Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals

The electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) methods and their equation-of-motion coupled-cluster (EOMCC) analogs provide an elegant framework for studying open-shell systems. As shown in this study, these schemes require the presence of higher-order excitations, such as the four-particle-three-hole (4p-3h) or four-hole-three-particle (4h-3p) terms, in the electron attaching or ionizing operator R in order to produce accurate ground- and excited-state potential energy surfaces of radicals along bond breaking coordinates. The full inclusion of the 4p-3h/4h-3p excitations in the EA/IP SAC-CI and EOMCC methods leads to schemes which are far too expensive for calculations involving larger radicals and realistic basis sets. In order to reduce the large costs of such schemes without sacrificing accuracy, the active-space EA/IP EOMCC methodology [J. R. Gour et al., J. Chem. Phys. 123, 134113 (2005)] is extended to the EA/IP SAC-CI approaches with 4p-3h/4h-3p excitations. The resulting methods, which use a physically motivated set of active orbitals to pick out the most important 3p-2h/3h-2p and 4p-3h/4h-3p excitations, represent practical computational approaches for high-accuracy calculations of potential energy surfaces of radicals. To illustrate the potential offered by the active-space EA/IP SAC-CI approaches with up to 4p-3h/4h-3p excitations, the results of benchmark calculations for the potential energy surfaces of the low-lying doublet states of CH and OH are presented and compared with other SAC-CI and EOMCC methods, and full CI results.     

Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

The method of moments of coupled-cluster equations (MMCC), which provides a systematic way of improving the results of the standard coupled-cluster (CC) and equation-of-motion CC (EOMCC) calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The MMCC theory and its generalized MMCC (GMMCC) extension that enables one to use the cluster operators resulting from the standard as well as nonstandard CC calculations, including those obtained with the extended CC (ECC) approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction (CI) and CC or EOMCC energies. These relationships can be used to design the noniterative corrections to the CC/EOMCC energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference CC/EOMCC methods fail. Several MMCC and GMMCC approximations are discussed, including the renormalized and completely renormalized CC/EOMCC methods for closed- and open-shell states, the quadratic MMCC approaches, the CI-corrected MMCC methods, and the GMMCC approaches for multiple bond breaking based on the ECC cluster amplitudes.     

Spectroscopic properties of gallium arsenide tetramers: Ga2As2, Ga2As2+ and Ga2As2-

Spectroscopic properties of the low-lying electronic states of Ga2As2 and its ions are studied using the complete active-space self-consistent field (CASSCF) and density function theory (DFT) followed by the coupled-cluster single and double substitutions (including triple excitations) (CCSD(T)) calculations. The stability of low-lying electronic states is examined by computing vibrational frequency. The energies of the ground states and a number of excited electronic states have been computed to predict the spectra of Ga2As2 and its ions. The ionization energy, electronic affinity, and atomization energy are estimated at the CCSD(T)/6-311+G(d) level and compared with the available experimental results.     

Thermodynamics of titanium and vanadium reduction in non-aqueous environment calculated at various levels of theory

Reduction of titanium and vanadium compounds is a process accompanying the activation of coordinative olefin polymerization catalysts. Four density functional theory (DFT) functionals, coupled cluster with single, double, and perturbative triple excitations method CCSD(T) as well as complete active-space second-order perturbation theory method CASPT2 with a complete active-space self-consistent field CASSCF reference wave function were applied to investigate the thermodynamics of titanium and vanadium reduction. The performance of these theoretical methods was assessed and compared with experimental values. The calculations indicate that vanadium(IV) chloride is more easily reduced by trimethylaluminum than the corresponding titanium compound; the energies of reaction calculated at the CCSD(T) level are equal -57.21 and -33.10 kcal/mol, respectively. The calculations deal with the redox reactions of metal chlorides in the gas phase, rather than solvated ions in the aqueous solution. This approach may be more appropriate for olefin polymerization, usually carried out in nonpolar solvents.     

Orbital-optimized coupled-cluster theory does not reproduce the full configuration-interaction limit

It is shown that due to the mixing of the usual projection approach of coupled cluster with variational orbital optimization, orbital-optimized coupled cluster (OCC) fails to reproduce the full configuration-interaction (full CI) limit when the cluster operator becomes complete. It is pointed out that the fulfillment of the projected singles equations, which define the orbital gradient in Brueckner coupled cluster (BCC), is mandatory for a correct behavior. As numerical examples we present general OCC and BCC calculations up to the full CI limit on CH(2) and an active-space model of ozone. The observed deviations of OCC from full CI are of the order of the correlation error obtained in calculations with up to quadruples excitations. Thus the failure of OCC may be considered tolerable in more approximate calculations but clearly prohibitive for any benchmark application. For applications to active-space models a hybrid approach for OCC is suggested in which for active particle-hole rotations the Brueckner orbital gradient is employed, whereas for the remaining orbital rotations the variational orbital gradient is retained.     

Electron dynamics in charge-transfer-to-solvent states of aqueous chloride revealed by Cl- 2p resonant Auger-electron spectroscopy

Charge-transfer-to-solvent (CTTS) excited states of aqueous chloride are studied by a novel experimental approach based on resonant inner-shell photoexcitation, Cl(-)aq 2p --> e(i), i = 1-4, which denotes a series of excitations to lowest and higher CTTS states. These states are clearly identified through the occurrence of characteristic spectator Auger decays to double Cl 3p valence-hole states, where the CTTS states can be more stabilized as compared to single Cl(-)aq 2p core excitations and optical valence excitations. Furthermore, we have found for the first time that the CTTS electron e(i) bound by a single Cl 2p hole not only behaves as a spectator e(i) --> e'(i), bound by a double valence-hole state before relaxation of the excited electron (i) itself, but also shows electron dynamics to the relaxed lowest state, e(i) --> e'(1*). This interpretation is supported by ab initio calculations. The key to performing photoelectron and Auger-electron spectroscopy studies from aqueous solutions is the use of a liquid microjet in ultrahigh vacuum in conjunction with synchrotron radiation.     

Dissociation dynamics of positive-ion and negative-ion fragments of gaseous and condensed Si(CH(3))(2)Cl(2) via Si 2p, Cl 2p, and Cl 1s core-level excitations

The state-selective positive-ion and negative-ion dissociation pathways of gaseous and condensed Si(CH(3))(2)Cl(2) following Cl 2p, Cl 1s, and Si 2p core-level excitations have been characterized. The excitations to a specific antibonding state (15a(1) (*) state) of gaseous Si(CH(3))(2)Cl(2) at the Cl 2p, Cl 1s, and Si 2p edges produce significant enhancement of fragment ions. This ion enhancement at specific core-excited states correlates closely with the ion kinetic energy distribution. The results deduced from ion kinetic energy distribution are consistent with results of quantum-chemical calculations on Si(CH(3))(2)Cl(2) using the ADF package. The Cl(-) desorption yields for Si(CH(3))(2)Cl(2)Si(100) at approximately 90 K are notably enhanced at the 15a(1) (*) resonance at both Cl 2p and Si 2p edges. The resonant enhancement of Cl(-) yield occurs through the formation of highly excited states of the adsorbed molecules. These results provide insight into the state-selective ionic fragmentation of molecules via core-level excitation.     

A SCF Xα MO study of the optical and Ti2p core photoemission spectra of TiCl4

SCF Xα MO calculations on the ground state and optical excitation transition states of TiCl₄ accurately predict the energies of its UV absorption peaks. Calculations on the Ti2p core ion state and associated transition states indicate that the recently observed low energy (4.0 eV) Ti2p satellite arises from ligand to metal charge transfer excitations while the satellite at high energy (9.4 eV), similar to those previously observed in Ti(IV) compounds, can be attributed to transitions from the highest filled orbitals to empty orbitals with Cl3pTi4s. 4p antibonding character.     

Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores

Almost all time-dependent density-functional theory (TDDFT) calculations of excited states make use of the adiabatic approximation, which implies a frequency-independent exchange-correlation kernel that limits applications to one-hole/one-particle states. To remedy this problem, Maitra et al. [N.T. Maitra, F. Zhang, R.J. Cave, K. Burke, Double excitations within time-dependent density functional theory linear response theory, J. Chem. Phys. 120 (2004) 5932 ] proposed dressed TDDFT (D-TDDFT), which includes explicit two-hole/two-particle states by adding a frequency-dependent term to adiabatic TDDFT. This paper offers the first extensive test of D-TDDFT, and its ability to represent excitation energies in a general fashion. We present D-TDDFT excited states for 28 chromophores and compare them with the benchmark results of Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P.A. Sauer, W. Thiel, Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3, J. Chem. Phys. 128 (2008) 134110]. We find the choice of functional used for the A-TDDFT step to be critical for positioning the 1h1p states with respect to the 2h2p states. We observe that D-TDDFT without HF exchange increases the error in excitations already underestimated by A-TDDFT. This problem is largely remedied by implementation of D-TDDFT including Hartree-Fock exchange.     

Excitation spectra of dibenzoborole containing pi-electron systems: controlling the electronic spectra by changing the p(pi)-pi* conjugation

We report time-dependent density functional theory calculations of the vertical excitation energies for the singlet states of three-coordinate 5H-dibenzoborole (DBB) derivatives and four-coordinate 5-fluoro-5H-dibenzoborole ion (FDBB) derivatives. These molecules show remarkable hypsochromic (blue) shifts in their fluorescence spectra and bathochromic (red) shifts in their absorption spectra when the bridging boron atoms change their coordination number from three to four. We constructed a series of derivatives of DBB and FDBB and studied how the energies of the electronic excitations change. The states with prominent oscillator strength in all of the DBB and FDBB derivatives show similar shifts of their excitation energies upon coordination. The three-coordinate DBB derivative 5-(2,4,6-triisopropylphenyl)-2,8-dimethoxy-3,7-bis[p-(N,N-diphenylamino)phenyl]-5H-dibenzo[d,b]borole has an intense absorption at 3.25 eV, which shifts in the four-coordinate FDBB derivative 5-fluro-5-(2,4,6-triisopropylphenyl)-2,8-dimethoxy-3,7-bis[p-(N,N-dip henylamino)phenyl]-5H-dibenzo[d,b]borole ion to 3.17 eV. The experimental absorption peaks are 3.43 and 3.31 eV, respectively. In addition, we investigated and analyzed the nature of these electronic excitations using attachment/detachment density plots, with which we characterized the changes in electron density that arose from the excitations.     

A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory

This study examines the radical nature and spin symmetry of the ground state of the quasi-linear acene and two-dimensional periacene series. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory and the COLUMBUS program package. A reference space consisting of restricted and complete active spaces is taken for the π-conjugated space, correlating 16 electrons with 16 orbitals with the most pronounced open-shell character for the acenes and a complete active-space reference approach with eight electrons in eight orbitals for the periacenes. This reference space is used to construct the total configuration space by means of single and double excitations. By comparison with more extended calculations, it is shown that a focus on the π space with a 6-31G basis set is sufficient to describe the major features of the electronic character of these compounds. The present findings suggest that the ground state is a singlet for the smaller members of these series, but that for the larger ones, singlet and triplet states are quasi-degenerate. Both the acenes and periacenes exhibit significant polyradical character beyond the traditional diradical.     

The electronic states of 1,2,3-triazole studied by vacuum ultraviolet photoabsorption and ultraviolet photoelectron spectroscopy, and a comparison with ab initio configuration interaction methods

The Rydberg states in the vacuum ultraviolet photoabsorption spectrum of 1,2,3-triazole have been measured and analyzed with the aid of comparison to the UV valence photoelectron ionizations and the results of ab initio configuration interaction (CI) calculations. Calculated electronic ionization and excitation energies for singlet, triplet valence, and Rydberg states were obtained using multireference multiroot CI procedures with an aug-cc-pVTZ [5s3p3d1f] basis set and a set of Rydberg [4s3p3d3f] functions. Adiabatic excitation energies obtained for several electronic states using coupled-cluster (singles, doubles, and triples) and complete active space self-consistent field procedures agree well with experimental values. Variations in bond lengths with the electronic state are discussed. The lowest energy UV band (～5.5-6.5 eV) is assigned to three electronically excited states and demonstrates the occurrence of a nonplanar upper state on the low energy side. A UV photoelectron spectrum with an improved resolution yielded adiabatic and vertical ionization energies and reorganization energies for several of the lowest cationic states. As well as excitations to the s, p, d-Rydberg states are the excitations consistent with an f-series.     

Size and isotope effects of helium clusters and droplets: identification of surface and bulk-volume excitations

We report a comprehensive investigation of the electronically excited states of helium clusters and droplets of sizes ranging from a few to several 10(7) atoms using time-resolved fluorescence excitation spectroscopy and quantum chemical ab initio calculations. We employ various approaches for our analysis considering the lifetime-dependence of the fluorescence intensity, spectral shifts, intensity scaling with cluster size, isotopic dependence, and density-dependence of the calculated electron wave function radii. A unique feature of helium clusters and droplets is their radially varying particle density. Our results show that short-lived fluorescence is sensitive to regions of increased density and probes excitations located in the bulk volume, whereas long-lived fluorescence is sensitive to regions of reduced density such as for small clusters or for the surface of large droplets. Spectra of (3)He droplets serve as a reference for low density, but are free from contributions of small clusters. This allows us to distinguish regions of reduced density as these can be due to both surface states or small clusters. Our analysis reveals a picture where spectral features are related to regions of different density due to isotopic composition, cluster size, and surface or bulk volume location of the excitations. The 2s and 2p related excitations appear as blue-shifted wings for small clusters or for excited atoms within the surface layer, whereas in the bulk-volume of large droplets, they appear as distinct bands with large intensities, dominating the entire spectrum. Excitations at energies higher than 23 eV are unambiguously assigned to regions of low and medium density location within the deeper parts of the surface layer but show no relation to the bulk volume. Our findings support the idea that in liquid helium high-lying states and, in particular, Rydberg states are quenched in favor of the 2s and 2p excitations.     

The cis—trans thermal and photochemical interconversion mechanism in the dimide N-oxide. A comparison of the results obtainable with different ab initio calculation techniques

Two possible pathways have been investigated for the cis—trans conversion in diimide N-oxide, viz. a rotation around the NN bond and an in-plane inversion. Calculations have been performed for the ground and lowest excited states by means of a Cl treatment including the configurations found to be the most important in large Cl calculations performed in a few points. It is shown that the rotational mechanism is favoured in the excited states and is probable also in the thermal reaction. Such investigation has been repeated in parallel by using other techniques of lower accuracy: (1) Cl limited to single excitations (EHP method); (2) rigid excitation to virtual orbitals; (3) the half electron methods. Deficiencies of such methods have been brought out and analyzed. In particular methods (2) and (3) lead to an erroneus interpretation of the actual mechanism of the photochemical conversion by rotation.     

Comparison of density functionals for energy and structural differences between the high- [5T2g: (t2g)4(eg)2] and low- [1A1g: (t2g)6(eg)0] spin states of the hexaquoferrous cation [Fe(H2O)6]2+

A comparison of density functionals is made for the calculation of energy and geometry differences for the high- [(5)T(2g): (t(2g))(4)(e(g))(2)] and low- [(1)A(1g): (t(2g))(6)(e(g))(0)] spin states of the hexaquoferrous cation [Fe(H(2)O)(6)](2+). Since very little experimental results are available (except for crystal structures involving the cation in its high-spin state), the primary comparison is with our own complete active-space self-consistent field (CASSCF), second-order perturbation theory-corrected complete active-space self-consistent field (CASPT2), and spectroscopy-oriented configuration interaction (SORCI) calculations. We find that generalized gradient approximations (GGAs) and the B3LYP hybrid functional provide geometries in good agreement with experiment and with our CASSCF calculations provided sufficiently extended basis sets are used (i.e., polarization functions on the iron and polarization and diffuse functions on the water molecules). In contrast, CASPT2 calculations of the low-spin-high-spin energy difference DeltaE(LH)=E(LS)-E(HS) appear to be significantly overestimated due to basis set limitations in the sense that the energy difference of the atomic asymptotes ((5)D-->(1)I excitation of Fe(2+)) are overestimated by about 3000 cm(-1). An empirical shift of the molecular DeltaE(LH) based upon atomic calculations provides a best estimate of 12 000-13 000 cm(-1). Our unshifted SORCI result is 13 300 cm(-1), consistent with previous comparisons between SORCI and experimental excitation energies which suggest that no such empirical shift is needed in conjunction with this method. In contrast, after estimation of incomplete basis set effects, GGAs with one exception underestimate this value by 3000-4000 cm(-1) while the B3LYP functional underestimates it by only about 1000 cm(-1). The exception is the GGA functional RPBE which appears to perform as well as or better than the B3LYP functional for the properties studied here. In order to obtain a best estimate of the molecular DeltaE(LH) within the context of density functional theory (DFT) calculations we have also performed atomic excitation energy calculations using the multiplet sum method. These atomic DFT calculations suggest that no empirical correction is needed for the DFT calculations.     

Can large active-space CASSCF calculation make sense to the reaction analysis of iron complex? A benchmark study of methane oxidation reaction by FeO+

A methane oxidation reaction by FeO⁺ cation was theoretically investigated based on the density functional theory (DFT) and the complete active-space self-consistent field (CASSCF) method as well as the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) to explore the active-space dependency to computational analyses in such strongly correlated reaction systems. A small active-space CASSCF(5e in 5o) calculation, which only includes five 3d orbitals of the Fe atom in the active-space, showed remarkable difference both in energy and geometry compared to those computed by the DFT and CCSD(T) methods. Interestingly, a large active-space CASSCF(17e in 17o) calculation, which includes almost all the valence orbitals gives a qualitative agreement with either the DFT or the CCSD(T) results in the first half part of the reaction, although it varies from them in the latter half part. Therefore, it is indicated that the active-space dependency is serious in some part of the reaction and the small active-space CASSCF might lead a wrong discussion. We further investigated the optimized geometry of the intermediate complex with the small and the large active-space CASSCF methods as well as the CCSD(T) method, and found that the CASSCF(5e in 5o)-optimized geometry is considerably different from the others. In consequence, a small active-space CASSCF/CASPT2 calculation does not really work for such a strongly correlated reaction system even qualitatively, and a sophisticated assessment using the large active-space CASSCF/CASPT2 method will be indispensable. © 2018 Wiley Periodicals, Inc.