Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and triples approximation. Special attention is paid to the artificial splitting of certain excited states which arises from the redundancy intrinsic to Mk-MRCC theory and hinders the straightforward application of the Mk-MRCC-LR method.     

Comprehensive relativistic ab initio and density functional theory studies on PtH, PtF, PtCl, and Pt(NH(3))(2)Cl(2)

Platinum monohydride is taken as an example to compare the performance of various relativistic and correlation approaches, such as all-electron DPT (direct perturbation theory), ECP (effective core potential); RSPT2, RSPT3 (second- and third-order multireference Rayleigh-Schr?dinger perturbation theory), CCSD(T) (coupled-cluster with singles, doubles, and perturbative triples), as well as the four-component relativistic density functional theory. It is shown that first-order DPT performs significantly better than the (first-order) Breit-Pauli Hamiltonian. The performance of different approaches for the excitation energies of the platinum diatomics is discussed critically. The molecular spectroscopic constants for PtF and PtCl are predicted for the first time. The geometric data for several isomers of cis- and trans-Pt(NH(3))(2)Cl(2) are reported. The corresponding energetic data are calculated at relativistic all-electron and ECP-CCSD(T) as well as four-component relativistic density functional levels of theory. Contrary to previous results, it is found that the two C(2v) isomers of cis-Pt(NH(3))(2)Cl(2) are marginally separated in energy, which could be ascribed to Cl-H interactions.     

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested for an extensive set of examples, and is shown to provide total energies that compare favorably with those obtained with the full singles, doubles, triples, and quadruples (CCSDTQ) method.     

Assessing the performance of density functional theory for the electronic structure of metal-salens: the 3d(0)-metals

A series of metal-salen complexes of the 3d(0) metals Sc(III), Ti(IV), V(V), Cr(VI), and Mn(VII) have been explored using high-level electronic structure methods including coupled-cluster theory with singles, doubles, and perturbative triples as well as complete active-space third-order perturbation theory. The performance of three common density functional theory approaches has been assessed for both the geometries and the relative energies of the low-lying electronic states. The nondynamical correlation effects are demonstrated to be extremely large in all of the systems examined. Although density functional theory provides reasonable results for some of the systems, the overall agreement is quite poor. This said, the density functional theory approaches are shown to outperform the single-reference perturbation theory and coupled-cluster theory approaches for cases of strong nondynamical correlation.     

UV and IR photoisomerization of acetylacetone trapped in a nitrogen matrix

UV- and IR-induced photoisomerization of acetylacetone trapped in a nitrogen matrix at 4.3 K have been carried out using a tunable optical parametric oscillator type laser, or a mercury vapor lamp, coupled with Fourier Transform IR and UV spectroscopies. After deposition, the main form present in the cryogenic matrix is that chelated (enol). Upon UV irradiation, the intramolecular H bond is broken leading to nonchelated isomers among seven possible open forms. These forms have then been irradiated by resonant pi* <-- pi UV irradiation, or by resonant nuOH irradiation. The selective UV irradiation allows us to suggest a first vibrational assignment while the nuOH irradiation leads us to observe interconversions between the nonchelated isomers. In order to support our vibrational assignment, we have carried out theoretical calculations at the B3LYP/6-311++G(2d,2p) level of theory. This study shows that only five isomers are observed among eight postulated.     

Coupled-cluster studies of the lowest excited states of the 11-cis-retinal chromophore

The first few excited states of the 11-cis-retinal (PSB11) chromophore have been studied at the coupled-cluster approximative singles and doubles (CC2) level using triple-zeta quality basis sets augmented with double sets of polarisation functions. The two lowest vertical excitation energies of 2.14 and 3.21 eV are in good agreement with recently reported experimental values of 2.03 and 3.18 eV obtained in molecular beam measurements. Calculations at the time-dependent density functional theory (TDDFT) level using the B3LYP hybrid functional yield vertical excitation energies of 2.34 and 3.10 eV for the two lowest states. Zero-point vibrational energy (ZPVE) corrections of -0.09 and -0.17 eV were deduced from the harmonic vibrational frequencies for the ground and excited states calculated at the density functional theory (DFT) and TDDFT level, respectively, using the B3LYP hybrid functional.     

Theoretical study of thermal rearrangements of 1-hexen-5-yne, 1,2,5-hexatriene, and 2-methylenebicyclo[2.1.0]pentane

In this research, a comprehensive theoretical investigation of the thermal rearrangements of 1-hexen-5-yne, 1,2,5-hexatriene, and 2-methylenebicyclo[2.1.0]pentane is carried out employing density functional theory (DFT) and high level ab initio methods, such as the complete active space self-consistent field (CASSCF), multireference second-order M?ller-Plesset perturbation theory (MRMP2), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)]. The potential energy surface (PES) for the relevant system is explored to provide a theoretical account of pyrolysis experiments by Huntsman, Baldwin, and Roth on the target system. The rate constants and product distributions are calculated using theoretical kinetic modelings. The rate constant for each isomerization reaction is computed using the transition state theory (TST). The simultaneous first-order ordinary-differential equations are solved numerically for the relevant system to obtain time-dependent concentrations, hence the product distributions at a given temperature. Our computed energy values (reaction energies and activation parameters) are in agreement with Roth's experiments and the product distributions of Huntsman's experiments at 340 and 385 °C with various reaction times, while simulated product fractions are in qualitative accordance with Baldwin's experiment.     

Accurate benchmark calculation of the reaction barrier height for hydrogen abstraction by the hydroperoxyl radical from methane. Implications for C(n)H(2n+2) where n = 2 --> 4

The CH4 + HO2(*) reaction is studied by using explicitly correlated coupled-cluster theory with singles and doubles (CCSD-R12) in a large 19s14p8d6f4g3h basis (9s6p4d3f for H) to approach the basis-set limit at the coupled-cluster singles-doubles level. A correction for connected triple excitations is obtained from the conventional CCSD(T) coupled-cluster approach in the correlation-consistent quintuple-zeta basis (cc-pV5Z). The highly accurate results for the methane reaction are used to calibrate the calculations of the hydroperoxyl-radical hydrogen abstraction from other alkanes. For the alkanes C(n)H(2n+2) with n = 2 --> 4, the reactions are investigated at the CCSD(T) level in the correlation-consistent triple-zeta (cc-pVTZ) basis. The results are adjusted to the benchmark methane reaction and compared with those from other approaches that are commonly used in the field such as CBS-QB3, CBS-APNO, and density functional theory. Rate constants are computed in the framework of transition state theory, and the results are compared with previous values available.     

Can a single-reference approach provide a balanced description of ground and excited states? A comparison of the completely renormalized equation-of-motion coupled-cluster method with multireference quasidegenerate perturbation theory near a conical intersection and along a photodissociation coordinate in ammonia

We calculated the two lowest electronically adiabatic potential energy surfaces of ammonia in the region of the conical intersection and at a sequence of geometries along which one of the N-H bonds is broken. We employed both a multireference (MR) method and a single-reference (SR) method. The MR calculations are based on multiconfiguration quasidegenerate perturbation theory (MC-QDPT) with a 6-311+G(3df,3pd) basis set. The SR calculations, carried out with the same basis, employ the completely renormalized equation-of-motion coupled-cluster method with singles and doubles, and a noniterative treatment of triples, denoted CR-EOMCCSD(T). At 91 geometries used for comparison, including geometries near a conical intersection, the surfaces agree to 7% on average.     

Theoretical study of vibrational and optical spectra of methylene-bridged oligofluorenes

We report a systematic characterization of methylene-bridged fluorene oligomers constructed of two, four, six, and eight aromatic rings using time-dependent density functional theory (TDDFT), the ab initio approximate coupled-cluster singles and doubles (CC2) method, and semiempirical spectroscopic Zerner's intermediate neglect of differential overlap method (ZINDO/S). Geometry optimizations have been performed for the ground state and for the first electronically excited state. Vertical excitations and the fluorescence transition from the lowest excited state have been calculated. Computed ground-state geometries and infrared spectra for fluorene are in good agreement with experimental results. The RI-CC2 and ZINDO/S absorption and fluorescence spectra agree very well with the available experimental data for studied fluorene oligomers and for para oligophenylenes films. On the other hand, TDDFT calculations underestimate excitation and fluorescence energies systematically for larger systems (N > 4) in comparison with the above-mentioned results. The effective conjugation length was estimated to 13-14 repeat units. The computed radiative lifetimes for the fluorene molecule show good agreement with experiment within realistic expectations. The decrease of the radiatiave fluorescence lifetime with the increase in the conjugation length has been discussed also.     

Ab initio MO study on the global minimum structure of C3H3 anion: propynl-1-yl versus allenyl anions

The geometrical structures of the C₃H⁻₃ anion are surveyed at the coupled-cluster doubles (CCD) level of theory with the aug-cc-pVDZ basis set. To clarify the CCD geometries, the stable two isomers -- propynl-l-yl 1 and allenyl 2 anions -- are further optimized at the coupled-cluster singles, doubles (triples) (CCSD(T)) level of theory both with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The final energies are calculated at the CCSD(T) and the complete active space self-consistent field (CASSCF) multi-reference internally contracted CI (MRCI) levels of theory with the aug-cc-pVTZ basis set. At the MRCI level of theory including both the corrections due to the cluster energies (MRCI+Q) and the zero-point vibrational energies, the allenyl anion 2 is about 1.3 kcal mol⁻¹ lower in energy than the propynl-l-yl anion 1. These results contrast with the previous theoretical estimates, where the propynl-l-yl anion 1 is 2-3 kcal mol⁻¹ lower in energy than the allenyl anion 2. The activation energies of the intramolecular hydrogen transfer in the 1 → 2 conversion reactions are 63.5 kcal mol⁻¹ at the MRCI+Q level of theory with the aug-cc-pVTZ basis set including the zero-point energy corrections. The adiabatic electron affinity of the planer propargyl (H₂CCCH) radical, which is the global minimum of the C₃H₃ radical, is calculated to be 0.976 eV (after correction for the zero-point energy changes) at the CCSD(T) level of theory with the aug-cc-pVTZ basis set. The present electron affinity is in fairly good agreement with the experimental one (0.893 eV) observed by Oakes and Ellison.     

C4Cl: bent or linear?

The ground state structure for the CCCCCl radical was computed by using symmetry-adapted cluster configuration-interaction (SAC-CI) theory along with density functional theory to overcome the differences raised in the recently published paper [Y. Sumiyoshi et al., Chem. Phys. Lett. 414, 82 (2005)] between the theory and the experiment. SAC-CI results clearly support the earlier experimental conclusion that the radical has the bent ground state structure corresponding to 2Pi symmetry. Contrarily, probably due to spin contamination, mixing of a bent doublet ground state with the quartet components of a linear structure, coupled-cluster singles and doubles (CCSD) calculations were unable to provide reliable results. Results obtained using density functional theory also show that the radical has a bent structure. Some low-lying doublet excited states were also studied using the SAC-CI theory. The energy difference between the ground Pi state and the nearby Sigma state is around 0.2 eV. The excitation energy for the transition with the largest oscillator strength agrees with the strongest absorption peak.     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.     

Electronic structure and vertical excitation spectrum of methylene amidogen CH2N

Ab initio electronic structure calculations are reported for five electronic states of the methylene amidogen radical. Structure parameters for the ground electronic state are predicted by RHF and D -MBPT (4) calculations. Vertical excitation energies were determined using four different theoretical chemical models: complete active space (CAS ) MCSCF , CAS /MCSCF plus singles and doubles Cl, fourth-order many-body perturbation theory SDQ -MBPT (4), and coupled-cluster theory.     

Theoretical characterization of intermolecular vibrational states through the multi-configuration time dependent Hartree approach: the He2,3ICl clusters

Benchmark, full-dimensional calculations on the ground and excited vibrational states for the tetra-, and penta-atomic weakly bound He(2,3)ICl complexes are reported. The representation of the potential energy surfaces includes three-body HeICl potentials parameterized to coupled-cluster singles, doubles, and perturbative triples ab initio data. These terms are important in accurately describing the interactions of such highly floppy systems. The corresponding 6D/9D computations are performed with the multi-configuration time dependent Hartree method, using natural potential fits, and a mode combination scheme to optimize the computational effort in the improved relaxation calculations. For these complexes several low-lying vibrational states are computed, and their binding energies and radial/angular probability density distributions are obtained. We found various isomers which are assigned to different structural models related with combinations of the triatomic isomers, like linear, T-shaped, and antilinear ones. Comparison of these results with recent experimental data is presented, and the quantitative deviations found with respect to the experiment are discussed.     

Structure and stability of (TiO2)n, (SiO2)n, and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] clusters

Structures, energetics, and vibrational spectra are investigated for small pure (TiO(2))(n), (SiO(2))(n), and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] oxide clusters by density functional theory (DFT). The BP86/ATZP level of theory is employed to obtain constitutional isomers of the oxide clusters. In accordance with previous studies, our calculations show three-dimensional compact structures are preferred for pure (TiO(2))(n) with oxo-stabilized higher hexavalent states, and linear chain structures are favored for pure (SiO(2))(n) with tetravalent states. However, the herein theoretically first reported mixed Ti(m)Si(n-m)O(2n) oxide clusters prefer either three-dimensional compact or linear chain structures depending upon the stoichiometry of the compound. Vibrational analysis of the important modes of some highly stable structures is provided. Coupled-cluster single and double excitation (with triples) [CCSD(T)] computed energy gaps for the TiO(2) dimers compare well with results from previous study. Excitation energies are computed by use of time-dependent (TD) DFT and equation-of-motion coupled-cluster calculations with singles and doubles (EOM-CCSD) for the most stable isomers.     

Electron affinity of Al13: a correlated electronic structure study

Neutral and anionic 13-atom aluminum clusters are studied with high-level, fully ab initio methods: second-order perturbation theory (MP2) and coupled cluster theory with singles, doubles, and perturbative triples (CCSD(T)). Energies and vibrational frequencies are reported for icosahedral and decahedral isomers, and are compared with density functional theory results. At the MP2 level of theory, with all of the basis sets employed, the icosahedral structure is energetically favored over the decahedral structure for both the neutral and anionic Al(13) clusters. Hessian calculations imply that only the icosahedral structures are potential energy minima. The CCSD(T)/aug-cc-pVTZ adiabatic electron affinity of Al(13) is found to be 3.57 eV, in excellent agreement with experiment.