Active Space Self Research Articles

Electronic structure of the ZnCl molecule with rovibrational and ionicity studies of the ZnX (X = F, Cl, Br, I) compounds

Based on the complete active space self consistent field (CASSCF) method with multi-reference configuration interaction MRCI calculations including single and double excitations with Davidson correction (+Q), twenty three low lying electronic states in the 2s+1Λ(±) representation of the zinc monochloride ZnCl molecule are investigated considering 7 and 9 valence electrons. The internuclear distance Re, the harmonic frequency ωe, the permanent dipole moment μ, the rotational constant Be and the electronic transition energy with respect to the ground state Te are calculated for the bound states. The transition dipole moment between some doublet states is used to determine the Einstein spontaneous A21 and induced emission B21ω coefficients, the spontaneous radiative lifetime τspon, the emission wavelength λ21, the oscillator strength f21 and the line strength S21. The fraction of the ground state ionic character f and equilibrium dissociation energy DE,e are also computed. Using the canonical function approach, the eigenvalues Ev, the rotational constants Bv, the centrifugal distortion constants Dv and the abscissas of the turning points Rmin and Rmax of the zinc monohalide molecules ZnX (X: F, Cl, Br, I) are calculated. The comparison between the values of the present work and those available in the literature for several electronic states shows good accordance.

Dipole Moment and Electronic Structure Calculations of the Electronic States of the molecular ion SiN+

<p class="1Body">A theoretical investigation of the lowest electronic states of the molecular ion SiN<sup>+</sup> has been performed via Complete Active Space Self Consistent Field (CASSCF) method with Multi Reference Configuration Interaction MRCI+Q (single and double excitations with Davidson correction) calculations. The potential energy curves of the low-lying 37 electronic states in the representation <sup>2s+1</sup>Λ<sup>(+/-)</sup>, up to 140000 cm<sup>-1 , </sup>have been investigated. The permanent dipole moment, the harmonic frequency ω<sub>e</sub>, the equilibrium internuclear distance R<sub>e</sub>, the rotational constants B<sub>e</sub> and the electronic energy with respect to the ground state T<sub>e</sub> have been calculated for these electronic states. The comparison between the values of the present work and those available in the literature for several electronic states shows a very good agreement. The permanent dipole moment, of the investigated 37 electronic states, have been calculated in the present work for the first time along with the investigation of nine new electronic states that have not been observed yet.</p>

Dissecting the bond-formation process of d 10-metal–ethene complexes with multireference approaches

The bonding mechanism of ethene to a nickel or palladium center is studied by the density matrix renormalization group algorithm, the complete active space self consistent field method, coupled cluster theory, and density functional theory. Specifically, we focus on the interaction between the metal atom and bis-ethene ligands in perpendicular and parallel orientations. The bonding situation in these structural isomers is further scrutinized using energy decomposition analysis and quantum information theory. Our study highlights the fact that when two ethene ligands are oriented perpendicular to each other, the complex is stabilized by the metal-to-ligand double-back-bonding mechanism. Moreover, we demonstrate that nickel-ethene complexes feature a stronger and more covalent interaction between the ligands and the metal center than palladium-ethene compounds with similar coordination spheres.

Electronic structure with dipole moment calculation of the low-lying electronic states of the molecule ZnI

The potential energy curves of the low-lying 26 doublet and quartet electronic states in the representation 2s+1Λ(+/−) of the ZnI molecule have been investigated using the Complete Active Space Self Consistent Field (CASSCF) with Multi-Reference Configuration Interaction (single and double excitation with Davidson correction) MRCI+Q method and the second order multi-reference Rayleigh Schrödinger perturbation theory RSPT2-RS2 method. The harmonic frequency ωe, the internuclear distance Re, the static dipole moment, and the electronic energy with respect to the ground state Te have been calculated for the considered bound electronic states. The comparison between the values of the present work and those available in the literature shows a good agreement. Twenty-three electronic states are studied here for the first time.

<i>Ab-Initio</i> Calculations of 27 Electronic States of the BP<sup>+</sup> Ion-Molecule

The theoretical investigation of the potential energy curves, in the representation 2s+1Λ(+/-), of the 27 low-lying Doublet and Quartet electronic states of the BP+ molecular ion has been performed with the methods in quantum chemistry, the Complete Active Space Self Consistent Field (CASSCF) and the Multireference Configuration Interaction (MRCI) calculations. The harmonic vibrational frequency ωe, the inter-nuclear distance at equilibrium Re, the rotational constant Be, the electronic energy with respect to the minimum ground state energy Te, and the permanent dipole moment have also been calculated. Twenty-three new electronic states have been investigated here for the first time. The comparison between the values of the present work and those available in the literature for several electronic states shows a good agreement. These investigated data can be a conducive to further work on BP+ molecular ion in both experimental and theoretical research.

Theoretical Study of the Triplet Electronic States of the BP Molecule

The Complete Active Space Self Consistent Field (CASSCF) with Multi Reference Configuration Interaction (single and double excitation with Davidson correction) MRCI + Q method has been used to investigate the potential energy curves of the 17 low-lying triplet electronic states of the molecule BP. The harmonic vibrational frequency ωe, the inter-nuclear distance at equilibrium Re, the rotational constant Be, the electronic energy with respect to the minimum ground state energy Te, and the permanent dipole moment have been also calculated. A literature review shows a strong correlation between our investigated data and those previously published either theoretically or experimentally. This work introduces, for the first time, a study of 14 new electronic states. Our spectroscopic data can be a conducive to further work on BP molecule in both experimental and theoretical research.

Probing deactivation pathways of DNA nucleobases by two-dimensional electronic spectroscopy: first principles simulations.

The SOS//QM/MM [Rivalta et al., Int. J. Quant. Chem., 2014, 114, 85] method consists of an arsenal of computational tools allowing accurate simulation of one-dimensional (1D) and bi-dimensional (2D) electronic spectra of monomeric and dimeric systems with unprecedented details and accuracy. Prominent features like doubly excited local and excimer states, accessible in multi-photon processes, as well as charge-transfer states arise naturally through the fully quantum-mechanical description of the aggregates. In this contribution the SOS//QM/MM approach is extended to simulate time-resolved 2D spectra that can be used to characterize ultrafast excited state relaxation dynamics with atomistic details. We demonstrate how critical structures on the excited state potential energy surface, obtained through state-of-the-art quantum chemical computations, can be used as snapshots of the excited state relaxation dynamics to generate spectral fingerprints for different de-excitation channels. The approach is based on high-level multi-configurational wavefunction methods combined with non-linear response theory and incorporates the effects of the solvent/environment through hybrid quantum mechanics/molecular mechanics (QM/MM) techniques. Specifically, the protocol makes use of the second-order Perturbation Theory (CASPT2) on top of Complete Active Space Self Consistent Field (CASSCF) strategy to compute the high-lying excited states that can be accessed in different 2D experimental setups. As an example, the photophysics of the stacked adenine-adenine dimer in a double-stranded DNA is modeled through 2D near-ultraviolet (NUV) spectroscopy.

Theoretical Calculation of the Low-Lying Electronic States of the Molecule BaS

Complete Active Space Self Consistent Field (CASSCF) with Multireference Configuration Interaction (MRCI) and Rayleigh-Schrodinger Perturbation Theory (RSPT2-RS2) methods have been used to investigate the potential energy curves for the 12 low-lying singlet and triplet electronic states in the representation 2s+1Λ(+/-) of the molecule BaS with Davidson corrections. The harmonic frequency we, the internuclear distance Re, the electronic energy with respect to the ground state Te, the rotational constants Be and the permanent dipole moment have been calculated for these electronic states. The eigenvalues Ev, the rotational constants Bv, the centrifugal distortion constant Dv and the abscissas of the turning points Rmin and Rmax have been investigated using the canonical functions approach. Nine new electronic states have been investigated here for the first time. The comparison between the values of the present work and those available in the literature for several electronic states shows a good agreement.

The potential energy surfaces of the ground and excited states of carbon dioxide molecule

Potential energy surfaces (PESs) of the 1Al(1Σ + ), 1B2 and 3B2 electronic states of CO2 have been computed as a function of the two bond distances and the bond angle. The calculations were based on the complete active space self consistent field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) electronic structure models. From our calculations no crossing point between 1B2 and 3B2 states was found, but there is a crossing point located between 1B2 and 3A2 state on the PESs. The energy of the crossing point is lie 0.23 eV above the CO + O (3P), which is in agreement with the value of 0.27 eV on the experiment. This implies that the mechanism of the recombination of an oxygen atom with a carbon monoxide molecule: CO(X 1Σ+, ν) + O(3P)→3CO2*→1CO2*→CO(X 1Σ+, ν = 0) + O(1 D) may occur through the 3A2 state crossing the 1B2 state. The equilibrium geometries and adiabatic excitation energies of 1,3B2, 1,3A2 states of CO2 were reported and discussed in this paper, too.

Theoretical Electronic Structure of the Lowest-Lying Electronic States of the CaCl Molecule

The potential energy curves of 10 doublet and 5 quartet low-lying electronic states of CaCl molecule have been investigated by using the Complete Active Space Self Consistent Field (CASSCF) with Multi Reference Configuration Interaction (MRCI) using effective core potential for both atoms. Based on the investigated PECs, the harmonic frequency we, the internuclear distance Re, the dipole moment, and the electronic energy with respect to the ground state Te have been calculated for the considered electronic states. A rovibrational study has been performed with the calculation of the eigenvalue Ev, the rotational constant Bv and the abscissas of the turning points Rmin and Rmax. The comparison between the values of the present work and those available in the literature for several electronic states shows a very good agreement. Nine new excited electronic states have been investigated here for the first time.

First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogenous broadening

We compute the line shape of absorption and emission electronic spectra of two different dyes, Coumarin C153 and N-methyl-6-Quinolinium betaine accounting for the vibronic structure, temperature effects and polar solvent inhomogeneous broadening, without using any phenomenological parameter. We exploit a number of recent developments including a time-dependent (TD) approach to the computation of vibronic spectra that provides fully converged line shapes at finite temperature accounting for both Duschinsky and Herzberg–Teller effects, and the state-specific (SS) implementation of Polarizable Continuum Model (PCM). This latter is adopted to compute the solvent reorganization energy connected to inhomogenoeus broadening. We compute the absorption and fluorescence spectra in the gas-phase, non-polar and polar solvents analyzing the relative importance of different sources of broadening. To this end we investigate the performance of TD Density Functional Theory, Complete Active Space Self Consistent Field (CASSCF) and Complete Active Space second-order Perturbation Theory (CASPT2) methods in the computation of inhomogeneous broadening.

The Triplet-Singlet Gap in the m-Xylylene Radical: A Not So Simple One.

Meta-benzoquinodimethane (MBQDM) or m-xylylene provides a model for larger organic diradicals, the triplet-singlet gap being the key property. In the present work this energy difference has been the object of a systematic study by means of several density functional theory-based methods including B3LYP, M06, M06-2X, HSE and LC-ωPBE potentials and a variety of wave function-based methods such as complete active space self consistent field (CASSCF), Multireference second-order Møller-Plesset (MRMP), difference dedicated configuration interaction (DDCI), and Multireference configuration interaction (MRCI). In each case various basis sets of increasing quality have been explored, and the effect of the molecular geometry is also analyzed. The use of the triplet and broken symmetry (BS) solutions for the corresponding optimized geometries obtained from B3LYP and especially M06-2X functionals provide the value of the adiabatic triplet-singlet gap closer to experiment when compared to the reported value of Wenthold, Kim, and Lineberger, (J. Am. Chem. Soc. 1997, 119, 1354) and also for the electron affinity. The agreement further improves using the full π-valence CASSCF(8,8) optimized geometry as an attempt to correct for the spin contamination effects on the geometry of the BS state. The CASSCF, MRMP, and MRCI, even with the full π valence CAS(8,8) as reference and relatively large basis set, systematically overestimate the experimental value indicating either that an accurate description must go beyond this level of theory, including σ electrons and higher order polarization functions, or perhaps that the measured value is affected by the experimental conditions.

Reaction selectivity in an ionized water dimer: nonadiabatic ab initio dynamics simulations

We study dynamical processes following water dimer ionization. The nonadiabatic dynamical simulations of the water dimer radical cation are performed using a surface hopping technique and a Complete Active Space-Self Consistent Field (CASSCF) method for the description of electronic structure. The main goal of this study is to find out whether a state-dependent reactivity is observed for the water dimer radical cation. We provide a detailed mapping of the potential energy surfaces (PESs) in the relevant coordinates for different electronic states. Dynamical patterns are discussed on the basis of static PES cuts and available experimental data. As a product of the reaction, we observed either proton transferred structure (H3O(+)···OH˙) or various dissociated structures (H3O(+) + OH˙, H2O˙(+) + H2O, H˙ + OH˙ + H2O˙(+)). The relative yields are controlled by the populated electronic state of the radical cation. The proton transfer upon the HOMO electron ionization is an ultrafast process, taking less than 100 fs, in cases of higher energy ionization the dynamical processes occur on longer timescales (200-300 fs). We also discuss the implications of our simulations for the efficiency of the recently identified intermolecular coulomb decay (ICD) process in the water dimer.

Electronic structure and rovibrational calculation of the low-lying states of the RbYb molecule

Complete Active Space Self Consistent Field (CASSCF) method with Multi Reference Configuration Interaction (MRCI) calculations is used to investigate the potential energy curves of the low-lying 29 electronic states in the representation 2s+1Λ(+/−) of the RbYb molecule (single and double excitations with Davidson corrections). The harmonic frequency ωe, the internuclear distance Re and the electronic energy with respect to the ground state Te have been calculated. The eigenvalues Ev, the rotational constant Bv, and the abscissas of the turning points Rmin and Rmax have been investigated using the canonical functions approach. The comparison between the values of the present work and those available in the literature for several states shows a very good agreement. Twenty-six new states have been studied here for the first time.

Transition energy and potential energy curves for ionized inner-shell states of CO, O2 and N2 calculated by several inner-shell multiconfigurational approaches

Potential energy curves and inner-shell ionization energies of carbon monoxide, oxygen and nitrogen molecules were calculated using several forms of the inner-shell multiconfigurational self-consistent field (IS-MCSCF) method-a recently proposed protocol to obtain specifically converged inner-shell states at this level. The particular forms of the IS-MCSCF method designated IS-GVB-PP, IS-FVBL and IS-CASSCF stand for perfect pairing generalized valence bond, full valence bond-like MCSCF and complete active space self consistent field, respectively. A comparison of these different versions of the IS-MCSCF method was carried out for the first time. The results indicate that inner-shell states are described accurately even for the simplest version of the method (IS-GVB-PP). Dynamic correlation was recovered by multireference configuration interaction or multireference perturbation theory. For molecules not having equivalent atoms, all methods led to comparable and accurate transition energies. For molecules with equivalent atoms, the most accurate results were obtained by multireference perturbation theory. Scalar relativistic effects were accounted for using the Douglas-Kroll-Hess Hamiltonian.

Localization of molecular orbitals on fragments

A non-iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single-determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments-in-molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree-Fock or Kohn-Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals.

Theoretical study of the spectroscopy of methyl substituted 2-Pyridones, tautomers and ions

We present an extended study on the structure and the properties of the low lying electronic states of methyl substituted 2-Pyridone, of their tautomers and of their positively charged ions. We performed these calculations using density functional theory method (PBE0 DFT) and the complete active space self consistent field (CASSCF) approach in connection with the aug-cc-pVDZ and aug-cc-pVTZ Dunning’s basis sets. Our results include their equilibrium geometries, their rotational and vibrational spectroscopic parameters, their vertical excitation spectra and their vertical and adiabatic ionization energies. The role of substitution by the methyl on the electronic structure, on the spectroscopy of the 2-Pyridone/2-Hydroxypyridine and on the tautomerism is examined. The lowest electronic excited states of these systems are found to lay relatively close in energy, which should favor their couplings and the mixing of their electronic wavefunctions.

Ab initio multireference singles and doubles configuration interaction study of the low‐energy states of iron mononitride

AbstractLow‐lying states of iron mononitride are studied using ab initio multireference singles and doubles configuration interaction (MR‐SDCI) calculations. For each one of the 2Δ, 4Π, 6Σ+, 2Π, 4Δ, 6Π, and 6Δ states the reference wavefunction has been obtained at the complete active space self consistent field (CASSCF) level and relativistic corrections were included. Potential energy curves are presented for all states. Spectroscopic constants have been determined for the 2Δ, 4Π, and 6Σ+ states assuming a Morse‐type potential function using a code written by one of us. For the 2Δ state, the calculated spectroscopic constants are Re = 1.567 Å, ωe = 827 cm−1, and μ = 1.68 D. Rotovibrational analysis suggests that the third vibrational level of the 2Δ state already surpasses the first vibrational levels of the 4Π and 6Σ+ states, what reassures the difficulty in correctly attributing the lines of the experimental spectrum. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

A Modified Resonance-Theoretic Framework for Structure−Property Relationships in a Halochromic Oxonol Dye

I demonstrate that a modification of the resonance color theory (in its form advocated by Brooker (Rev. Mod. Phys. 1942, 14, 275) and by Platt (J. Chem. Phys. 1956, 25, 80)) provides an accurate framework for rationalizing the ab initio excitation energies of the protonation states of the green fluorescent protein (GFP) chromophore (an asymmetric oxonol dye). I suggest that the original model space used in the resonance theory (specifically, a pair of Lewis structures) is formally inconsistent with a core aspect of the theory (specifically, a relationship between excitation energies and group-specific basicities (Brooker basicities) of the terminal rings). I argue that a more appropriate model space would consist of a complete active space ansatz based on group-localized orbitals. I then show that there is a solution to the state-averaged complete active space self consistent field (SA-CASSCF) problem with exactly this form. This family of SA-CASSCF solutions provides an objectively rigorous foundation for the resonance color theory. The solutions can be expressed in a localized set of active space orbitals, which display the same transferability pattern implied by the Brooker basicity scale. Using Platt’s model Hamiltonian formulation of the resonance theory, I show that the accuracy of the set of excitation energies calculated with these solutions can be accurately reproduced using only two parameters per dye in the set. One of these parameters is the isoenergetic energy of the dye—the harmonic mean of the excitation energies of its symmetric parent dyes. The other parameter is a local basicity index (Brooker basicity), which is specific to each terminal ring and independent of the ring to which it is conjugated in a given dye. I proceed to show that the Brooker basicities, defined by differences between many-electron states, are also basicities in the usual (one-electron) sense and, finally, that Platt’s construction of the color theory is an approximation to a ab initio effective Hamiltonian obtained by a minimum-norm block diagonalization procedure. What emerges is a powerful, simple, and accurate conceptual framework for thinking generally about color in monomethine dyes, and specifically about color tuning in the chromophore of green fluorescent proteins.

An Unusual Stable Mononuclear MnIII Bis‐terpyridine Complex Exhibiting Jahn–Teller Compression: Electrochemical Synthesis, Physical Characterisation and Theoretical Study

The mononuclear manganese bis-terpyridine complex [Mn(tolyl-terpy)(2)](X)(3) (1(X)(3); X=BF(4), ClO(4), PF(6); tolyl-terpy=4'-(4-methylphenyl)-2,2':6',2"-terpyridine), containing Mn in the unusual +III oxidation state, has been isolated and characterised. The 1(3+) ion is a rare example of a mononuclear Mn(III) complex stabilised solely by neutral N ligands. Complex 1(3+) is obtained by electrochemical oxidation of the corresponding Mn(II) compound 1(2+) in anhydrous acetonitrile. Under these conditions the cyclic voltammogram of 1(2+) exhibits not only the well-known Mn(II)/Mn(III) oxidation at E(1/2)=+0.91 V versus Ag/Ag(+) (+1.21 V vs. SCE) but also a second metal-based oxidation process corresponding to Mn(III)/Mn(IV) at E(1/2)=+1.63 V (+1.93 V vs. SCE). Single crystals of 1(PF(6))(3)2 CH(3)CN were obtained by an electrocrystallisation procedure. X-ray analysis unambiguously revealed its tetragonally compressed octahedral geometry and high-spin character. The electronic properties of 1(3+) were investigated in detail by magnetic measurements and theoretical calculations, from which a D value of +4.82 cm(-1) was precisely determined. Density functional and complete active space self consistent field ab initio calculations both correctly predict a positive sign of D, in agreement with the compressed tetragonal distortion observed in the X-ray structure of 1(PF(6))(3)2 CH(3)CN. The different contributions to D were calculated, and the results show that 1) the spin-orbit coupling part (+2.593 cm(-1)) is predominant compared to the spin-spin interaction (+1.075 cm(-1)) and 2) the excited triplet states make the dominant contribution to the total D value.