Electronic structure and bonding of the 3d transition metal borides, MB, M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu through all electron ab initio calculations

The electronic structure and bonding of the ground and some low-lying states of all first row transition metal borides (MB), ScB, TiB, VB, CrB, MnB, FeB, CoB, NiB, and CuB have been studied by multireference configuration interaction (MRCI) methods employing a correlation consistent basis set of quintuple cardinality (5Z). It should be stressed that for all the above nine molecules, experimental results are essentially absent, whereas with the exception of ScB and CuB the remaining seven species are studied theoretically for the first time. We have constructed full potential energy curves at the MRCI/5Z level for a total of 27 low-lying states, subsequently used to extract binding energies, spectroscopic parameters, and bonding schemes. In addition, some 20 or more states for every MB species have been examined at the MRCI/4Z level of theory. The ground state symmetries and corresponding binding energies (in kcal/mol) are 5Sigma-(ScB), 76; 6Delta(TiB), 65; 7Sigma+(VB), 55; 6Sigma+(CrB), 31; 5Pi(MnB), 20; 4Sigma-(FeB), 54; 3Delta(CoB), 66; 2Sigma+(NiB), 79; and 1Sigma+(CuB), 49.     

Electronic and geometric structure of the 3d-transition metal monocarbonyls MCO, M=Sc, Ti, V, and Cr

The electronic and geometric structure of the 3d-transition metal monocarbonyls MCO, M=Sc, Ti, V, and Cr was investigated through coupled cluster (CC) and multireference variational methods (MRCI) combined with large basis sets. For the ground and a few low-lying excited states complete potential energy profiles were constructed at the CC-level of theory. The M-CO dissociation energies of the ground states X 4Sigma-,X 5Delta,X 6Sigma+, and X 7A' are calculated to be 36, 27, 18, and 2 kcal/mol for ScCO, TiCO, VCO, and CrCO, with respect to Sc(4F),Ti(5F),V(6D),Cr(7S)+CO(X 1Sigma+). The bonding is rather complicated and could be attributed mainly to pi-conjugation effects between the M and CO pi-electrons, along with weak sigma-charge transfer from CO to M atoms. Almost in all cases the metal atoms appear to be slightly positively charged, at least according to the direction of the dipole moment vectors and the MRCI population densities.     

Density functional theory and multireference configuration interaction studies on low-lying excited states of TiO2

Using density functional theory at the BPW916-311+G(3df) level, optimized geometries and energies of the lowest singlet, triplet, and quintet A(1), A(2), B(1), B(2)(C(2v)) states of the TiO(2) molecule were obtained. TiO(2) has a (1)A(1) ground state in C(2v) symmetry. Adiabatic excitation energies of the low-lying singlet and triplet states range from 2.1 to 3.0 eV. The (1,3)A(2) states optimize at bond angles of about 140 degrees , lying only 0.06 eV below linear (1,3)Delta(u), whereas (1,3)B(1) and (1,3)B(2), with bond angles of 120 degrees and 96 degrees , respectively, lie 0.3-0.4 eV below the respective (1,3)Pi(u) or (1,3)Delta(u) states. Minima with short O-O distances of approximately 1.46 A, at energies of 4.2 and 4.7 eV, were found for (1)A(1) and (3)A(1). The C(2v) minima of the lowest (1)B(1) and (3)B(1) states are saddle points, suggesting lower-energy structures in C(s) symmetry. The C(2v) quintet states start at energies of 5.7 eV. Multireference configuration interaction (MRCI) methods, employing a polarized valence triple-zeta basis set, lead to similar geometries and energies. MRCI vertical excitation energies up to 4.6 eV and oscillator strengths are given. The calculated excitation energy of 2.2 eV for (1)B(2) agrees well with 2.3 eV from a fluorescence spectrum. The vertical electron detachment energy of TiO(2) (-) is 1.5 eV, in good agreement with 1.6 eV from anion photoelectron spectroscopy. An observed second photoelectron band corresponds to (1)B(2) and/or (3)B(2), but the assignment of a third band could not be verified. Vibrational frequencies, ionization energies, electron affinities, and dissociation energies are given.     

Low-lying singlet and triplet electronic states of RhB

The low-lying XSigma+, a3Delta, A1Delta, b3Sigma+, B1Pi, c3Pi, C1Phi, D1Sigma+, E1Pi, d3Phi, and e3Pi electronic states of RhB have been investigated at the ab initio level, using the multistate multiconfigurational second-order perturbation (MS-CASPT2) theory, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the eleven electronic states included in this work, only three (the X1Sigma+, D1Sigma+, and E1Pi states) have been investigated experimentally. Potential energy curves, spectroscopic constants, dipole moments, binding energies, and chemical bonding aspects are presented for all electronic states.     

Dissociation of the OCS+ ion in low-lying electronic states studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent-field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with atomic natural orbital basis sets were performed to investigate the S-loss direct dissociation of the 1 2Pi(X 2Pi), 2 2Pi(A 2Pi), 1 2Sigma+(B 2Sigma+), 1 4Sigma-, 1 2Sigma-, and 1 2Delta states of the OCS+ ion and the predissociations of the 1 2Pi, 2 2Pi, and 1 2Sigma+ states. Our calculations indicate that the S-loss dissociation products of the OCS(+) ion in the six states are the ground-state CO molecule plus the S+ ion in different electronic states. The CASPT2//CASSCF potential energy curves were calculated for the S-loss dissociation from the six states. The calculations indicate that the dissociation of the 1 4Sigma- state leads to the CO + S+ (4Su) products representing the first dissociation limit; the dissociations of the 1 2Pi, 1 2Sigma-, and 1 2Delta states lead to the CO + S+(2Du) products representing the second dissociation limit; and the dissociations of the 2 2Pi and 1 2Sigma+ states lead to the CO + S+(2Pu) products representing the third dissociation limit. Seams of the 1 2Pi-1 4Sigma-, 2 2Pi-1 4Sigma-, 2 2Pi-1 2Sigma-, 2 2Pi-1 2Delta, and 1 2Sigma(+)-1 4Sigma- potential energy surface intersections were calculated at the CASPT2 level, and the minima along the seams were located. The calculations indicate that within the experimental energy range (15.07-16.0 eV) the 2 2Pi(A 2Pi) state can be predissociated by 1 4Sigma- forming the S+(4Su) ion and can undergo internal conversion to 1 2Pi followed by the direct dissociation of 1 2Pi forming S+(2Du) and that within the experimental energy range (16.04-16.54 eV) the 1 2Sigma+(B 2Sigma+) state can be predissociated by 1 4Sigma- forming the S+(4Su) ion and can undergo internal conversion to 2 2Pi followed by the predissociation of 2 2Pi by 1 2Sigma- and 1 2Delta forming the S+(2Du) ion. These indications are in line with the experimental fact that both the 4Su and 2Du states of the S+ ion can be formed from the 2 2Pi and 1 2Sigma+ states of the OCS+ ion.     

Multireference configuration interaction study of the electronic states of ZrC

The potential energy curves and spectroscopic constants of the ground and 32 low-lying electronic states of ZrC have been studied by employing multireference configuration interaction methods, in conjunction with relativistic effective core potentials and 5s3p3d1f, 3s3p1d basis sets con Zr and C, respectively. We have determined that the ground state is (3)Sigma(+). However there are two low-lying (1)Sigma(+) states (below 5000 cm(-1)) which strongly interact resulting in avoided crossings. The lowest (1)Sigma(+) state corresponds to a combination of 1sigma(2) Xsigma(2) 1pi(4) configurations whereas the second is an open shell singlet 1sigma(2) 2sigma(1) 3sigma(1) 1pi(4). Several avoided crossings were observed, for (1)Pi, (3)Pi, (1)Delta, (3)Sigma(+), and (3)Delta states. We have identified (3)Pi and (1)Pi lying at 4367 and 5797 cm(-1), respectively. The results are in good agreement with the recent experimental findings of Rixon et al. [J. Mol. Spectrosc. 228, 554 (2004)], and indicate that the (3)Pi-(3)Sigma(+), and (1)Pi-(1)Sigma(+), bands located between 16 000-19 000 cm(-1) are extremely complex due to near degeneracy of several (1)Pi and (3)Pi states. We also have identified a (1)Sigma(+) state in the same region that may interfere with the (1)Pi emission bands. The present results not only shed further light into the spectra of ZrC but also predict yet to be observed systems.     

Electronic states and potential energy curves of molybdenum carbide and its ions

The potential energy curves and spectroscopic constants of the ground and 29 low-lying excited states of MoC with different spin and spatial symmetries within 48 000 cm(-1) have been investigated. We have used the complete active space multiconfiguration self-consistent field methodology, followed by multireference configuration interaction (MRCI) methods. Relativistic effects were considered with the aid of relativistic effective core potentials in conjunction with these methods. The results are in agreement with previous studies that determined the ground state as X (3)Sigma(-). At the MRCISD+Q level, the transition energies to the 1 (3)Delta and 4 (1)Delta states are 3430 and 8048 cm(-1), respectively, in fair agreement with the results obtained by DaBell et al. [J. Chem. Phy. 114, 2938 (2001)], namely, 4003 and 7834 cm(-1), respectively. The three band systems located at 18 611, 20 700, and 22 520 cm(-1) observed by Brugh et al. [J. Chem. Phy. 109, 7851 (1998)] were attributed to the excited 11 (3)Sigma(-), 14 (3)Pi, and 15 (1)Pi states respectively. At the MRCISD level, these states are 17 560, 20 836, and 20 952 cm(-1) above the ground state respectively. We have also identified a (3)Pi state lying 14 309 cm(-1) above the ground state. The ground states of the molecular ions are predicted to be (4)Sigma(-) and (2)Delta for MoC(-) and MoC(+), respectively.     

Ab initio configuration-interaction study of the ground and low-lying electronic states of NiI

For the first time, we have studied the potential-energy curves, spectroscopic terms, vibrational levels, and the spectroscopic constants of the ground and low-lying excited states of NiI by employing the complete active space self-consistent-field method with relativistic effective core potentials followed by multireference configuration-interaction calculations. We have identified six low-lying electronic states of NiI with doublet spin multiplicities, including three states of Delta symmetry and three states of Pi symmetry of the molecule within 15 000 cm(-1). The lowest (2)Delta state is identified as the ground state of NiI, and the lowest (2)Pi state is found at 2174.56 cm(-1) above it. These results fully support the previous conclusion of the observed spectra although our computational energy separation of the two states is obviously larger than that of the experimental values. The present calculations show that the low-lying excited states [13.9] (2)Pi and [14.6] (2)Delta are 3 (2)Pi and 3 (2)Delta electronic states of NiI, respectively. Our computed spectroscopic terms, vibrational levels, and spectroscopic constants for them are in good agreement with the experimental data available at present. In the present work we have not only suggested assignments for the observed states but also computed more electronic states that are yet to be observed experimentally.     

Spectroscopic constants and potential energy curves of yttrium carbide (YC)

The potential energy curves of the low-lying electronic states of yttrium carbide (YC) and its cation are calculated at the complete active space self-consistent field and the multireference single and double excitation configuration interaction (MRSDCI) levels of theory. Fifteen low-lying electronic states of YC with different spin and spatial symmetries were identified. The X (4)Sigma- state prevails as the ground state of YC, and a low-lying excited A (4)Pi state is found to be 1661 cm(-1) higher at the MRSDCI level. The computations of the authors support the assignment of the observed spectra to a B (4)Delta(Omega=72)<--A (4)Pi(Omega=52) transition with a reinterpretation that the A (4)Pi state is appreciably populated under the experimental conditions as it is less than 2000 cm(-1) of the X (4)Sigma- ground state, and the previously suggested (4)Pi ground state is reassigned to the first low-lying excited state of YC. The potential energy curves of YC+ confirm a previous prediction by Seivers et al. [J. Chem. Phys. 105, 6322 (1996)] that the ground state of YC+ is formed through a second pathway at higher energies. The calculated ionization energy of YC is 6.00 eV, while the adiabatic electron affinity is 0.95 eV at the MRSDCI level. The computed ionization energy of YC and dissociation energy of YC+ confirm the revised experimental estimates provided by Seivers et al. although direct experimental measurements yielded results with greater errors due to uncertainty in collisional cross sections for YC+ formation.     

Low-lying electronic states of FeNC and FeCN: a theoretical journey into isomerization and quartet/sextet competition

With several levels of multireference and restricted open-shell single-reference electronic structure theory, optimum structures, relative energetics, and spectroscopic properties of the low-lying (6)Delta, (6)Pi, (4)Delta, (4)Pi, and (4)Sigma(-) states of linear FeNC and FeCN have been investigated using five contracted Gaussian basis sets ranging from Fe[10s8p3d], C/N[4s2p1d] to Fe[6s8p6d3f2g1h], C/N[6s5p4d3f2g]. Based on multireference configuration interaction (MRCISD+Q) results with a correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis set, appended with core correlation and relativistic corrections, we propose the relative energies: T(e)(FeNC), (6)Delta(0)<(6)Pi (2300 cm(-1))<(4)Delta (2700 cm(-1))<(4)Pi (4200 cm(-1))<(4)Sigma(-); and T(e)(FeCN), (6)Delta(0)<(6)Pi (1800 cm(-1))<(4)Delta (2500 cm(-1))<(4)Pi (2900 cm(-1))<(4)Sigma(-). The (4)Delta and (4)Pi states have massive multireference character, arising mostly from 11sigma-->12sigma promotions, whereas the sextet states are dominated by single electronic configurations. The single-reference CCSDT-3 (coupled cluster singles and doubles with iterative partial triples) method appears to significantly overshoot the stabilization of the quartet states provided by both static and dynamical correlation. The (4,6)Delta and (4,6)Pi states of both isomers are rather ionic, and all have dipole moments near 5 D. On the ground (6)Delta surface, FeNC is predicted to lie 0.6 kcal mol(-1) below FeCN, and the classical barrier for isocyanide/cyanide isomerization is about 6.5 kcal mol(-1). Our data support the recent spectroscopic characterization by Lei and Dagdigian [J. Chem. Phys. 114, 2137 (2000)] of linear (6)Delta FeNC as the first experimentally observed transition-metal monoisocyanide. Their assignments for the ground term symbol, isotopomeric rotational constants, and the Fe-N omega(3) stretching frequency are confirmed; however, we find rather different structural parameters for (6)Delta FeNC:r(e)(Fe-N)=1.940 A and r(N-C)=1.182 A at the cc-pVQZ MRCISD+Q level. Our results also reveal that the observed band of FeNC originating at 27 236 cm(-1) should have an analog in FeCN near 23 800 cm(-1) of almost equal intensity. Therefore, both thermodynamic stability and absorption intensity factors favor the eventual observation of FeCN via a (6)Pi<--(6)Delta transition in the near-UV.     

AuX (X=O,S)低电子态的理论研究

通常要用多参考态方法才能合理处理需考虑旋轨耦合（SOC）效应的开壳层分子如AuO和AuS的低电子态. 事实上,通过选取合适的参考态,采用运动方程耦合簇方法（EOM-CC）也能计算这些分子的一些低电子态,而且EOM-CC方法是单参考态方法,使用起来比多参考态方法更加简单. 本文采用最近发展的含旋轨耦合的EOM-CC 计算电离能的方法（EOMIP-CC）,选取对应的负离子为参考态,在CCSD 级别上计算了AuO 和AuS低电子态的性质. 在不考虑旋轨耦合时,通过比较EOMIP-CCSD和EOMIP-CCSDT的结果考察EOMIPCCSD的精度. 此外,与EOMIP-CCSDT结果相比,如果自旋污染较为显著而且T₁的模较大时,UCCSD（T）方法对能量最低的某一特定对称性的电子态的所对应的电离能误差约为0.1-0.15 eV. 在考虑了旋轨耦合效应后,我们的方法得到的键长和振动频率与实验值吻合较好. 另一方面,虽然EOMIP-SOC-CCSD高估了能量较高的²Δ_3/2态、²Σ_1/2⁺态和²Π_1/2态的能量,但是对于其它能量更低的电子态,它们的能量与已有实验值误差在0.2 eV 左右. 这显示我们所用的含SOC的EOMIP-CCSD方法对原本需要用多参考态方法才能处理的AuO和AuS低电子态能给出可靠的结果.     

Ab initio study of KN

The potential energy curves for the lowest (3)Sigma(-), (3)Pi, and (5)Sigma(-) states of the KN molecule have been calculated by the multireference singles and doubles configuration interaction method, including Davidson's corrections for quadruple excitations [MRCI(+Q)]. It is shown that the former two are bound, while the last one is repulsive. The electronic ground state of KN is predicted as (3)Sigma(-) state, although the term energy of the (3)Pi state is very small, 177.3 cm(-1). The binding energy for the (3)Sigma(-) state is evaluated as 0.838 eV, the rotational constant B(0) as 0.250 63 cm(-1), and harmonic frequency as 324.4 cm(-1). The spin-orbit coupling effects between the (3)Sigma(-) and (3)Pi states of KN are evaluated and discussed. The same MRCI(+Q) computational procedures are applied to the isovalent LiN, KC, KO, and KCl to confirm the accuracy of present calculations. Theoretical spectroscopic constants presented here will inspire experimental studies of KN.     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Theoretical investigations of the electronic states of porphyrins. III. Low-lying electronic states of porphinatoiron(II)

Ab initio configuration interaction calculations are reported on the lowest quintet, triplet, and singlet states of Fe^II(P). Due to the large number of states found, a catalog of the low-lying states is presented. Novel triplet and quintet charge-transfer states are reported as low as 1.3 eV. These states are d⁵ (S = 5/2) on the iron low-spin-coupled to the radical anion excited porphyrin ring (S = 1/2 or 3/2). Oscillator strengths originating from each of three low-energy triplet states are reported.     

The intermolecular potentials of the O2-O2 dimer: a detailed ab initio study of the energy splittings for the three lowest multiplet states

Intermolecular potentials for the three lowest multiplet states (singlet, triplet and quintet) of the O(2)((3)Sigma)-O(2)((3)Sigma) dimer have been investigated in detail by means of high level ab initio calculations. The methods used include MRCI, ACPF, CASPT2, using different active spaces and basis sets. The results for the quintet state are compared with benchmark CCSD(T) calculations. As expected, the former methods do not account accurately for dispersion interactions, although the CASPT2 method performs better than the CI based ones. On the other hand, it is shown that highly correlated methods are necessary to accurately describe the splittings among the multiplet states. We propose to obtain singlet and triplet interaction potentials by combining CCSD(T) quintet potentials and multiconfigurational singlet-quintet and triplet-quintet splittings, respectively. The calculated splittings are quite stable regarding the method employed, except for the well region of the singlet and triplet states within the rectangular configuration, which corresponds to the absolute minima of these multiplet states. Nevertheless, we have been able to assess adequate upper and lower bounds to the interaction potential for this particular region.     

Theoretical investigation of the ground and low-lying excited states of nickel carbide, NiC

The electronic structure and bonding of 19 states of the diatomic nickel carbide (NiC) has been studied by multireference methods. Potential energy curves have been constructed for all states, whereas for the three lowest states of symmetries X (1)Sigma(+), a (3)Pi, and A (1)Pi well separated from the rest of the states, special attention was paid through the use of very large basis sets and the calculation of core-valence correlation and scalar relativistic effects. The recommended binding energies for these states are 91, 67, and 54 kcal/mol with respect to the ground state atoms. Our results in general can be considered in fair agreement with the limited experimental findings.     

Fluorescence and metastability of N2O2+: theory and experiment

State-selective mass spectrometry has revealed one conclusive and another probable metastable state of the N2O2+ dication, assigned respectively as 1 3Pi at 38.5 eV and 2 3Pi at 42.5 eV. Photon coincidence experiments confirm that dissociation of 1 3Pi is preceded by a fluorescent transition to X 3Sigma- and also indicate that an identical mechanism occurs for 2 3Pi. Highly correlated MRCI calculations are performed at a range of N2O2+ geometries, from which both N-N and N-O bond stretching curves are generated. Substantial barriers along both coordinates are observed for 1 3Pi and 2 3Pi, although the increasing density of states at higher energy may allow spin-orbit or vibronic predissociation for 2 3Pi. Fragment emissions derived from N2O+ and N2O2+ are analyzed with the aid of glass filters, from which NO (X 2Pi<--A 2Sigma+) and vibrationally excited N2+ (X 2Sigmag+<--B 2Sigmau+) transitions are deduced.     

Ground and lowest-lying electronic states of CoN. A multiconfigurational study

The lowest-lying X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II electronic states of CoN have been investigated at the ab initio MRCI and MS-CASPT2 levels, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the singlet states, the A1Phi and B1II states have been described for the first time. Potential energy curves, excitation energies, spectroscopic constants, and bonding character for all states are reported. Comparison with other early transition-metal nitrides (ScN, TiN, VN, and CrN), isoelectronic (NiC) and isovalent (RhN and IrN) species has been made, besides analyzing the B1II <=> X1+ electronic transition in terms of Franck-Condon factors, Einstein coefficients, and radiative lifetimes. At both levels of theory, the following energetic order has been obtained: X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II, with good agreement with experimental results. In contrast, previous DFT and MRCI calculations predicted the ground state to be the 5Delta state.     

Extensive ab initio study of the valence and low-lying Rydberg states of BBr including spin-orbit coupling

The electronic states of the BBr molecule, including 12 valence states and 12 low-lying Rydberg states, have been studied at the theoretical level of MR-CISD+Q with all-electron aug-cc-pVQZ basis sets and Douglas-Kroll [Ann. Phys. (N.Y.) 82, 89 (1974)] scalar relativistic correction. The spin-orbit coupling effect in the valence states was calculated by the state interaction approach with the full Breit-Pauli Hamiltonian. This is the first multireference ab initio study of the excited electronic states of BBr. Potential energy curves of all states were plotted with the help of the avoided crossing rule between electronic states of the same symmetry. The structural properties of these states were analyzed. Computational results reproduced most experimental data well. The transition properties of the a (3)Pi(0(+) ), a (3)Pi(1), and A (1)Pi(1) states to the ground state X (1)Sigma(0(+) ) (+) transitions were obtained, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The evaluated radiative lifetime of the a (3)Pi(0(+) ), and a (3)Pi(1) states are near 1 ms, much longer than that of the A (1)Pi(1) state.