Multiconfiguration Self-consistent Field Method Research Articles

The electronically excited states of cyclooctatetraene-An analysis of the vacuum ultraviolet absorption spectrum by ab initio configuration interaction methods.

A new synchrotron-based study of the vacuum ultraviolet (VUV) absorption spectrum for cyclooctatetraene (COT) shows a series of broad peaks. A significant sharp structure was extracted from the strongest band between 5.9 and 6.3 eV by fitting this range of the spectrum to a polynomial; the regular residuals show a set of sharp peaks. Comparison of this region of the VUV with the photoelectron spectrum demonstrates the presence of several Rydberg states, all based on the lowest observed ionization energy ionic state. The UV onset contains a broad band in the range 4.0 eV-5.3 eV. Theoretical vertical excitation energies, determined by configuration interaction (CI) studies at the multireference multiroot singles and doubles CI level, enabled interpretation of the principal absorption bands of the VUV spectrum. Adiabatic excitation energies (AEEs) for several singlet and triplet valence states (V) were evaluated by multiconfiguration self-consistent field methods. Theoretical Rydberg series AEEs were obtained by use of extremely diffuse Gaussian orbitals in highly correlated wave-functions. The second moments of the charge distribution identify which roots are valence or Rydberg states. A contrast was found between some density functional methods and Hartree-Fock (HF) wave-functions during single-excitation CI, when degenerate orbitals were involved in the leading configurations. The 7a16e* state contained the expected 8-membered ring in the density functional theory calculations. The HF wave-functions led to a 1,5-cross-ring interaction which converged on a singlet excited state of a bicyclo[3,3,0]octatriene; this is reminiscent of the photochemical conversion of COT to semibullvalene.

Implementation of state-averaged MCSCF method to RISM- and 3D-RISM-SCF schemes

The state-averaged multiconfiguration self-consistent field (MCSCF) method was implemented to the reference interaction site model and three-dimensional reference interaction site model (RISM and 3D-RISM) SCF schemes, where the electronic structures of multiple states and solvation structure are determined simultaneously by the state-averaged MCSCF method and state-specific RISM-SCF/3D-RISM-SCF scheme, respectively, in a single calculation. The method was applied to the potential energy curves of the low-lying states of NaCl in aqueous solution and solvation shifts of the excitation energy of formaldehyde and p-nitroaniline. The results showed good agreement with those of the state-specific MCSCF and/or experiments.

Accurate all-electron calculation on the vibrational and rotational spectra of ground states for O2 and its ions**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300), the National Natural Science Foundation of China (Grant Nos. 91750104, 11574114, and 11874177), and the Natural Science Foundation of Jilin Province, China (Grant No. 20160101332JC).

The potential energy curves, spectroscopic constants, and low-lying vibration–rotation levels of ground-state O2 and its cation and anion were calculated with the explicitly correlated multireference configuration interaction method. The zeroth-order reference wavefunction was treated with the complete active space multiconfigurational self-consistent field method, in which the active space was carefully selected, and an additional molecular orbital was added into the full valence active space. The electron correlation of the 1s core in the oxygen atom was considered in the computations. The Davidson correction on molecular energy was considered to account for higher electron excitation. The relativistic effects, including the scalar relativistic effect and spin–orbit coupling, were considered in the computation of potential energy curves. These physical effects on the spectroscopic constants were examined. The low-lying levels of vibration–rotation spectra of O2 and its ions were determined based on the computed potential energy curves. Comparisons with available experiments were made and excellent agreement was obtained for the vibrational and rotational parameters. The spectroscopic constants and vibration–rotation spectrum of , which is sparse in experiments, were provided. Our study will shed some light on further theoretical and experimental studies on these simple but important molecular systems.

The 13C nuclear magnetic shielding constants at the singlet excited states in CH2CCH2, CH2O, CH3CHO, CH3NH2, and CO

Abstract Quantum-chemical calculations of excited state nuclear shielding constants are reported for singlet states in CH2CCH2, CH2O, CH3CHO, CH3NH2, and CO. The multiconfigurational self-consistent field method is used to account for static correlation in the excited states. With one exception, the molecules considered had larger shielding constants in their excited states than in their ground states. This tendency towards deshielding is rationalized using the sum-over-states expression for magnetic response.

Spectroscopy of gold atoms and gold oligomers in helium nanodroplets.

The 6p 2P1/2 ← 6s 2S1/2 and 6p 2P3/2 ← 6s 2S1/2 transitions (D lines) of gold atoms embedded in superfluid helium nanodroplets have been investigated using resonant two-photon ionization spectroscopy. Both transitions are strongly blue-shifted and broadened due to the repulsive interaction between the Au valence electron and the surrounding helium. The in-droplet D lines are superimposed by the spectral signature of Au atoms relaxed into the metastable 2D states. These features are narrower than the in-droplet D lines and exhibit sharp rising edges that coincide with bare atom transitions. It is concluded that they originate from metastable 2D state AuHen exciplexes that have been ejected from the helium droplets during a relaxation process. Interestingly, the mechanism that leads to the formation of these complexes is suppressed for very large helium droplets consisting of about 2 × 106 He atoms, corresponding to a droplet diameter on the order of 50 nm. The assignment of the observed spectral features is supported by ab initio calculations employing a multiconfigurational self-consistent field method and a multi-reference configuration interaction calculation. For large helium droplets doped with Au oligomers, excitation spectra for mass channels corresponding to Aun with n = 2, 3, 4, 5, 7, and 9 are presented. The mass spectrum reveals even-odd oscillations in the number of Au atoms that constitute the oligomer, which is characteristic for coinage metal clusters. Resonances are observed close by the in-droplet D1 and D2 transitions, and the corresponding peak forms are very similar for different oligomer sizes.

Reference dependence of the two-determinant coupled-cluster method for triplet and open-shell singlet states of biradical molecules.

We study the performance of the two-determinant (TD) coupled-cluster (CC) method which, unlike conventional ground-state single-reference (SR) CC methods, can, in principle, provide a naturally spin-adapted treatment of the lowest-lying open-shell singlet (OSS) and triplet electronic states. Various choices for the TD-CC reference orbitals are considered, including those generated by the multi-configurational self-consistent field method. Comparisons are made with the results of high-level SR-CC, equation-of-motion (EOM) CC, and multi-reference EOM calculations performed on a large test set of over 100 molecules with low-lying OSS states. It is shown that in cases where the EOMCC reference function is poorly described, TD-CC can provide a significantly better quantitative description of OSS total energies and OSS-triplet splittings.

Quantum Chemical Study of the Water Exchange Mechanism of the Neptunyl(VI) and -(V) Aqua Ions.

The water exchange reaction of the neptunyl(VI) and -(V) aqua ions was investigated with quantum chemical methods. Associative ( a) and dissociative ( d) exchange mechanisms were studied. The geometries and vibrational frequencies were computed with density functional theory (DFT) and multiconfiguration self-consistent field (MCSCF) methods. The Gibbs activation energies (Δ G‡) for a and d pathways were calculated with DFT and wave function theory (WFT), extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2) including spin-orbit (SO) coupling at the SO configuration interaction (CI) level. The DFT-WFT agreement for Δ G‡ was poor for the investigated functionals except for LC-BOP-LRD. Due to ligand-field effects, Δ G‡ for the associatively activated exchange reaction of NpO2(OH2)52+ with a fδ1 electron configuration is higher than for the actinyl(VI) aqua ions of U, Pu, and Am exhibiting f0, fδ2, and fδ2fϕ1 electron configurations.

Computational Study of Methane C–H Activation by Earth-Abundant Metal Amide/Aminyl Complexes

Density functional theory, augmented by multiconfiguration SCF (MCSCF) simulations, was used to understand the factors that control methane C–H activation by Earth-abundant, 3d metal (Cr - Ni) [(κ3-CNC)M(NH2)] complexes via hydrogen atom abstraction (HAA) and [2 + 2] pathways. Calculations suggest a significant amide/aminyl, i.e., [(κ3-CNC)2–M3+(NH2)−] ⇔ [(κ3-CNC)2–M2+(NH2)•], admixture in the electronic ground states of these complexes and thus significant unpaired electron density (radical character) on the NH2 ligand. The spin coupling between the aminyl radical and spin density on the central metal ion is interesting, particularly for the cobalt aminyl complex, in which both ferromagnetic and antiferromagnetic triplet states are found to be close in energy via both DFT and MCSCF methods. Modeled complexes are computed to have reasonable barriers to methane activation, with ΔG⧧ values being in approximately the upper 20s to mid 30s kcal/mol, generally decreasing toward the right in the 3d series, which...

An explanation of the very low fluorescence and phosphorescence in pyridine: a CASSCF/CASMP2 study

ABSTRACTIn this work, we applied the multiconfigurational complete active space self-consistent field method and the multiconfigurational second-order perturbation theory CASMP2 to study the fundamental excited states of pyridine and its possible photophysical and photochemical transformations. Our calculations, which are in agreement with the experimental results corresponding to excitations around the 0–0 transition, showed that the very low experimentally observed fluorescence of pyridine is due to the presence of two almost isoenergetic crossings, one of triple character, S1/T1/S0 and the other of S1/S0 character. Both crossings are below the minimum of S1(nπ*) and have a common transition state (S1(TS)) with a very low energy barrier (1.85 kcal/mol or 0.08 eV at the CASMP2 level of theory) separating them. A third triple crossing of the type S1/T1/S0 lying lower with respect to the other two elucidates the observed T1→S0 radiationless transition. This explains not only pyridine's very low fluorescence and phosphorescence but also its almost negligible photochemistry, showing that photophysics is the prevalent process in this molecule.

Two-photon absorption of the spatially confined LiH molecule.

In the present contribution we study the influence of spatial restriction on the two-photon dipole transitions between the X1Σ+ and A1Σ+ states of lithium hydride. The bond-length dependence of the two-photon absorption strength is also analyzed for the first time in the literature. The highly accurate multiconfiguration self-consistent field (MCSCF) method and response theory are used to characterize the electronic structure of the studied molecule. In order to render the effect of orbital compression we apply a two-dimensional harmonic oscillator potential, mimicking the topology of cylindrical confining environments (e.g. carbon nanotubes, quantum wires). Among others, the obtained results provide evidence that at large internuclear distances the TPA response of lithium hydride may be significantly enhanced and this effect is much more pronounced upon embedding of the LiH molecule in an external confining potential. To understand the origin of the observed variation in the two-photon absorption response a two-level approximation is employed.

Single metal catalysis: DFT and CAS modelling of species involved in the Fe cation assisted transformation of acetylene to benzene

ABSTRACTGas phase conversion of acetylene to benzene, assisted by a single metal cation such as Fe(+), Ru(+) and Rh(+), offers an attractive prospect for application of computational modelling techniques to catalytic processes. Gas phase processes are not complicated by environmental effects and the participation of a single metal atom is a significant simplification. Still the process is complex, owing to the possibility of several low-energy spin states and the abundance of alternative structures. By density functional theory modelling using recently developed models with range and dispersion corrections, we locate and characterise a number of extreme points on the FeC6H6(+) surface, some of which have not been described previously. These include eta-1, eta-2 and eta-3 complexes of Fe(+) with the C4H4 ring. We identify new FeC6H6(+) structures as well, which may be landmarks for the Fe(+)-catalysed production of benzene from acetylene. The Fe(+) benzene complex is the most stable species on the FeC6H6 cation surface. With the abundant energy of complexation available in the isolated gas phase species, detachment of the Fe(+) and production of benzene can be efficient. We address the issue raised by other investigators whether multi-configurational self-consistent field methods are essential to the proper description of these systems. We find that the relative energy of intrinsically multi-determinant doublets is strongly affected, but judge that the density functional theory (DFT) description provides more accurate estimates of energetics and a more plausible reaction path.

Numerical Estimation of the Pseudo-Jahn-Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules.

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.

Study of double core hole excitations in molecules by X-ray double-quantum-coherence signals: a multi-configuration simulation.

The multi-configurational self-consistent field method is employed to simulate the two-dimensional all-X-ray double-quantum-coherence (XDQC) spectroscopy, a four-wave mixing signal that provides direct signatures of double core hole (DCH) states. The valence electronic structure is probed by capturing the correlation between the single (SCH) and double core hole states. The state-averaged restricted-active-space self-consistent field (SA-RASSCF) approach is used which can treat the valence, SCH, and DCH states at the same theoretical level, and applies to all types of DCHs (located on one or two atoms, K-edge or L-edge), with both accuracy and efficiency. Orbital relaxation introduced by the core hole(s) and the static electron correlation is properly accounted for. The XDQC process can take place via different intermediate DCH state channels by tuning the pulse frequencies. We simulate the XDQC signals for the three isomers of aminophenol at 8 pulse frequency configurations, covering all DCH pathways involving the N1s and O1s core hole (N1sN1s, O1sO1s and N1sO1s), which reveal different patterns of valence excitations.

Peroxynitrite in the hemoglobin composition

Electronic characteristics of trHbN hemoglobin whose composition contains the (ONOO) group with the structure close to the structure of 1) peroxynitrite and 2) a nitrate anion in the gas phase are calculated. Electron correlation is considered by the multiconfigurational self-consistent field (MCSCF) method during the optimization of the geometry of the whole structure. Localized molecular orbitals (MOs) are used as starting ones. In the wave function of the MCSCF method two complete active subspaces (CASs) are set. These are the subspace of iron atom 3d orbitals and the subspace describing chemical bonds in peroxynitrite (bonding and antibonding MOs plus the orbital of one lone pair on the O2 moiety. The composition of the system involves two water molecules. The peroxynitrite structure is considered in two different spin states that correspond to the singlet and triplet states of this anion in the gas phase where the vibrational spectrum is characterized by frequencies of about (70-30) cm−1. The protective reaction of the active center of the tubercule bacillus is discussed.

Theoretical study of second-order hyperpolarizability for nitrogen radical cation

We report calculations of the static and dynamic hyperpolarizabilities of the nitrogen radical cation in doublet state. The electronic contributions were computed analytically using density functional theory and multi-configurational self-consistent field method with extended basis sets for non-resonant excitation. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The second-order optical properties of nitrogen radical cation have been calculated as a function of bond length starting with the neutral molecular geometry (S0 minimum) and stretching the N–N triple bond, reaching the ionic D0 relaxed geometry all the way toward dissociation limit, to investigate the effect of internuclear bond distance on second-order hyperpolarizability.

Structure and magnetic properties of iron-silicon clusters in a multiconfigurational calculation

The structure and spin moments of iron-silicon clusters FeSin are calculated by a multiconfigurational self-consistent field (MCSCF) method in order to refine the spin moments in the ground state and their changes during the transition from the ground electronic state to excited ones. Transition energies to the first singlet state are obtained for the first time; the degree of stability of magnetic properties with temperature is evaluated in a wide range. The limiting number of silicon atoms, which corresponds to the disappearance of the cluster magnetic moment is found. The non-empirical calculation is compared with the data of the elecron density functional method in its different variants. The presence of iron-silicon clusters in the substance can be the reason for a local alteration of the magnetic field.

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree-Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self-consistent field method, Møller-Plesset perturbation theory method, and time-dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self-consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations-All Atom (OPLS-AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented.

A Neoteric Neodymium Model: Ground and Excited Electronic State Analysis of NdF2+

Neodymium monofluoride dication was studied as a model of the Nd-F bond in NdFx. Multiconfigurational self-consistent field (MCSCF) and second order multireference quasi-degenerate perturbation theory (MCQDPT2) methods were used with a variety of active spaces to elucidate the roles of the Nd 4f, 5d, and 6s orbitals. Spin-orbit coupling calculations were performed at the SO-MCQDPT2 level, and potential energy curves were obtained for the four lowest energy quartet states as well as for the four lowest doublet states and the lowest sextet state. Inclusion of spin-orbit coupling splits these states into 30 levels. Equilibrium bond lengths, dissociation energies, transition energies, and crossing points were determined.

The multi-configuration self-consistent field method within a polarizable embedded framework

We present a detailed derivation of Multi-Configuration Self-Consistent Field (MCSCF) optimization and linear response equations within the polarizable embedding scheme: PE-MCSCF. The MCSCF model enables a proper description of multiconfigurational effects in reaction paths, spin systems, excited states, and other properties which cannot be described adequately with current implementations of polarizable embedding in density functional or coupled cluster theories. In the PE-MCSCF scheme the environment surrounding the central quantum mechanical system is represented by distributed multipole moments and anisotropic dipole-dipole polarizabilities. The PE-MCSCF model has been implemented in DALTON. As a preliminary application, the low lying valence states of acetone and uracil in water has been calculated using Complete Active Space Self-Consistent Field (CASSCF) wave functions. The dynamics of the water environment have been simulated using a series of snapshots generated from classical Molecular Dynamics. The calculated shifts from gas-phase to water display between good and excellent correlation with experiment and previous calculations. As an illustration of another area of potential applications we present calculations of electronic transitions in the transition metal complex, [Fe(NO)(CN)5](2-) in a micro-solvated environment. This system is highly multiconfigurational and the influence of solvation is significant.

Analytical energy gradients for second-order multireference perturbation theory using density fitting

We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.