Spectrum of trans-Stilbene

The electronic spectrum of trans-stilbene in the energy range up to 6 eV has been studied using multiconfigurational second-order perturbation theory (CASPT2). The study includes a geometry determination of the ground state. In all, 12 singlet and one triplet excited states were studied. The calculated spectrum makes it possible to assign the valence excited singlet states corresponding to the three bands observed in the low-energy region of the one-photon absorption spectrum. The most intense feature of the calculated spectrum corresponds to the 11Ag → 21Bu transition at 4.07 eV. The weakly allowed 11Bu state was found 0.3 eV below 21Bu. Transition to the 31Ag state, computed at 4.95 eV, i…

The chemical bonds in CuH, Cu2, NiH, and Ni2 studied with multiconfigurational second order perturbation theory

The performance of multiconfigurational second order perturbation theory has been analyzed for the description of the bonding in CuH, Cu2, NiH, and Ni2. Large basis sets based on atomic natural orbitals (ANOS) were employed. The effects of enlarging the active space and including the core‐valence correlation contributions have also been analyzed. Spectroscopic constants have been computed for the corresponding ground state. The Ni2 molecule has been found to have a 0+g ground state with a computed dissociation energy of 2.10 eV, exp. 2.09 eV, and a bond distance of 2.23 Å. The dipole moments of NiH and CuH are computed to be 2.34 (exp. 2.4±0.1) and 2.66 D, respectively. pou@uv.es ; merchan@…

Theoretical characterization of the lowest-energy absorption band of pyrrole

The lowest-energy band of the electronic spectrum of pyrrole has been studied with vibrational resolution by using multiconfigurational second-order perturbation theory (CASPT2) and its multistate extension (MS–CASPT2) in conjunction with large atomic natural orbital-type basis sets including Rydberg functions. The obtained results provide a consistent picture of the recorded spectrum in the energy region 5.5–6.5 eV and confirm that the bulk of the intensity of the band arises from a ππ∗ intravalence transition, in contradiction to recent theoretical claims. Computed band origins for the 3s,3p Rydberg electronic transitions are in agreement with the available experimental data, although new…

A theoretical study of the collinear reaction F+H2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)

Abstract The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2 →HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-el…

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the syste…

On the low-lying singlet excited states of styrene: a theoretical contribution

The present contribution analyses the trans–cis photoisomerization mechanism of ethene and styrene on the singlet manifold. Within the framework of multiconfigurational second-order perturbation theory (CASPT2), the extended multistate approach (MS-CASPT2) is found to be flexible enough to describe energy hypersurfaces adiabatically. For ethene, torsion about the CC bond towards a perpendicular structure leads to a situation where the energy difference between the ground and the lowest excited state is still too large (2.5 eV) for efficient radiationless decay. However, the energy gap decreases to 0.4 eV when one of the methylene moieties is, in addition, pyramidalized from the twisted stru…

ChemInform Abstract: A Theoretical Determination of the Dissociation Energy of the Nitric Oxide Dimer.

Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N2O2 molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional…

A theoretical study of the electronic spectrum of bithiophene

The electronic spectrum of bithiophene in the energy range up to 6.0 eV has been studied using multiconfigurational second order perturbation theory (CASPT2) and a basis set of ANO type, with split valence quality and including polarization functions on all heavy atoms. Calculations were performed at a planar (trans) and twisted geometry. The calculated ordering of the excited singlet states is 1Bu, 1Bu, 1Ag, 1Ag, and 1Bu with 0–0 transition energies: 3.88, 4.15, 4.40, 4.71, and 5.53 eV, respectively. The first Rydberg transition (3s) has been found at 5.27 eV. The results have been used in aiding the interpretation of the experimental spectra, and in cases where a direct comparison is poss…

A theoretical study of the 1B2u and 1B1u vibronic bands in benzene

The two lowest bands, 1B2u and 1B1u, of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space (CAS) self-contained field (SCF) method (with six active π-orbitals) was used to compute harmonic force field for the ground state and the 1B2u and 1B1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory (CASPT2) was used to obtai…

A very short uranium-uranium bond: The predicted metastable U22+

Quantum chemical calculations, based on multiconfigurational wave functions and including relativistic effects, show that the U(2)2+ system has a large number of low-lying electronic states with S of 0 to 2 and Lambda ranging from zero to ten. These states share a very small bond length of about 2.30 A, compared to 2.43 A in neutral U2. The Coulomb explosion to 2 U+ lowers the energy by only 1.6 eV and is separated by a broad barrier.

Theoretical study of the electronic spectrum of magnesium-porphyrin

Multiconfigurational self-consistent field (SCF) and second order perturbation methods have been used to study the electronic spectrum of magnesium-porphyrin (MgP). An extended ANO-type basis set including polarization functions on all heavy atoms has been used. Four allowed singlet states of E1u symmetry have been computed and in addition a number of forbidden transitions and a few triplet states. The results lead to a consistent interpretation of the electronic spectrum, where the Q band contains one transition, the B band two, and the N band one. The computed transition energies are consistently between 0.1 and 0.5 too low compared to the measured band maxima. The source of the discrepan…

A theoretical determination of the electronic spectrum of formaldehyde

The electronically excited states of formaldehyde are examined by means of multiconfigurational second-order perturbation (CASPT2) theory with extended ANO-type basis sets. The calculations comprised five valence excited states plus all singlet 3s, 3p, and 3d members of the Rydberg series converging on the first ionization. The computed vertical excitation energies were found to be within 0.2 eV of the available experimental energies. Full geometry optimization has been performed for five valence excited states. Assuming a planar geometry, the “0-0” transition for the valence1A1(π → π*) state is calculated to appear near 7.9 eV, close to the (n y → 3p) region. This state is, however, not pl…

Multiconfigurational Perturbation Theory: Applications in Electronic Spectroscopy

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 1A1 valence state at 5.33 eV, below the 1 1B2 valence state at 5.72 eV, and the most intense valence transitions at 6.69 eV (3 1A1) and 7.32 eV (4 1B2) with oscillator strengths 0.19 and 0.39, respective…

A combined theoretical and experimental determination of the electronic spectrum of acetone

A combined ab initio and experimental investigation has been performed of the main features of the electronic spectrum of acetone. Vertical transition energies have been calculated from the ground to the ny→π∗, π→π∗, σ→π∗, and the n=3 Rydberg states. In addition, the 1A1 energy surfaces have been studied as functions of the CO bond length. The 1A1 3p and 3d states were found to be heavily perturbed by the π→π∗ state. Resonant multiphoton ionization and polarization‐selected photoacoustic spectra of acetone have been measured and observed transitions were assigned on internal criteria. The calculated vertical transition energies to the ny→π∗ and all Rydberg states were found to be in agreeme…

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 …

A theoretical study of the electronic spectrum of cis-stilbene

Abstract The valence and Rydberg electronic excited singlet states of cis -stilbene have been studied using multiconfigurational second-order perturbation theory (CASPT2). The study includes a geometry determination of the ground state. The geometry of the lowest 1 B state has also been optimized, leading to a structure where the two benzyl groups are nearly perpendicular. The calculated vertical spectrum is in agreement with the occurrence of three main bands in the observed one-photon absorption spectrum. Below the relatively intense transition to the 2 1 B (HOMO→LUMO) state at 4.61 eV, two weak transitions have been computed at 4.11–4.45 eV, which correspond to transitions to the 1 1 B a…

Theoretical studies of isomers of C 3 H 2 using a multiconfigurational approach

The C3H2 isomers are important molecules in interstellar space. An understanding of their electronic structure can contribute significantly to the interpretation of interstellar spectra. In a theoretical study of the C3H2 isomers a multiconfigurational treatment is of interest because many of the isomers are carbenes or diradicals. We present such an investigation of all possible C3H2 isomers. The most important features of their electronic and vibrational spectra are calculated. Earlier theoretical studies are reviewed and it is shown that the present study yields the same order of stability for the singlet and triplet states as most previous studies.

Theoretical Study of the Electronic Spectrum of Imidazole

The complete active space (CAS) self-consistent field (SCF) method and multireference second-order perturbation theory (CASPT2) have been used to study the electronic spectrum of imidazole and the imidazolium ion. The calculations comprise a large number of, both singlet and triplet, valence and Rydberg excited states. A newly developed continuum model has been used to compute solvatochromic shifts. In the gas phase the first and second π → π* excited singlet valence states of imidazole are computed at 6.72 and 7.15 eV, and they shift to 6.32 and 6.53 eV upon solvation. The gas-phase values are somewhat too large (≈0.3 eV) due to an erroneous valence−Rydberg mixing in the CASSCF wave functi…

The multi-state CASPT2 method

Abstract An extension of the multiconfigurational second-order perturbation approach CASPT2 is suggested, where several electronic states are coupled at second order via an effective-Hamiltonian approach. The method has been implemented into the MOLCAS-4 program system, where it will replace the single-state CASPT2 program. The accuracy of the method is illustrated through calculations of the ionic-neutral avoided crossing in the potential curves for LiF and of the valence-Rydberg mixing in the V-state of the ethylene molecule.

Ground state and electronic spectrum of Cu(ii) and Cu(iii) complexes of N,N′-1,2-phenylenebis-2-mercaptoacetamide

The electronic structure and the UV-vis spectrum of reduced and oxidized model systems of the N,N'-1,2-phenylenebis(2-mercapto-2-methylpropionamide) copper complex have been studied using a multiconfigurational quantum chemical method (CASSCF/CASPT2). The bonds between Cu and the two sulfur ligand atoms have a large covalent character in the oxidized Cu(III) form. As a result of the increased covalency, the effective charge on the Cu atom is actually smaller in the oxidized form. The electronic spectrum for both oxidation states of the complex is in agreement with the experiment for excitation energies and intensities showing that the theoretical description of the electronic structure is e…

An ab initio study of the electron affinity of O2

Abstract Coupled pair functional, multiconfigurational second-order perturbation theory, and multireference CI methods have been applied in a calculation of the electron affinity of the oxygen molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis and the multireference CI wavefunction. The best calculated value, 0.39 eV, is 0.06 eV smaller than the recent experimental value 0.45±0.01 eV.

Interpretation of the electronic absorption spectrum of free base porphin by using multiconfigurational second-order perturbation theory

Abstract Multiconfigurational second-order perturbation (CASPT2) calculations have been performed on the low-lying optically allowed valence excited states of the free base porphin molecule in order to assign the four lowest bands of the spectrum. The low-lying triplet states have also been characterized. A basis set of the atomic natural orbital type of split-valence plus polarization quality for first-row atoms has been employed. Polarization functions are important for an accurate description of the transitions. These CASPT2 results provide a consistent picture of the experimental spectrum. Each band of the spectrum up to 4.5 eV is composed of a pair of states, which become degenerate in…

The Coordination of Uranyl in Water: A Combined Quantum Chemical and Molecular Simulation Study

The coordination environment of uranyl in water has been studied using a combined quantum mechanical and molecular dynamics approach. Multiconfigurational wave function calculations have been performed to generate pair potentials between uranyl and water. The quantum chemically determined energies have been used to fit parameters in a polarizable force field with an added charge transfer term. Molecular dynamics simulations have been performed for the uranyl ion and up to 400 water molecules. The results show a uranyl ion with five water molecules coordinated in the equatorial plane. The U-O(H(2)O) distance is 2.40 A, which is close to the experimental estimates. A second coordination shell…

A Theoretical Study of the Electronic Spectra of N9 and N7 Purine Tautomers

The complete active space (CAS) SCF method and multiconfigurational second-order perturbation theory (CASPT2) have been used to study electronic spectra of the N(9)H and N(7)H tautomers of purine. The calculations include vertical excitation energies, oscillator strengths, dipole moments, and transition moment directions in gas phase. In accord with experiment in nonpolar solvents, the two lowest π → π* excited singlet valence states are predicted to be located at 4.7 and 5.1 eV. The latter is expected to shift to the red in aqueous solutions. A satisfactory interpretation of the electronic spectra above 5.5 eV is obtained if the experimental data are assumed to consist of the superposition…

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra- μ -acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxi…

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 (…

A theoretical study of the electronic spectrum of biphenyl

Abstract The electronic spectrum of biphenyl in the energy range up to 6.0 eV has been studied using multiconfigurational second-order perturbation theory (CASPT2) and a basis set of ANO type, including polarization functions on all carbon atoms. The calculated spectrum gives conclusive assignments to all valence excited singlet states and the low-lying triplet states. The change of the torsional angle between the two benzene rings in the different excited states is shown to be of considerable importance and explains the different excitation energies observed in the gas phase as compared to solution or crystalline biphenyl at low temperatures. The intense transition to the 1 1B1u state is m…

Quantum Chemical Calculations Show that the Uranium Molecule U2 Has a Quintuple Bond.

Covalent bonding is commonly described by Lewis's theory1, with an electron pair shared between two atoms constituting one full bond. Beginning with the valence bond description2 for the hydrogen molecule, quantum chemists have further explored the fundamental nature of the chemical bond for atoms throughout the periodic table, confirming that most molecules are indeed held together by one electron pair for each bond. But more complex binding may occur when large numbers of atomic orbitals can participate in bond formation. Such behaviour is common with transition metals. When involving heavy actinide elements, metal–metal bonds might prove particularly complicated. To date, evidence for ac…

On the theoretical determination of the electron affinity of ozone

Multiconfigurational electron correlation methods have been analyzed in order to theoretically compute the electron affinity (EA) of ozone. The near-degeneracy correlation effects, which are so important in O3 and O 3 − , have been described using complete active space (CAS) SCF wave functions. Remaining dynamic correlation effects are computed using second-order perturbation theory (the CASPT2 method). The best calculated adiabatic value (including zero-point energy corrections), 2.19 eV, is about 0.09 eV larger than the experimental value. Comparative studies using size-consistent coupled pair functional approaches (CPF and ACPF) have also been performed. The harmonic frequencies in O 3 −…

2MOLCAS as a development platform for quantum chemistry software

This work presents the quantum chemistry package MOLCAS, with emphasis on its usefulness as a platform for developing new quantum chemical codes, and the reader is assumed to be familiar with such a process. The development of new codes for quantum chemistry is a time-consuming job that can be dramatically simplified by using libraries for standard problems (such as calculation of integrals), and tools to surmount computer language and operating system limitations. The MOLCAS quantum chemistry software contains modules for a variety of quantum chemical methods, such as Hartree-Fock (HF), density functional theory (DFT), coupled-cluster (CC), and multiconfigurational (MCSCF) approaches, incl…

An Accurate Quartic Force Field and Fundamental Frequencies for the Ozonide Anion: A Rare Positive Anharmonicity for the Antisymmetric Stretch

The CCSD(T) method has been used to compute a highly accurate quartic force field and fundamental frequencies for all 16O and 18O isotopomers of the ozonide anion. The CCSD and CASPT2 methods have also been used to verify the reliability of the CCSD(T) fundamental frequencies. The computed fundamental frequencies are in agreement with gas-phase experiments, but disagree with matrix isolation experiments for the antisymmetric stretch, ν3. CASPT2 calculations show that the antisymmetric part of the O3- potential surface is sensitive to the external environment. It is concluded that the antisymmetric stretch exhibits a significant matrix shift in the matrix isolation experiments and that the m…

Photochemical Nitration by Tetranitromethane. Part XL. Regiochemistry of Trinitromethyl Attachment in the Photolysis of Benzofuran with Tetranitromethane.

Theoretical spectroscopy of organic systems

Abstract The complete active space (CAS) SCF method in conjunction with the multiconfigurational second-order perturbation theory (CASPT2) has been applied to study the electronically excited states of basic organic compounds. As shown in the lecture with a number of examples, the CASPT2 method is capable of yielding accurate results for relative energies and other properties of excited states, provided that flexible one-electron basis sets are employed. The applications comprise an ample range of systems and problems, including polyenes, conjugated and unconjugated dienes, alternant and nonalternant hydrocarbons, polyenals, etc. As a whole these studies enable both qualitative and quantita…