Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3

A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.     

Excited states of acetylene: a CASPT2 study

Valence and low-lying Rydberg states of acetylene (C₂H₂) are reexamined in the singlet as well as in the triplet manifold. The major goal of this work is a better understanding of the valence states that contribute to the low-energy electron-energy-loss spectrum recorded under conditions where transitions to triplet states are enhanced. An appropriate theoretical treatment of these states has to include the low-lying Rydberg states because of their energetic proximity to some of the valence states. The CASSCF/CASPT2 method provides a suitable framework for such a task. For some important states the geometry was optimized at the CASPT2 level to allow a comparison with the results of other highly accurate methods that have been applied to acetylene in the past. Received: 11 June 1998 /Accepted: 30 July 1998 / Published online: 19 October 1998     

The reductive dimerization of some 1,3-dienes and of 1,3,5-cycloheptatriene in the presence of trimethylchlorosilane: a DFT investigation

Treatment of 1,3-dienes and 1,3,5-cycloheptatriene by chlorotrimethylsilane in the presence of wire of lithium led mainly to reductive dimerization with formation of bis(allylsilane) derivatives. Bis-silyl compounds obtained: from 1,3-butadiene, 1,8-bis(trimethylsilyl)-2,6-octadiene (70%); from isoprene, (Z,Z)-2,7-dimethyl-1,8-bis(trimethylsilyl)-2,6-octadiene (44%) and 2,6-dimethyl-1,8-bis(trimethylsilyl)-2,6-octadiene (19%); from butadiene-isoprene mixture (1:1), 3-methyl-1,8-bis(trimethylsilyl)-2,6-octadiene (55%); from 2,3-dimethylbutadiene, (E,E)-2,3,6,7-tetramethyl-1,8-bis(trimethylsilyl)-2,6-octadiene (36%), from 1,3-cyclohexadiene, 4,4′-bis(trimethylsilyl)-bicyclohexyl-2,2′-diene (48%); from 1,3,5-cycloheptatriene, 1,1′-bi[(S^∗,S^∗)-6-(trimethylsilyl)cyclohepta-2,4-dien-1-yl] (53%). The structure of the various intermediates (radical anion, dianion, silylated radical, silylated anion) has been established by calculations at the B3LYP/6-311++G(d,p) level of theory with zero-point energy correction. These results are in accordance with a pathway including the formation of a radical anion, its silylation furnishing to a γ-silylated allylic radical followed by a dimerization reaction in the head to head manner.     

DFT and CASPT2 study on the mechanism of ethylene dimerization over Cr(II)OH+ cation

In this work, the ethylene coordination and dimerization mechanism over Cr(II)OH(+) cation were systematically investigated using density functional theory (DFT) and complete active space second-order perturbation theory (CASPT2). It was found that Cr(II)OH(+) cation can coordinate with up to four ethylene molecules which gives seven possible stable Cr(II)OH(+)·(C(2)H(4))(n) (n = 1-4) π-complexes. We investigated whether ethylene dimerization over Cr(II)OH(+) cation proceeds through either a carbene mechanism or a metallacycle mechanism. The potential energy surfaces were characterized using four different functionals (M06L, BLYP, B3LYP, and M06). It was found that the potential energy profiles calculated at the M06 level agreed well with the CASPT2 energy profiles. Since the intermediates involved in the proposed catalytic cycles showed different ground spin states, a reaction pathway involving a spin crossing between two potential energy surfaces was observed. The minimum-energy crossing points (MECPs) that connect the two potential energy surfaces were successfully located. The two-state metallacycle reaction pathway with the formation of chromacyclopentane as the rate-determining step was found to be energetically more favorable than the carbene reaction pathway. 1-Butene was formed from the chromacyclopentane by a two-step reductive elimination pathway through a chromium(IV) hydride intermediate.     

The elusive excited states of bithiophene: a CASPT2 detective story

A systematic multi-reference perturbation theory investigation of the excitation energies and oscillator strengths for the lowest excited states of 2,2′-bithiophene unequivocally shows that its optical spectrum is produced by two ¹ B _u states separated from each other by approximately 1 eV. This picture is confirmed by additional calculations with alternative quantum chemical methods. Our findings are in strong contrast with the previous CASPT2 results of Rubio et al. [J Chem Phys 102:3580 (1995) and Chem Phys Chem 4:1308 (2003)], who predicted that the two lowest ¹ B _u states are quasi-degenerate. The methodological reasons responsible for the previous seemingly erroneous assignment of the optical spectrum of bithiophene are identified and explained in terms of unusually large coupling between the ¹ B _u states introduced by dynamical correlation effects. A general discussion of applicable computational techniques is offered aiming at avoiding similar problems for other molecular systems.     

A theoretical investigation of the excited states of OCLO radical, cation, and anion using the CASSCF/CASPT2 method

Using the complete active space self-consistent field method with a large atomic natural orbital basis set, 10, 13, and 9 electronic states of the OClO radical, OClO(+) cation, and OClO(-) anion were calculated, respectively. Taking the further correlation effects into account, the second-order perturbation (CASPT2) calculations were carried out for the energetic calibration. The photoelectron spectroscopy of the OClO radical and OClO(-) anion were extensively studied in the both case of the adiabatic and vertical ionization energies. The calculated results presented the relatively complete assignment of the photoelectron bands of the experiments for OClO and its anion. Furthermore, the Rydberg states of the OClO radical were investigated by using multiconfigurational CASPT2 (MS-CASPT2) theory under the basis set of large atomic natural orbital functions augmented with an adapted 1s1p1d Rydberg functions that have specially been built for this study. Sixteen Rydberg states were obtained and the results were consistent with the experimental results.     

Activation energies of pericyclic reactions: performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions

Activation barriers and reaction energetics for the three main classes of 1,3-dipolar cycloadditions, including nine different reactions, were evaluated with the MPW1K and B3LYP density functional methods, MP2, and the multicomponent CBS-QB3 method. The CBS-QB3 values were used as standards for 1,3-dipolar cycloaddition activation barriers and reaction energetics, and the density functional theory (DFT) and MP2 methods were benchmarked against these values. The MPW1K/6-31G* method and basis set performs best for activation barriers, with a mean absolute deviation (MAD) value of 1.1 kcal/mol. The B3LYP/6-31G* method and basis set performs best for reaction enthalpies, with a MAD value of 2.4 kcal/mol, while the MPW1K method shows large errors for reaction energetics. The MP2 method gives the expected systematic underestimation of barriers. Concerted and nearly synchronous transition structures are predicted by all DFT and MP2 methods. Also reported are revised estimated 0 K experimental activation enthalpies for a standard set of hydrocarbon pericyclic reactions and updated comparisons to experiment for DFT, ab initio, and multicomponent methods. B3LYP and MPW1K methods with MAD values of 1.5 and 2.1 kcal/mol, respectively, fortuitously outperform the multicomponent CBS-QB3 method, which has a MAD value of 2.3. The MAD value of the O3LYP functional improves to 2.4 kcal/mol from the previously reported 3.0 kcal/mol.     

Structural and vibrational studies of molecular conductors using quantum mechanical methods: 1,3-Dithiole-2-thione, 1,3-dithiole-2-one, 1,3-dioxole-2-one and 1,3-dioxole-2-thione

Computations were carried out by employing the RHF and density functional theory (DFT) methods to investigate the geometries, atomic charges, harmonic vibrational frequencies for the 1,3-dithiole-2-thione (DTT), 1,3-dithiole-2-one (DTO), 1,3-dioxole-2-thione (DOT) and 1,3-dioxole-2-one (DOO) molecules and their radical cations. The geometrical parameters and atomic charges on various atomic sites of the DTT and DOT molecules and their radical cations suggest extended conjugation in these systems. Contrary to this, for the DOO⁺ and DTO⁺ ions there is no evidence in favour of such conjugation, however, the neutral molecules exhibit some conjugation. Harmonic forced field and vibrational mode calculations provided convincing theoretical evidence for the reassignment of some fundamental vibrational modes for all the four molecules. In going from the neutral species to the charged ions for all the four cases the CC stretching frequency is found to decrease drastically. The CS stretching frequency reduces drastically for the DTT and DOT molecules as compared to their radical cations whereas the CO stretching frequency is found to increase in going from the neutral molecule to its radical cation for the DOO and DTO molecules. The ring stretching mode with a₁ symmetry and CC and CO/S stretching modes in these molecules appear to help in conversion of neutral molecule into respective radical cation and neighbouring radical cation into respective neutral molecule. Thus, there appears the feasibility of stretching vibrational mode coupling with electron transfer.     

Low-lying electronic states of HNCS and its ions: a CASSCF/CASPT2 study

Complete active space self-consistent-field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) calculations in conjunction with the ANO-L basis set were performed to investigate systematically the low-lying electronic states of HNCS and its ions in C _s symmetry. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground-state X ¹A′ are in good agreement with observed experimental data. The geometry of triplet HNCS is clearly favored C ₁ symmetry, and the relative energy is predicted to be 3.000 eV (69.2 kcal/mol). The vertical transition energies for the selected excited states of HNCS were calculated at CASSCF/CASPT2/ANO-L level of theory based on CASSCF optimized geometry. Except for a few linear states of X ²Π (1²A′, 1²A″), 1⁴Σ⁻ (1⁴A″), and 1²Σ⁺ (3²A′) states of HNCS⁺, our results confirmed that the majority of excited states are twisted trans-bend structures. The existence of bound excited anion states has been found for the first time in HNCS⁻. A more elaborate examination of ionization potential of HNCS (AIP, VIP) than previous reports has been presented.     

Active space and basis set effects in CASPT2 models of the 1,3‐butadiene‐ethene cycloaddition and the 1,3‐butadiene dimerization

The first step of the asynchronous biradical, stepwise biradical, and concerted mechanisms of the 1,3‐butadiene Diels–Alder reactions with both ethene and itself was studied using CASPT2 to determine the influence of basis set and active space on reaction barriers. CASPT2(6,6) with the cc‐pVDZ, 6‐311+G(3df,2p) and cc‐pVTZ basis sets provided the best results with average errors below 3.1 kJ mol^?1 with respect to the experimental result. Increasing the active space size also had little effect on the calculated reaction barriers. With respect to experimental results, uncontracted multireference averaged quadratic coupled cluster (MRAQCC) produced superior barriers than internally contracted MRAQCC by 16.1–39.3 kJ mol^?1. The inability of CASSCF to locate transition states for some of the cycloadditions across the butadiene‐ethene and butadiene dimerization reactions is also rationalized. CASPT2 suggests a preference for the concerted mechanism of the butadiene‐ethene reaction, however, no basis set yielded a preference for any of the butadiene dimerization pathways. © 2015 Wiley Periodicals, Inc.     

A CASSCF and CASPT2 study on the excited states of s-trans-formaldazine

The low-lying excited states of s-trans-formaldazine (H2CN-NCH2) have been investigated using the complete active space self-consistent field (CASSCF) and the multiconfigurational second-order perturbation (CASPT2) methods. The vertical excitation energies have been calculated at the state-average CASSCF and multistate CASPT2 levels employing the cc-pVTZ basis set. The photodissociation mechanisms starting from the S1 state have been determined. The lowest energy points along the seams of surface intersections have been located in both the Franck-Condon region and the N-N dissociation pathway in the S1 state. Once the system populates the S1 state, in the viewpoint of energy, the radiationless decay via S1/S0(3) conical intersection followed by the N-N bond fission in the ground-state is more favorable in comparison with the N-N dissociation process in the S1 state. A three-surface crossing region (S1/T1/T2), where the S1, T1, and T2 states intersect, was also found. However, the intersystem crossing process via S1/T1/T2 is not energetically competitive with the internal conversion via S1/S0(3).     

Pre-catalyst resting states: a kinetic, thermodynamic and quantum mechanical analyses of [PdCl2(2-oxazoline)2] complexes

The treatment of cold ( approximately 3 degrees C) methanolic solutions of Li(2)PdCl(4) with two equivalents of 2-phenyl-2-oxazoline (Phox) results in the isolation of [PdCl(2)(Phox)(2)] (3). This complex undergoes remarkably slow isomerisation (CHCl(3)-d) at room temperature to a corresponding thermodynamic form. In addition to a theoretical treatment (DFT), the isomerisation behaviour has been analysed both kinetically and thermodynamically. These investigations lead to the conclusion that the initially formed (i.e. kinetic) isomer of 3 is the cis-form which undergoes conversion to the corresponding thermodynamic trans-form via a dissociative (D) mechanism involving loss of a Phox ligand. The activation parameters DeltaS(double dagger) and DeltaH(double dagger) are found to be +304 (+/-3) J K(-1) mol(-1) and +176 (+/-1) kJ mol(-1), respectively and indicate a high barrier to Pd-N bond cleavage under these conditions. The thermodynamic parameters show the expected endothermic nature of this process (+140 +/- 17 kJ mol(-1)) and a slight positive overall entropy (DeltaS degrees = +17 +/- 2 J K(-1) mol(-1)); this latter parameter is presumably due to the formation of the lower dipole moment trans-product when compared to the cis-isomer. Calculated (DFT) values of DeltaG(double dagger) and DeltaH(double dagger) are in excellent agreement to those found experimentally. Further theoretical investigation suggests that two 14-electron three-coordinate T-shaped transition states (i.e., [PdCl(2)(Phox)](double dagger)) are involved; the form pre-disposed to yield the thermodynamic trans-product following re-attachment of the released oxazoline is found to be energetically favoured. The analogous alkyloxazoline system [PdCl(2)(Meox)(2)] (4: Meox = 2-methyl-2-oxazoline) has likewise been investigated. This material gives no indication of cis-trans isomerisation behaviour in solution (NMR) and is shown to exist (X-ray) in the trans-form in the solid-state (as do previously reported crystalline samples of 3). A DFT study of 4 reveals similar values of DeltaS(double dagger) and DeltaH(double dagger) if a D type mechanism were operating to rapidly convert cis- to trans-4. However, a significantly higher thermodynamic stability of the trans-isomer relative to the cis-form is revealed versus similar calculations of the Phox derivative 3. This suggests the possibility that (i) reactions of Meox with Li(2)PdCl(4) may lead directly to the trans-form of [PdCl(2)(Meox)(2)] or alternatively (ii) that alkyloxazoline complexes such as 4 may have a different, and presumably much more rapid, mechanism for isomerisation. The results are placed into the context that isomerisation behaviour, or lack thereof, could play a key preliminary role in later substrate modification. This is due to the fact that [PdX(2)(oxazoline)(2)] compounds are well-known (pre-)catalysts for C-C bond forming chemistry.     

Dimerisation of urea in water solution: a quantum mechanical investigation

The effect of water solvation on the structure and stability of cyclic dimers of urea has been investigated with the aid of density functional theory at the B3LYP/6-311++G** level. Several hydration models have been discussed. Specific solvent effects have been simulated through single and multiple water-urea interactions involving all the hydration sites of urea. The bulk solvent effects have been estimated through polarised continuum models. Under all the hydration patterns cyclic dimers continue to be stable structures although the solvent weakens the urea-urea interaction. Single and multiple specific urea-water interactions are competitive with urea dimerisation. The anticooperative nature of the two intermolecular interactions is largely due to the changes on sigma- and pi-electron density of urea caused by hydrogen bonding with water. The stability of the dimer is however, lost within a few ps when the hydrated dimer is described by a quantum mechanical molecular dynamics approach (ADMP). The cyclic dimer evolves towards structures where urea molecules are linked not more directly but through water molecules which have a bridge function.     

Electronic spectra of uranyl chloride complexes in acetone: a CASSCF/CASPT2 investigation

A theoretical study is presented of the electronic spectra of the complexes UO(2)Cl(2)ac(4), UO(2)Cl(2)ac(3), [UO(2)Cl(3)ac(2)](-) and [UO(2)Cl(3)ac](-) (ac = acetone) using perturbation theory based on a complete-active-space type wavefunction (CASSCF/CASPT2). Both scalar relativistic effects and spin-orbit coupling were included in the calculations. The calculated excitation energies and oscillator strength values have been compared to the experimental absorption spectrum for uranyl chloride complexes in acetone solution, for chloride-to-uranyl ratios between two and three. The main purpose of this work was to investigate the origin of the remarkable intensity increase observed in the lower part of the experimental absorption spectra, upon addition of chloride to uranyl complexes in acetone. The calculated excitation energies for the different complexes are similar and closely correspond to the experimental data. However, in none of the theoretical spectra, the high intensities observed in the lower part of the experimental spectrum are reproduced.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

The guanine cation radical: investigation of deprotonation states by ESR and DFT

This work reports ESR studies that identify the favored site of deprotonation of the guanine cation radical (G*+) in an aqueous medium at 77 K. Using ESR and UV-visible spectroscopy, one-electron oxidized guanine is investigated in frozen aqueous D2O solutions of 2'-deoxyguanosine (dGuo) at low temperatures at various pHs at which the guanine cation radical, G*+ (pH 3-5), singly deprotonated species, G(-H)* (pH 7-9), and doubly deprotonated species, G(-2H)*- (pH > 11), are found. C-8-deuteration of dGuo to give 8-D-dGuo removes the major proton hyperfine coupling at C-8. This isolates the anisotropic nitrogen couplings for each of the three species and aids our analyses. These anisotropic nitrogen couplings were assigned to specific nitrogen sites by use of 15N-substituted derivatives at N1, N2, and N3 atoms in dGuo. Both ESR and UV-visible spectra are reported for each of the species: G*+, G(-H)*, and G(-2H)*-. The experimental anisotropic ESR hyperfine couplings are compared to those obtained from DFT calculations for the various tautomers of G(-H)*. Using the B3LYP/6-31G(d) method, the geometries and energies of G*+ and its singly deprotonated state in its two tautomeric forms, G(N1-H)* and G(N2-H)*, were investigated. In a nonhydrated state, G(N2-H)* is found to be more stable than G(N1-H)*, but on hydration with seven water molecules G(N1-H)* is found to be more stable than G(N2-H)*. The theoretically calculated hyperfine coupling constants (HFCCs) of G*+, G(N1-H)*, and G(-2H)*- match the experimentally observed HFCCs best on hydration with seven or more waters. For G(-2H)*-, the hyperfine coupling constant (HFCC) at the exocyclic nitrogen atom (N2) is especially sensitive to the number of hydrating water molecules; good agreement with experiment is not obtained until nine or 10 waters of hydration are included.