On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACT

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths

We present two new modifications of the second-order polarization propagator approximation (SOPPA), SOPPA(SCS-MP2) and SOPPA(SOS-MP2), which employ either spin-component-scaled or scaled opposite-spin MP2 correlation coefficients instead of the regular MP2 coefficients. The performance of these two methods, the original SOPPA method as well as SOPPA(CCSD) and RPA(D) in the calculation of vertical electronic excitation energies and oscillator strengths is investigated for a large benchmark set of 28 medium-sized molecules with 139 singlet and 71 triplet excited states. The results are compared with the corresponding CC3 and CASPT2 results from the literature for both the TZVP set and the larger and more diffuse aug-cc-pVTZ basis set. In addition, the results with the aug-cc-pVTZ basis set are compared with the theoretical best estimates for this benchmark set. We find that the original SOPPA method gives overall the smallest mean deviations from the reference values and the most consistent results.     

The singlet electronic states of pyrrole: a theoretical study by both ab initio multi-reference configuration interaction methods and time-dependent density functional theory and a reconsideration of the experimental VUV spectral data

The singlet electronic excitation spectrum of pyrrole has been reinvestigated by both multi-reference multi-root configuration interaction (CI) calculations and time-dependent density functional theory (DFT) with asymptotically corrected exchange-correlation potentials. The methods used a triple zeta valence + polarization + Rydberg (TZVPR) basis set and a much larger active space than in our previous CI study [Palmer, M. H., Walker, I. C., and Guest, M. F., 1998, Chem. Phys., 238, 179]. Computed vertical excitation energies, oscillator strengths and electronic charge distributions were used to characterize and assign the valence and Rydberg excited states over an energy range of 5–12 eV.

A comparison of the present methods with other high-level ab initio studies has been made, including the effects of basis sets and size of CI, and some statistical relationships determined. The present CI vertical excitation energies are generally in closer agreement with the cluster-type methods, especially CC3, than to the various second-order perturbation-type methods (CASPT2, CASPT2-MS, ADC(2) and MRMP).

The influence on the excitation energies from exact orbital exchange and multiplicative potentials in hybrid functional development has been investigated. Differences between the CI and the DFT methods vary in the order B97-2 < B97-1 < HCTH < LDA. The differences between hybrid DFT and CI excitations are minimized when the fraction of orbital exchange (ξ) lies in the approximate range 0.2–0.3. The Rydberg and valence-type excitations are seen to be less sensitive than the static polarizability to the inclusion of orbital exchange or multiplicative potentials in hybrid functional development.

In order to allow a realistic assessment of the performance of the theoretical studies, the assignment of the experimental electronic spectrum of pyrrole is discussed in detail. Previous conclusions have led to incorrect numbers of Rydberg s- and d-type states, while f-type states have previously been ignored. Some excitations from the second IP, which must occur in the 5–10 eV range, have been reassigned in light of the known small differences between other spectroscopic states and quantum defects. There is an urgent need for higher-resolution studies of pyrrole and related molecules.     

Assessment of a composite CC2/DFT procedure for calculating 0–0 excitation energies of organic molecules

The task to assess the performance of quantum chemical methods in describing electronically excited states has in recent years started to shift from calculation of vertical (ΔE_ve) to calculation of 0–0 excitation energies (ΔE₀₀). Here, based on a set of 66 excited states of organic molecules for which high-resolution experimental ΔE₀₀ energies are available and for which the approximate coupled-cluster singles and doubles (CC2) method performs particularly well, we explore the possibility to simplify the calculation of CC2-quality ΔE₀₀ energies using composite procedures that partly replace CC2 with more economical methods. Specifically, we consider procedures that employ CC2 only for the ΔE_ve part and density functional theory methods for the cumbersome excited-state geometry optimisations and frequency calculations required to obtain ΔE₀₀ energies from ΔE_ve ones. The results demonstrate that it is indeed possible to both closely (to within 0.06–0.08 eV) and consistently approximate ‘true’ CC2 ΔE₀₀ energies in this way, especially when CC2 is combined with hybrid density functionals. Overall, the study highlights the unexploited potential of composite procedures, which hitherto have found widespread use mostly in ground-state chemistry, to also play an important role in facilitating accurate studies of excited states.     

Perturbative order analysis of the similarity transformed Hamiltonian in Fock-space coupled cluster theory: difference energy and electric response properties

A perturbative analysis of the ground-state similarity transformed Hamiltonian and its effect on the various Fock-space coupled cluster (FSCC) sectors is presented through calculation of ionisation potential, electron affinity, excitation energies and response properties. Various truncation schemes of the effective Hamiltonian are presented with explicit form of the defining equations. Based on such a truncation, the approximate methods are labelled as FSCC(n), where n represents the correlation energy of the ionised, electron attached or excited states corrected at least up to nth order within coupled cluster singles and doubles scheme (CCSD). A lower scaling CC2 type of approach (abbreviated as FS-CC2) is compared against the group of FSCC(n) methods for energies. Electric response properties have been compared and contrasted for the two lower scaling methods: FSCC(2) and FS-CC2. The various truncated methods are tested for a number of small molecules. The results obtained from a range of truncated methods are compared against full FSCCSD calculations.     

Assessment of oscillator strengths with multiconfigurational short-range density functional theory for electronic excitations in organic molecules

ABSTRACT

We have in a series of recent papers investigated electronic excited states with a hybrid between a complete active space self-consistent field (CASSCF) wave function and density functional theory (DFT). This method has been dubbed the CAS short-range DFT method (CAS–srDFT). The previous papers have primarily focused on the excitation energies, and not on the oscillator strengths, although they comprise an important part of the absorption spectrum. In this study, we have carried out a quantitative analysis of oscillator strengths obtained with CAS–srDFT. As target molecules, we have considered the large collection of organic molecules whose excited states were investigated with a range of electronic structure methods by Thiel et al. As a by-product of our calculations of oscillator strengths, we also obtain electronic excitation energies, which enable us to compare the performance of CAS–srPBE for excitation energies, using a larger set of chromophores compared to previous studies.     

Electronic states of the c is - and trans - H3ONO molecules: a CASPT2 study

The CASPT2 calculations for the S₀, T₁, S₁, T₂, and S₂ states of the cis- and trans-CH₃ONO molecules predict the energy levels and geometries of the cis- and trans-isomers in the different states. The CASPT2 adiabatic (T ₀) and vertical (T _v) excitation energies are in good agreement with available experimental data (for the S₁ cis- and trans-isomers). The CH₃O-NO dissociation potential energy curves were calculated at the CASPT2//CASSCF level, and the CASPT2 calculations were performed for the transition states along the T₁, S₁, and T₂ dissociation paths. For the repulsive S₂ state the calculations predict the T _v values larger than 5.4 eV and dissociation products of CH₃O (1²A″) + NO (X²Π).     

Transition energies, wavelengths, oscillator strengths and transition probabilities between 1s, 1sns and 1snp (2?n?9) states for He-like Silicon

Multiconfiguration Hartree-Fock calculations with Breit-Pauli relativistic corrections are reported for electric dipole transition (E1) energies, wavelengths, weighted oscillator strengths and transition probabilities between all of the 1s², 1sns and 1snp (2?n?9) states for He-like silicon. The results are found to compare very well with available other results except Δn=0 due to differences in the calculated excitation energies.     

Electronic Excitations in Pyrrole: A Test Case for Determination of Chromophores in the Chromogenic Effects of Neurotoxic Hydrocarbons by Time-Dependent Density Functional Theory and Single-Excitation Configuration Interaction Methods

Time-dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) calculations on the electronic excitations in pyrrole have been performed to examine the reliability of these first-principles electronic structure methods in predicting electronic excitation spectraof pyrrole-containing compounds. Both the TD-DFT and CIS calculations led to satisfactory results when compared to available experimental data, particularly for low-lying excited states. The TD-DFT and CIS calculations provide lower and upper limits of the excitation energies, respectively, for low-lying singlet excited states. These results suggest that these methods can be used for the prediction of the excitation spectra, particularly the excitation energies for low-lying excited states, of chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons, which are believed to be substituted pyrroles and their adducts with proteins. As an example of a practical application, the spectrum of the widely used 2,5-dimethylpyrrole has been calculated. It is shown that the 2,5-dimethylpyrrole molecule does not have an absorption in the region of the visible spectrum (400-700 nm), suggesting that the absorption observed at 530 nm and the color of 2,5-dimethylpyrrole is due to another species, probably a product of possible 2,5-dimethylpyrrole autoxidation. This suggests that the conclusions from previously reported experimental studies of biochemical reactions of neurotoxic γ-diketones need to be reexamined in terms of the relationship of chromogenicity to neurotoxicity.     

Excited‐state hydrogen bonding dynamics of pyruvic acid and geminal‐diol, 2,2‐dihydroxypropanoic acid in aqueous solution: a DFT/TDDFT study

In this work, we present the optimized ground state geometrical structures, electronic excitation energies and corresponding oscillation strengths of the low‐lying electronically excited states for the isolated Tce‐CH3COCOOH and Tce‐CH3C(OH)2COOH as well as their corresponding hydrogen‐bonded dimers Tce‐CH3COCOOH‐H2O and Tce‐CH3C(OH)2COOH‐H2O through time‐dependent density functional theory method. It is found that the intermolecular hydrogen bonds C=O···H‐O are strengthened in the electronically excited states of the hydrogen‐bonded dimers Tce‐CH3COCOOH‐H2O and Tce‐CH3C(OH)2COOH‐H2O, in that the excitation energies of the related excited states for the hydrogen‐bonded dimers are decreased compared with those of the corresponding monomers. The calculated results are consistent with the rules that are first demonstrated by Zhao on the excited‐state hydrogen bonding dynamics. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi-reference calculations of the photodissociation of HSCH3 molecule

This paper performs multi-reference second-order perturbation theory calculations on the ground state and a number of low-lying excited states of HSCH3 molecule, and calculates the vertical excitation energies and low-energy potential-energy curves, based on which the photodissociation channels of HSCH3 at 193,222,248 nm are clarified.     

Fluctuations in the level density of a fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many-body density of states, related to shell effects, are obtained. The fluctuations depend nontrivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single-particle motion.     

Relativistic coupled cluster method

Relativistic coupled cluster method (CCM) is applied to compute the low lying excited and ion states of strontium and ytterbium atom. The resulting excitation and ionization energies are in excellent agreement with experimental data and with other correlated calculations. The nuclear magnetic dipole hyperfine constants (A) and electric quadrupole hyperfine constants (B) of excited states are also evaluated and are in accord with experiment. We further address the basis set dependency of the computed properties.     

Brueckner-type reference determinants in applications of coupled cluster methods to excited states

Model studies have been undertaken of the efficiency of single-reference state coupled cluster (SR-CC) methods defined in terms of several Brueckner type orbitals in applications to excited states of a predominately closed shell structure. The H4 model was used, which offers an easy way of representing any set of symmetry adapted orbitals together with the possibility of varying the degree of quasi-degeneracy of the states considered. Standard Brueckner orbitals (BOs) and orbitals generated in the projective and variational Brueckner CC (BCC) methods have been obtained and compared for the first time for excited states. Some attention has been paid to the stability of the BOs. Results of applying Brueckner-type and RHF orbitals in CCD, CCSD, and CCSDT calculations for excited states of rather strong degrees of quasi-degeneracy are presented. It is shown that in most cases proceeding from RHF orbitals to Brueckner-type orbitals results in an improvement in the accuracy of the SR-CC energies. Differences and similarities in the characteristics of Brueckner-type orbitals and SR-CC results for excited states and the ground state are identified and discussed.     

High-resolution investigation of the 112Sn(p,p')112Sn reaction

The ¹¹²Sn(p, p') reaction was studied at proton energies of 20.51 and 25.0 MeV. The outgoing protons were momentum analysed with an Enge split-pole spectrograph and recorded with position-sensitive solid-state detectors with a total resolution between 10 and 15 keV. Excitation energies and angular distributions for states below 5.5 MeV excitation energy were obtained. The angular distributions were compared with macroscopic DWBA calculations in order to extract L-values and deformation parameters. Coupled-channels calculations were performed to investigate two-phonon excitations and the mixing between one- and two-phonon states. The results of the present experiment are compared with previous experimental results and with number-projected BCS calculations. The results for some of the excited states were compared with similar results for the other even Sn isotopes.     

Determination of static dipole polarizabilities of Yb atom

We determine the static values of the scalar and tensor dipole polarizabilities of the ground, 6s6p~3P_0~o, and 6s6p~3P_1~o states of the Yb atom. These results can be useful in many experiments undertaken using this atom. We employed a combined configuration interaction(CI) method and a second-order many-body perturbation theory(MBPT) to evaluate energies and electric dipole(E1) matrix elements of many low-lying excited states of the above atom. These values are compared with the other available theoretical calculations and experimental values. By combining these E1 matrix elements with the experimental excitation energies, we estimate the dominant valence correlation contributions to the dipole polarizabilities of the above states. The core contribution is obtained from the finite field approach. We also compare these values with the other theoretical results as there are no precise experimental values that are available for these properties.     

Multiphonon resonances in the Debye-Waller factor of atom surface scattering

He atom surface scattering by dispersionless phonons is treated employing coupled channel (CC) calculations. At low energies, they predict a behavior opposite to perturbative Born or "exponentiated" Born approximation: strong resonant phonon stimulated elastic and inhibited inelastic scattering. The corresponding resonances have not been observed in earlier CC results since these have considered only the temperature dependence of the Debye-Waller factor at higher energy or omitted the attractive well. The resonances can be interpreted in terms of bound states in the attractive well with several excited vibrational quanta. They may be observable for, e.g., He scattering by a cold Xe/Cu surface.     

非相对论性和相对论性原子组态相互作用理论——激发能量和辐射跃迁几率

我们建立的非相对论性和相对论性原子组态相互作用理论计算方法可用来计算低度激发态的激发能量和辐射跃迁几率(包括允许跃迁和禁戒跃迁)。为了检查我们的计算程序,分别用两种方法计算了氦原子N=2激发态的激发能和相应的辐射跃迁几率。结果表明:非相对论性理论和相对论性理论计算结果基本一致。原子激发能量的精度为千分之几,振子强度的精度为百分之几。上述原子组态相互作用理论方法可用于计算任何原子或离化态原子。 关键词：     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.