A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference (MR) algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F(2) ground state wave function.     

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states.     

Photodissociation dynamics of the NO dimer. I. Theoretical overview of the ultraviolet singlet excited states

Molecular orbital theory and calculations are used to describe the ultraviolet singlet excited states of NO dimer. Qualitatively, we derive and catalog the dimer states by correlating them with monomer states, and provide illustrative complete active space self-consistent field calculations. Quantitatively, we provide computational estimates of vertical transition energies and absorption intensities with multireference configuration interaction and equations-of-motion coupled-cluster methods, and examine an important avoided crossing between a Rydberg and a valence state along the intermonomer and intramonomer stretching coordinates. The calculations are challenging, due to the high density of electronic states of various types (valence and Rydberg, excimer and charge transfer) in the 6-8 eV region, and the multiconfigurational nature of the ground state. We have identified a bright charge-transfer (charge-resonance) state as responsible for the broadband seen in UV absorption experiments. We also use our results to facilitate the interpretation of UV photodissociation experiments, including the time-resolved 6 eV photodissociation experiments to be presented in the next two papers of this series.     

Charge-transfer excited states in a pi-stacked adenine dimer, as predicted using long-range-corrected time-dependent density functional theory

The lowest few electronic excitations of a pi-stacked adenine dimer in its B-DNA geometry are investigated, in the gas phase and in a water cluster, using a long-range-corrected version of time-dependent density functional theory (TD-DFT) that asymptotically incorporates Hartree-Fock exchange. Long-range correction is shown to eliminate the catastrophic underestimation of charge-transfer (CT) excitation energies that plagues conventional TD-DFT, at the expense of introducing one adjustable parameter, mu, that determines the length scale on which Hartree-Fock exchange is turned on. This parameter allows us to interpolate smoothly between hybrid density functionals and time-dependent Hartree-Fock theory. Excitation energies for CT states (in which an electron is transferred from one adenine molecule to the other) are found to increase dramatically as a function of mu. Uncorrected hybrid functionals underestimate the CT excitation energies, placing them well below the valence excitations, while time-dependent Hartree-Fock calculations place these states well above the valence states. Values for mu determined from certain benchmark calculations place the CT states well above the valence pipi* and npi* states at the Franck-Condon point.     

Electronic structure of the calcium monohydroxide radical

Effective valence shell Hamiltonian H(v) calculations are used to map out three-dimensional potential energy surfaces for the 12 lowest electronic states of the CaOH radical. Excitation energies and spectroscopic constants are compared with experiment and prior computations where available, but many previously unavailable data are provided, including excited state dipole moments and oscillator strengths. Particular attention is paid to clarify the nature of nonlinear and quasilinear excited states, Renner-Teller couplings, and state mixings. The F (2)Pi and G (2)Pi (6 (2)A(') and 8 (2)A(')) states are both found to possess nonlinear local minima, due to an avoided crossing. Attention is also focused on the characteristics of basis sets necessary in high-accuracy calculations for the CaOH radical.     

All-valence-electron CI treatment of the electronic spectrum of trans-butadiene

An all-valence-electron CI treatment is reported for the low-lying valence and Rydberg states of butadiene. All singly- and doubly-excited configurations relative to a series of the leading terms in a given CI expansion are taken into account, with resulting secular equation orders of as high as 150 000. The agreement between calculated and experimental transition energies is invariably better than 0.2 eV where comparison is possible, with all low-lying valence triplet and Rydberg singlet excited states being unambiguously assigned. The valence-shell excitation to the 2 ¹A_g species is concluded to correspond to the 7.06 eV band system, while the forbidden singlet—singlet transition reported by McDiarmid is assigned as x₂ → 3s. The possibility of an avoided crossing between Rydberg valence ¹B_u excited states having a determining influence on the appearance of the broad intense V₁—N absorption is also discussed.     

Rydberg-valence interactions of CO, and spectroscopic evidence characterizing the C' 1Sigma+ valence state

Rotationally cold absorption and two-photon ionization spectra of CO in the 90-100 nm region have been recorded at a resolution of 0.3-1.0 cm(-1). The analyses of up to four isotopomers seek to clarify the observations in regions where the Rydberg levels built on the ground state X (2)Sigma(+) of the ion interact with valence states of (1)Sigma(+) and (1)Pi symmetry. Previous observations of the 3ssigma, B (1)Sigma(+) Rydberg state, reviewed by Tchang-Brillet et al. [J. Chem. Phys. 96, 6735 (1992)], have been extended to energies above its avoided crossing with the repulsive part of the D(') (1)Sigma(+) valence state where resonances of varying intensities and widths have been attributed to the fully coupled 3ssigma or 4ssigma and D(') potentials, and where the B state approaches a second avoided crossing with the C(') (1)Sigma(+) valence state [Cooper and Kirby, J. Chem. Phys. 87, 424 (1987); 90, 4895 (1989); Chem. Phys. Lett. 152, 393 (1988)]. Fragments of a progression of weak and mostly diffuse bands, observed for all four isotopomers, have been assigned to the C(')<--X transition. The least-squares modeling of the 4p and 5p complexes reveals the 3ppi, E (1)Pi Rydberg state to be one of the perturbers, violating the Deltav=0 selection rule for Rydberg-Rydberg interactions on account of its rapid transition with increasing v from Rydberg to valence state. A second (1)Pi perturber, very loosely bound and clearly of valence type, contributes to the confusion in the published literature surrounding the 5p, v=0 complex.     

Full configuration interaction calculation of the low lying valence and Rydberg states of BeH

The all-electron full configuration interaction (FCI) vertical excitation energies for some low lying valence and Rydberg excited states of BeH are presented in this article. A basis set of valence atomic natural orbitals has been augmented with a series of Rydberg orbitals that have been generated as centered onto the Be atom. The resulting basis set can be described as 4s2p1d/2s1p (Be/H) + 4s4p3d. It allows to calculate Rydberg states up to n= {3,4,5} of the s, p, and d series of Rydberg states. The FCI vertical ionization potential for the same basis set and geometry amounts to 8.298 eV. Other properties such as FCI electric dipole and quadrupole moments and FCI transition dipole and quadrupole moments have also been calculated. The results provide a set of benchmark values for energies, wave functions, properties, and transition properties for the five electron BeH molecule. Most of the states have large multiconfigurational character in spite of their essentially single excited nature and a number of them present an important Rydberg-valence mixing that is achieved through the mixed nature of the particle MO of the single excitations.     

Calculation of near-edge X-ray absorption fine structure with the CIS(D) method

We report an investigation into the calculation of near-edge X-ray absorption fine structure with the CIS(D) method. Core excitation energies computed with time-dependent density functional theory using standard exchange-correlation functionals are systematically underestimated. CIS(D) predicts core excitation energies that are closer to experiment. However, excitation energies for Rydberg states are too low with respect to valence states, and for some systems spectra that are qualitatively incorrect are obtained. A scaled opposite spin only approach is proposed that reduces the error in the computed core excitation energies, and results in spectra that are in good agreement with experiment.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen M?ller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.     

SCF wavefunctions and energies for valence states and excited states of carbon and nitrogen

Wavefunctions and energies are reported for the (2s)ⁿ(2p)^m states of neutral carbon and nitrogen using the fixed double-zeta bases employed by Clementi to describe the ground state of these atoms. In addition, the wavefunctions and energies for a number of valence states are given, including the so-called sp³ valence state of carbon. Calculated energies of the valence states agree well with those obtained from experiment. The corresponding valence-state orbitals are useful in semi-empirical quatum-mechanical calculators, such as the maximum overlap method.     

Electronic and cationic states of 2-methylpropene (isobutene) studied by VUV absorption,scattered electron spectroscopy and AB initio multireference configuration interaction calculations

VUV (6.2–9 eV) and electron scattering spectra (1–9 eV) have been recorded for 2-methylpropene (isobutene). Also, electronic states of the molecule, including the ground state and cationic states, have been investigated using ab initio multi-reference configuration interaction calculations. Some Koopmans-type in the UV photoelectron spectrum are reassigned and a number of shake-up states computed. In the electronic spectrum, Rydberg excited have been assigned and a second valence excited state (σ π*) located within about 1 eV of the V(ππ*) state. The experiments show, and theory confirms, that the Rydberg R(π3s) state has a positive electron affinity. Some interesting correlations between ionisation energies, energies of shake-up state electronic excitation energies are identified.     

Halogen-Driven Bandgap Opening in Graphdiyne for Overall Photocatalytic Water Splitting

In this work, we studied the electronic band structure of the halogen (F, Cl, and Br) functionalized graphdiynes (GDYs) by using hybrid density functional theory. The results revealed that the bandgap energies of modified GDYs increase as the number of halogen atoms increases. It is also found that the position of the valence band maximum (VBM) is influenced by the electronegativity of halogen atoms. The higher the electronegativity, the deeper the VBM of the GDYs modified by the same number of halogen atoms. Importantly, our results revealed that the bandgap of GDY could be effectively tuned by mixing types of halogen atoms. The new generated conduction band and valence band edges are properly aligned with the oxidation and reduction potentials of water. Further thermodynamic analysis confirms that some models with mixing types of halogen atoms exhibit higher performance of overall photocatalytic water splitting than non-mixing models. This work provides useful insights for designing efficient photocatalysts that can be used for overall water splitting.     

XPS determination of uranium oxidation states

This contribution is both a review of different aspects of X‐ray photoelectron spectroscopy that can help one determine U oxidation states and a personal perspective on how to effectively model the X‐ray photoelectron spectroscopy of complicated mixed‐valence U phases. After a discussion of the valence band, the focus lingers on the U4f region, where the use of binding energies, satellite structures, and peak shapes is discussed in some detail. Binding energies were shown to be very dependent on composition/structure and consequently unreliable guides to oxidation state, particularly where assignment of composition is difficult. Likewise, the spin orbit split 4f_7/2 and 4f_5/2 peak shapes do not carry significant information on oxidation states. In contrast, both satellite‐primary peak binding energy separations, as well as intensities to a lesser extent, are relatively insensitive to composition/structure within the oxide–hydroxide–hydrate system and can be used to both identify and help quantify U oxidation states in mixed valence phases. An example of the usefulness of the satellite structure in constraining the interpretation of a complex multivalence U compound is given. Copyright © 2011 John Wiley & Sons, Ltd.     

Valence-band electronic structure of iron phthalocyanine: an experimental and theoretical photoelectron spectroscopy study

The electronic structure of iron phthalocyanine (FePc) in the valence region was examined within a joint theoretical-experimental collaboration. Particular emphasis was placed on the determination of the energy position of the Fe 3d levels in proximity of the highest occupied molecular orbital (HOMO). Photoelectron spectroscopy (PES) measurements were performed on FePc in gas phase at several photon energies in the interval between 21 and 150 eV. Significant variations of the relative intensities were observed, indicating a different elemental and atomic orbital composition of the highest lying spectral features. The electronic structure of a single FePc molecule was first computed by quantum chemical calculations by means of density functional theory (DFT). The hybrid Becke 3-parameter, Lee, Yang and Parr (B3LYP) functional and the semilocal 1996 functional of Perdew, Burke and Ernzerhof (PBE) of the generalized gradient approximation (GGA-)type, exchange-correlation functionals were used. The DFT/B3LYP calculations find that the HOMO is a doubly occupied π-type orbital formed by the carbon 2p electrons, and the HOMO-1 is a mixing of carbon 2p and iron 3d electrons. In contrast, the DFT/PBE calculations find an iron 3d contribution in the HOMO. The experimental photoelectron spectra of the valence band taken at different energies were simulated by means of the Gelius model, taking into account the atomic subshell photoionization cross sections. Moreover, calculations of the electronic structure of FePc using the GGA+U method were performed, where the strong correlations of the Fe 3d electronic states were incorporated through the Hubbard model. Through a comparison with our quantum chemical calculations we find that the best agreement with the experimental results is obtained for a U(eff) value of 5 eV.