Second-order Configuration Interaction Research Articles

Fundamental vibrational frequencies of pnictogen (Pn) containing linear triatomic anions: OCPn - and SCPn - where Pn = N, P, As and Sb

The fundamental vibrational frequencies of the isolated OCAs − and SCAs − ions, as well as their heavier antimony analogues, are reported for the first time. A thorough analysis of basis set convergence of the bond lengths and harmonic vibrational frequencies, as well as the examination of anharmonic corrections, is conducted using the MP2 and CCSD(T) ab initio methods with robust basis sets for the OC P n − and SC P n − anions moving down the pnictogen series from Pn = N to Sb. Second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) theory are used to compute the fundamental vibrational frequencies of each triatomic anion approaching the MP2 and CCSD(T) complete basis set (CBS) limits. While fundamental vibrational frequencies have been reported for OCN − and SCN − in the gas phase, only experimental vibrational frequencies of the salts for the heavier pnictogen analogues (P and As) have been reported. Experimental Raman vibrational frequencies for OCAs − and SCAs − salts were found to be coincidentally in good agreement with the CCSD(T) VCI frequencies near the CBS limit, differing by at most 13 cm − 1 from the former and 9 cm − 1 from the latter. These modest differences are likely due to the presence of counter-ions and other environmental effects in the solid state, and the overall agreement between the salts and gas-phase frequencies is quite similar to that observed for the OCP − and SCP − ions.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues.

Aminoborane, H2 NBH2 and its isotopologues, H2 N10 BH2 , D2 NBD2 , and D2 N10 BD2 , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν7 band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Fundamental vibrational frequencies of isolated 2-phosphaethynolate and 2-phosphaethynthiolate anions: OCP– and SCP–

Both second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) theory have been employed to compute the fundamental vibrational frequencies of the isolated 2-phosphaethynolate and 2-phosphaethynthiolate anions (OCP and SCP) near the CCSD(T) complete basis set (CBS) limit. Our best estimates of the fundamental frequency associated with the doubly degenerate bending mode of these linear triatomic ions () are 492 cm for OCP and 362 cm for SCP. Due to strong coupling, the stretching motions of SCP are best described as pseudo-symmetric () and pseudo-antisymmetric () stretches that we estimate to be 588 cm and 1367 cm, respectively. For OCP, our best predictions are 792 cm for and 1795 cm for , with the latter having predominantly CO stretching character. In the absence of experimental gas-phase vibrational spectra for these species, these computed anharmonic frequencies provide important reference values to help quantify spectroscopic perturbations induced by environmental effects such as those from solvents or counter ions.

Spin-Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods.

The spin-orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ nd] q ( q = 1-4 and 6-9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin-orbit couplings (SOC) using one-electron Breit-Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations-relativistic elimination of small components (RESC), third-order Douglas-Kroll-Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction-were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ nd]5, the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d] q configuration ( q = 2-4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d] q configuration ( q = 6-8), the energy lowering of all 4F7/2, 5D1, and 5D3 states due to the SOC effects is smaller than those of the other SM states. This difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

All-electron relativistic computations on the low-lying electronic states, bond length, and vibrational frequency of CeF diatomic molecule with spin-orbit coupling effects.

Ab initio all-electron computations have been carried out for Ce+ and CeF, including the electron correlation, scalar relativistic, and spin-orbit coupling effects in a quantitative manner. First, the n-electron valence state second-order multireference perturbation theory (NEVPT2) and spin-orbit configuration interaction (SOCI) based on the state-averaged restricted active space multiconfigurational self-consistent field (SA-RASSCF) and state-averaged complete active space multiconfigurational self-consistent field (SA-CASSCF) wavefunctions have been applied to evaluations of the low-lying energy levels of Ce+ with [Xe]4f1 5d1 6s1 and [Xe]4f1 5d2 configurations, to test the accuracy of several all-electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA-RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(-DKH3)-2012-QZP basis set were carried out to determine the energy levels of the low-lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.

Multiconfiguration Self-Consistent Field Study on Formonitrile Imine and N-Substituted Nitrile Imines HCN2-R: Energy Component Analysis of the Pseudo-Jahn-Teller Effect.

Stable geometrical structures for formonitrile imine (1) and N-substituted nitrile imines HCN2-R (R = Li, BeH, BH2, CH3, CN, CCH, C6H5, NH2, OH, and F) (2-11) were examined by using the multiconfiguration self-consistent-field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations and second-order multiconfiguration quasi-degenerate perturbation theory (MCQDPT2) calculations, together with the aug-cc-pVTZ basis sets. The results show that 1 suffers a pseudo-Jahn-Teller (JT) distortion from a linear C∞v structure to a C1 structure via a planar bent Cs structure. Each of the others is found to undergo pseudo-JT distortion from a symmetrical structure to a planar bent Cs structure for 2, 3, and 7 and to a C1 structure for 4, 5, 6, 8, 9, 10, and 11. At the stationary structures of 1-11, the structural characteristics were briefly discussed in terms of allenic and propargylic. To elucidate the nature of pseudo-JT distortions, energy component analyses were carried out at the MCSCF+SOCI level of theory at all of the stationary structures for the relevant molecules. In most of the molecules examined, pseudo-JT stabilizations were classified into two groups, one in which the stability arises from a lowering of the energy of the attractive term Ven and the other in which the stability results from a lowering of the energy of the repulsive terms Vnn and Vee. In addition to the above two groups, it was also found that the following three groups are responsible for the pseudo-JT stabilizations in a certain stage of the structural changes. Namely, one is a lowering of the energy of the term Vee observed in 6, another is a lowering of the energy of the terms Vee and Ven observed in 9-11, and the other is a lowering of the energy of the terms Ven and Vnn observed in 10. These energetic behaviors were accounted in terms of an elongation or a contraction of the molecular skeleton, a migration of electrons from one part of the molecule to other parts, and the combined effects arising from these two factors.

Spin–orbit coupling analyses of phosphorescence: the effects of cyclometalated ligand replacement in fac-Ir(ppy)3with various bpy ligands on blue phosphorescence

Multi-configuration self-consistent field (MCSCF) calculations followed by second-order configuration interaction (SOCI) and spin–orbit coupling (SOC) calculations were performed using one of the effective core potentials and its associated basis set, the Stevens–Basch–Krauss–Jasien–Cundari (SBKJC) basis set referred to here as SBKJC+p, in order to examine the effects of replacement of a methine group in each phenylpyridine (ppy) ligand of the facial (fac) isomer of tris(2-phenylpyridinato)iridium(III)[fac-Ir(ppy)3] by a nitrogen atom for the purpose of obtaining deep blue phosphorescence. Only replacements of the methine group at the 3′ or 5′ site of each ppy ligand by nitrogen atoms were calculated to induce a spectral shift to the blue region. These results can be explained by the strong electronegativity of nitrogen atoms and by the magnitude of the electron density at the 2′ carbon atom of the ppy or bipyridine (bpy) ligands. Subsequently, the substituent effects in the fac isomer of tris(bipyridinato)iridium(III)[fac-Ir(bpy)3] were investigated and found to be similar to those in fac-Ir(ppy)3 as reported in our previous study (RSC Adv., 2015, 5, 35760–35772). Based on systematic calculations and theoretical consideration, the most effective modification for deep blue phosphorescence should be the introduction of a nitrogen atom into the 3′ or/and 5′ site of benzene rings of the ppy ligands in fac-Ir(ppy)3 together with the combination of the substituents X = F, NR2, or OR (R = alkyl group) and Y = CN or NO2.

Structure and Properties of Precursor/Successor Complex and Transition State of the FeCl2+/Fe2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway

The electron self-exchange reaction FeCl(OH2)5(2+) + Fe(OH2)6(2+) → Fe(OH2)6(2+) + FeCl(OH2)5(2+), proceeding via the inner-sphere pathway, was investigated with quantum chemical methods. Geometry and vibrational frequencies of the precursor/successor complex, (H2O)5Fe(III)ClFe(II)(OH2)5(4+)/(H2O)5Fe(II)ClFe(III)(OH2)5(4+) (P/S), and the transition state, (H2O)5FeClFe(OH2)5(4+⧧) (TS), were computed with the LC-BOP functional and CPCM hydration. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (Hab) and the electronic energies were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2) and spin-orbit configuration interaction (SO-CI). Since the Fe···Fe distance changes considerably along the electron transfer step, the transformation P → TS → S, equations based on the hypothesis of a fixed donor-acceptor distance cannot be applied. Hence, the rate constant for the electron transfer step (ket) was calculated as described previously (Rotzinger, F. P. Inorg. Chem. 2014, 53, 9923). ket is very fast, ∼9.4 × 10(8)-6.6 × 10(9) s(-1) at 0 °C. The experimental rate constant of the title reaction (k) is much slower and controlled by the formation of the precursor complex. The substitution of a water ligand by FeCl(OH2)5(2+) at Fe(OH2)6(2+) is rate-determining.

Probing electronic states of TaC and observation of a stable excited state ofTaC−by anion-photoelectron spectroscopy

We report the experimental value of electron affinity for TaC to be 1.928(0.056) eV by performing photodetachment of its anion at 355 nm. An excited-electronic state of the anion, stable against autodetachment, is observed lying 0.828 eV above the ground-electronic state. Five low-lying electronic states of TaC are observed and identified by comparison with restricted second-order configuration interaction (SOCI) calculations. Vibrational frequencies for the electronic states are obtained from the analysis of the measured data. We also present the results of density functional theory (DFT) calculations performed on the adiabatic electron affinity, yielding a value of 1.9236 eV and vertical detachment energy value of 1.924 eV.

Construction of the energy matrix for complex atoms Part IV: Excitation of one electron from a closed shell into an open shell

This work is a continuation of the previous series related to the construction of the energy matrix for complex atoms. The effects of the second-order configuration interaction perturbations on the energy-level structure of \(nl^{N}\), \( nl^{N}n_{1}l_{1}^{N_{1}}\) and \( nl^{N}n_{1}l_{1}^{N_{1}}n_{2}l_{2}\) configurations were studied. In this paper we consider one-electron core excitations for and between the configurations under study. This work combined with Part II and III is a complete description of an electrostatic interaction. In Part I we presented a method which allows to analyse complex electronic systems. They constitute the basis for the design of an efficient computer program package allowing large scale calculations which provide accurate wave functions.

Construction of the energy matrix for complex atoms Part III: Excitation of two equivalent electrons from a closed shell into an open shell or an empty shell

The effects of the second-order configuration interaction perturbations on the energy-level structure of nl N , $$nl^N n_1 l_1^{N_1 }$$ and $$nl^N n_1 l_1^{N_1 } n_2 l_2$$ configurations have been studied. In the previous works (see Part I and II) we presented a method, which allows to analyse complex electronic systems composed of configurations including up to four open shells and the formulae for the first-order electrostatic interaction between sophisticated configurations. In the present paper we consider two-electron core excitations for and between the configurations under study. They constitute the basis for the design of an efficient computer program package allowing large-scale calculations providing accurate wave functions.

Theoretical Analyses on Phosphorescent Processes in Pt(thpy)2 and Its Derivatives

Theoretical estimation of the peak wavelengths of phosphorescence was performed at the MCSCF+SOCI/SBKJC+p level of theory for several typical platinum complexes in the research field of organic-light-emitting-diodes (OLEDs), where MCSCF+SOCI is the abbreviation of multiconfiguration self-consistent field calculations followed by second-order configuration interaction calculations. The spin–orbit coupling (SOC) integrals among low-lying electronic states of different spin multiplicities were explicitly calculated within the Zeff approximation. By using these computational methods, the experimental results for peak wavelengths of phosphorescence were reasonably explained for cis-bis[2-(2′-thienyl)pyridinato-N,C3′]platinum(II) and its derivatives. The replacement of one of the 2-(2′-thienyl)pyridinate (thpy) ligands by a 2,4-pentanedionate (acac) ligand causes a blue shift of the phosphorescent peak by about 10 nm. The use of a 1,3-bis(phenyl)propane-1,3-dionate (bpp), 1,3-bis(n-methoxyphenyl)propane-1,3-dio...

Fundamental Vibrational Frequencies and Spectroscopic Constants of cis- and trans-HOCS, HSCO, and Isotopologues via Quartic Force Fields

Highly accurate, coupled-cluster-based quartic force fields (QFFs) have been employed recently to provide spectroscopic reference for a myriad of molecules. Here, we are extending the same approach to provide vibrational and rotational spectroscopic reference data for the sulfur analogues of HOCO, HSCO, and HOCS, in both the cis and trans conformations as well as the D and (34)S isotopologues of each system. The resulting energies corroborate previous computations showing that trans-HSCO is the lowest-energy isomer for this system. The vibrational frequencies are computed with both second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) methods. The VPT2 and VCI QFF frequencies largely agree with one another to better than 5.0 cm(-1) (often better than 1.0 cm(-1)) and are also consistent with the type of behavior exhibited in previous studies. As such, the reference data provided here should assist in analysis of environments in which these sulfur systems may be found, including the interstellar medium, combustion flames, or laboratory simulations of either.

Radical O–O coupling reaction in diferrate-mediated water oxidation studied using multireference wave function theory

The O-O (oxygen-oxygen) bond formation is widely recognized as a key step of the catalytic reaction of dioxygen evolution from water. Recently, the water oxidation catalyzed by potassium ferrate (K2FeO4) was investigated on the basis of experimental kinetic isotope effect analysis assisted by density functional calculations, revealing the intramolecular oxo-coupling mechanism within a di-iron(vi) intermediate, or diferrate [Sarma et al., J. Am. Chem. Soc., 2012, 134, 15371]. Here, we report a detailed examination of this diferrate-mediated O-O bond formation using scalable multireference electronic structure theory. High-dimensional correlated many-electron wave functions beyond the one-electron picture were computed using the ab initio density matrix renormalization group (DMRG) method along the O-O bond formation pathway. The necessity of using large active space arises from the description of complex electronic interactions and varying redox states both associated with two-center antiferromagnetic multivalent iron-oxo coupling. Dynamic correlation effects on top of the active space DMRG wave functions were additively accounted for by complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) based methods, which were recently introduced by our group. These multireference methods were capable of handling the double shell effects in the extended active space treatment. The calculations with an active space of 36 electrons in 32 orbitals, which is far over conventional limitation, provide a quantitatively reliable prediction of potential energy profiles and confirmed the viability of the direct oxo coupling. The bonding nature of Fe-O and dual bonding character of O-O are discussed using natural orbitals.

Vibrational Frequencies and Spectroscopic Constants for 1 3A′ HNC and 1 3A′ HOC+ from High-Accuracy Quartic Force Fields

The spectroscopic constants and vibrational frequencies for the 1 (3)A' states of HNC, DNC, HOC(+), and DOC(+) are computed and discussed in this work. The reliable CcCR quartic force field based on high-level coupled cluster ab initio quantum chemical computations is exclusively utilized to provide the anharmonic potential. Then, second-order vibrational perturbation theory and vibrational configuration interaction methods are employed to treat the nuclear Schrödinger equation. Second-order perturbation theory is also employed to provide spectroscopic data for all molecules examined. The relationship between these molecules and the corresponding 1 (3)A' HCN and HCO(+) isomers is further developed here. These data are applicable to laboratory studies involving formation of HNC and HOC(+) as well as astronomical observations of chemically active astrophysical environments.

An ab Initio Investigation of Fluorobromo Carbene

Fluorobromo carbene, an important halogenated carbene in the stratospheric ozone depletion, has long been received considerable interest. However, the energy, structure, and dynamics of even the lowest excited states have not been well understood. In this paper, we performed a detail ab initio study on CFBr using complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) method. We investigated the effect of basis set on the CASPT2 results of the ground X(1)A' state and the first excited singlet A(1)A" state. The potential energy surface (PES) of the A(1)A" state along C-Br bond distance was carefully examined at CASPT2/cc-pV5Z level, by optimizing C-F bond and F-C-Br angle at every C-Br bond length in contrast to fix them at the equilibrium values. On the basis of the PES, a reliable barrier height of the A(1)A" state was obtained from CASPT2 and MRCI+Q calculations with different basis sets, considering the scalar relativistic effect, spin-orbit coupling, and core-valence correlation. Finally, we carried out the first theoretical study on higher excited state with energy up to 7 eV. The present calculated results were compared with previous experimental and theoretical results where available. Our results will add some understanding and shed more light on the structure and dynamics of electronic states of CFBr radical.

ChemInform Abstract: Geometries and Energies of GeHn and GeH+ n (n = 1-4)

Complete active space MCSCF (multiconfiguration self‐consistent field) (CASSCF) followed by second‐order configuration interaction (SOCI) and multireference singles and doubles CI (MRSDCI) are carried out on the ground states of GeHn and GeH+n (n=1–4). The equilibrium geometries of these species, adiabatic ionization potentials, and stepwise bond energies [De(Hn−1Ge–H) and De(Hn−1Ge+–H)] are calculated. The ground sate of GeH+4 is a Jahn–Teller distorted 2A1(C2v) state with a GeH+2⋅H2 complex structure. The adiabatic ionization potentials (IPS) of GeHn exhibit even–odd alternation. GeH4 is the most stable among the neutral GeHn species while GeH+3 is the most stable of the GeH+n.

Configuration interaction and screening in the s2p4d and sp6 configurations

The method of Racah and Stein is applied to the calculation of second-order configuration interaction in the open shells sp6 and s2p4d. The excited configuration sp4d2 is found to be important in screening the matrix element G1 (ps; dp) which is responsible for the mixing of sp6 and s2p4d, 2S. This mixing is calculated. The second-order interaction strongly affects the value of G3 (p, d) deduced from term analysis of the configuration s2p4d and brings it into agreement with theory. However, the value of G1 (p, d) shows only a small improvement, indicating the need for further work on this configuration.

Computational studies of one-electron properties of lithium hydride in confinement

Dipole moments, dipole polarizabilities, and electric field gradients of the ground and the first 1Σ+ excited electronic state as well as the dissociative state a 3Σ+ of a LiH molecule subjected to a cylindrical harmonic confining potential were calculated by means of the second-order configuration interaction method. The response of these quantities to the confining potential was discussed in terms of the bonding characteristics of the electronic states of a LiH molecule.

Ab initio study of the reaction of H2 with an AuPt3 cluster

The study of the interaction of a pyramidal tetramer of AuPt3 with H2 is carried out by means of Hartree-Fock self-consistent field (SCF) calculations using relativistic effective core potentials and multiconfigurational SCF plus multireference variational and perturbational on second-order Moller-Plesset configuration interaction calculations. The AuPt3-H2 interaction was carried out in C(s) symmetry. The three lowest electronic states X 2A", A 2A', and a 4A' of the bare cluster were considered in order to study this interaction. The AuPt3+H2 reaction by a Pt vertex shows that AuPt3 cluster in the three lowest-lying electronic states can spontaneously capture and dissociate the H2 molecule. While, by the AuPt2 face side, the AuPt3 cluster only in the A 2A' electronic state can capture and dissociate the H2 molecule after surmounting a small energy barrier. For the Au vertex, this cluster in the three electronic states can also spontaneously capture and dissociate the H2 molecule. On the other hand, by the Pt3 face side, the AuPt3 cluster is able to capture and dissociate the H2 molecule after surmounting energy barriers, where the AuPt3 (X 2A" and 4A'-H2 adsorption are slightly activated.