Direct Elucidation of the Vibrationally Averaged Structure of Benzene: A Path Integral Molecular Dynamics Study.

Path integral molecular dynamics (PIMD) simulations for C6H6, C6D6, and C6T6 have been carried out to directly estimate the distribution of projected C-H(D,T) bond lengths onto the principal axis plane. The average values of raw C-H(D,T) bond lengths obtained from PIMD simulations are in the order of ⟨RC-H⟩ > ⟨RC-D⟩ > ⟨RC-T⟩ due to the anharmonicity of the potential energy curve. However, the projected C-H(D,T) bond lengths are almost the same as those reported by Hirano et al. [J. Mol. Struct. 2021, 1243, 130537]. Our PIMD simulations directly and strongly support the explanation by Hirano et al. for the experimental observations that almost the same projected C-H(D) bond lengths are found for C6H6 and C6D6. The PIMD simulations also predicted the same projected bond lengths for C6T6 as those of C6H(D)6. In addition to the previous local mode analysis, the present PIMD simulations predicted, for benzene isotopologues, that the vibrationally averaged structure is planar but non-flat.

Electronic structure and rovibrational properties of ZnOH in the X̃²A' electronic state: a computational molecular spectroscopy study.

The three-dimensional ground-state potential energy surface of ZnOH has been calculated ab initio at the MR-SDCI+Q_DK3/[QZP ANO-RCC (Zn, O, H)] level of theory and used as basis for a study of the rovibrational properties carried out by means of the program MORBID (Morse Oscillator Rigid Bender Internal Dynamics). The electronic ground state is (2)A' (correlating with (2)Σ(+) at the linear configuration). The equilibrium structure has r(e)(Zn-O) = 1.8028 Å, r(e)(O-H) = 0.9606 Å, and ∠e(Zn-O-H) = 114.9°. The Zn-O bond is essentially ionic, with appreciable covalency. The bonding character is compared with those of FeOH (quasi-linear) and CsOH (linear). The rovibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are ⟨r(Zn-O)⟩0 = 1.8078 Å, ⟨r(O-H)⟩0 = 0.9778 Å, and ⟨∠(Zn-O-H)⟩0 = 117°. The Yamada-Winnewisser quasi-linearity parameter is found to be γ0 = 0.84, which is close to 1.0 as expected for a bent molecule. Since no experimental rovibrational spectrum has been reported thus far, this spectrum has been simulated from the ab initio potential energy and dipole moment surfaces. The amphoteric character of ZnOH is also discussed.

The Renner effect in the X 2A" and à 2A' electronic states of HSO/HOS.

We report a theoretical investigation of the X (2)A" and à (2)A' electronic states of HSO/HOS. Three-dimensional potential energy surfaces for the X (2)A" and à (2)A' electronic states of HSO/HOS have been calculated ab initio by the core-valence MR-SDCI+Q/[aug-cc-pCVQZ(S,O),aug-cc-pVQZ(H)] method, and near-global potential energy surfaces have been constructed. These surfaces have been used, in conjunction with our computer program DR, for calculating HSO/HOS rovibronic energies in the electronic states X (2)A" and à (2)A'. Both electronic states have nonlinear equilibrium geometries and they correlate with (2)Π states at the H-S-O and H-O-S linear configurations so that they exhibit the double Renner effect. The present DR calculation of the rovibronic energies for the X (2)A" and à (2)A' electronic states of HSO/HOS is complicated by the Renner-interaction breakdown of the Born-Oppenheimer approximation and by HSO/HOS isomerization. Calculated energies are reported together with analyses of the rovibronic wave functions for selected states. These analyses explore the interplay between the effects of, on one hand, Renner interaction and, on the other hand, isomerization tunneling in the rovibronic dynamics of HSO/HOS.

Geometries and electronic structures of the ground and low-lying excited states of FeCO: an ab initio study.

FeCO is a molecule of astrophysical interest. We report here theoretical calculations of its geometrical parameters, electronic structures, and molecular constants (such as dipole moment and spin-orbit coupling constant) in the electronic ground state X(3)Σ(-) and the low-lying triplet and quintet excited states. The calculations were made at the MR-SDCI+Q_DK3/[5ZP ANO-RCC (Fe, C, O)] and MR-AQCC_DK3/[5ZP ANO-RCC (Fe, C, O)] levels of theory. A multi-reference calculation was required to describe correctly the wavefunctions of all states studied. For all triplet states, the σ-donation through the 10σ molecular orbital (MO) as well as the π-back-donation through the 4π MO are observed, and the dipole moment vector points from O toward Fe as expected. However, in the excited quintet states (5)Π, (5)Φ, and (5)Δ, the almost negligible contribution of Fe 4s to the 10σ MO makes the dipole moment vector point from Fe toward O, i.e., in the same direction as in CO. In the X(3)Σ(-) state, the electron provided by the σ-donation through the 10σ MO is shared between the Fe atom and the C end of the CO residue to form a coordinate-covalent Fe-C bond. In the ã(5)Σ(-) state (the high-spin counterpart of X(3)Σ(-)), the σ-donation through the 10σ MO is not significant and so the Fe-C bond is rather ionic. The π-back-donation through the 4π MO is found to be of comparable importance in the two electronic states; it has a slightly larger magnitude in the X(3)Σ(-) state. The difference in the molecular properties of the low-spin X(3)Σ(-) and the high-spin ã(5)Σ(-) states can be understood in terms of the dynamical electron correlation effects.

[An elderly gastric cancer patient with multiple-node metastases treated successfully using S-1].

A n 83-year-old male presented with a leg edema. Gastrointestinal endoscopic examination showed advanced gastric cancer type 2, which was diagnosed as mod~well-differentiated adenocarcinoma. Computed tomography (CT) showed enlarged multiple lymph nodes. He was treated with oral S-1, 80 mg/day for 14 days, followed by a 7-day rest. After two courses of treatment, CT showed reduction of the lymph nodes. After 8 courses of treatment, total gastrectomy and lymph node dissection were performed. The histological diagnoses were tub 2>tub 1, pSS, pN0, pStage I B. One year and 10 months postoperatively, the patient is alive without recurrence.

Electronic structures and rovibronically averaged geometries of the X 6Ai' and A 6Ai" states of FeOH.

We have recently reported a theoretical prediction of the rovibronic spectra of the FeOH molecule. These spectra have not been observed experimentally. In the present work, we complement the previously published information by reporting the details of the electronic structure of FeOH together with rovibrationally averaged structural parameters. The electronic ground state is X (6)A(i)', which is Renner-degenerate with the A (6)A(i)" state; the two states correlate with a (6)Delta state at linearity. We have calculated the three-dimensional potential energy surfaces (PESs) of the X and A states, which are close in energy over the range of geometries studied, at the MR-SDCI+Q+E(rel)/[Roos ANO (Fe), aug-cc-pVQZ (O, H)] level of theory. The equilibrium structure of the X state is bent with r(e)(Fe-O)=1.806 A, r(e)(O-H)=0.952 A, and angle(e)(Fe-O-H)=134.2 degrees. The barrier to linearity is 273 (266) cm(-1) in the X (A) state so that FeOH is quasilinear in the X and A states. The Fe-O bonds in both states are ionic and the bending potentials are shallow, resulting in large amplitude bending motion. The rovibrationally averaged structures of the X (6)A' and A (6)A" electronic states have been calculated for the average of the X and A PESs by the variational MORBID method as expectation values in terms of rotation-vibration wave functions. FeOH is said to be quasilinear, but the rovibrationally averaged structure is bent with (0)=1.805 A, (0)=0.967 A, and (0)=141(14) degrees (where the quantity in parentheses is the quantum mechanical uncertainty), which is close to the equilibrium structure. We demonstrate that by means of the Yamada-Winnewisser quasilinearity parameter we can distinguish linear and quasilinear molecules.

Calculation of rovibronic intensities for triatomic molecules in double-Renner-degenerate electronic states: Application to the X (2)A(") and A (2)A(') electronic states of HO(2).

An algorithm and a computer program implementing it are presented for calculation of the rovibronic intensities for a triatomic molecule in a "double-Renner-degenerate" electronic state. The program has been applied to investigate, by theoretical simulation, the absorption spectrum of HO(2) in the X (2)A(") and A (2)A(') electronic states. The spectrum simulations are based on potential energy functions, electric dipole moment functions, and electric dipole transition moment functions constructed from ab initio values calculated at the core-valence MR-SDCI+Q/[cc-pVQZ (H), aug-cc-pCVQZ (O)] level of theory.

Ab initio calculation of the electronic structures of the (7)Sigma+ ground and A (7)Pi and a (5)Sigma+ excited states of MnH.

Electronic structures and molecular constants of the ground (7)Sigma(+) and low-lying A (7)Pi and a (5)Sigma(+) electronic excited states of the MnH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI) with Davidson's correction (+Q) calculations under exact C(infinity v) symmetry using Slater-type basis sets. To correctly describe the (7)Sigma(+) electronic ground state, X (7)Sigma(+), at the MR-SDCI+Q calculation, we employed a large number of reference configurations in terms of the state-averaged complete active space self-consistent field (CASSCF) orbitals, taking into account the contribution from the B (7)Sigma(+) excited state. The A (7)Pi and a (5)Sigma(+) states can well be described by the MR-SDCI wave functions based on the CASSCF orbitals obtained for the lowest state only. In the MR-SDCI+Q, calculations of the X (7)Sigma(+), A (7)Pi, and a (5)Sigma(+) states required 16, 7, and 17 reference configurations, respectively. Molecular constants, i.e., r(e) and omega(e) of these states and excitation energy from the X (7)Sigma(+) state, obtained at the MR-SDCI+Q level, showed a good agreement with experimental values. The small remaining differences may be accounted for by taking relativistic effects into account.

The double Renner effect in the X(2)A" and A(2)A' electronic states of HO(2).

A theoretical investigation of the X(2)A" and A(2)A' electronic states of the HO(2) radical is reported. Both electronic states have nonlinear equilibrium geometries and they correlate with a (2)Pi state at linear geometries so that they exhibit the Renner effect. In highly excited bending states, there is tunneling between two equivalent minima (with geometries where the H nucleus is bound to one, or the other, of the two O nuclei), and the two linear geometries H-O-O and O-O-H become accessible to the molecule. Thus, HO(2) affords an example of the so-called double Renner effect. Three-dimensional potential energy surfaces for the X(2)A" and A(2)A' electronic states of HO(2) have been calculated ab initio and the global potential energy surfaces for the states have been constructed. These surfaces have been used, in conjunction with the computer program DR [Odaka et al., J. Mol. Structure 795, 14 (2006); Odaka et al., J. Chem. Phys. 126, 094301 (2007)], for calculating HO(2) rovibronic energies in the "double-Renner"-degenerate electronic states X(2)A" and A(2)A'. The results of the ab initio calculations, the rovibronic energies obtained, and analyses of the wavefunctions for selected states are presented.

Pathways and reduced-dimension five-dimensional potential energy surface for the reactions H3+ + CO-->H2+HCO+ and H3+ + CO-->H2+HOC+.

To obtain theoretical insight regarding the stability and formation dynamics of the interstellar ions HCO(+) and HOC(+), stationary points and the associated vibrational frequencies on the full nine-dimensional potential energy surface for the electronic ground state have been calculated using coupled-cluster theory with both single and double substitutions (CCSD). The energetics were refined with a higher-level coupled-cluster method CCSD(T), with core-valence electron correlation treated at the complete basis set limit. To elucidate the formation mechanism and internal relaxation processes, the reaction paths for the reactions H(3) (+)+CO-->H(2)+HCO(+) and H(3) (+)+CO-->H(2)+HOC(+) were calculated at the second-order Moller-Plesset (MP2) level, and corresponding single-point energies were obtained at the higher CCSD(T)/aug-cc-pVTZ level. Based on the analysis of the main reaction processes, a reduced-dimension five-dimensional potential energy surface for this system was constructed from 128 440 ab initio points calculated at the CCSD(T)/aug-cc-pVTZ level.

Ab initio molecular orbital study of ground and low-lying electronic states of CoCN.

The ground and low-lying excited states of CoCN have been studied by ab initio multireference single and double excitation configuration interaction (MR-SDCI) calculations with Davidson's correction Q and Cowan-Griffin's relativistic corrections. The electronic ground state of CoCN is (3)Phi(i) and the equilibrium geometry is linear with bond lengths of r(e)(Co-C)=1.8540 A and r(e)(C-N)=1.1677 A, substantially different from the experimentally derived values of r(0)(Co-C)=1.8827(7) A and r(0)(C-N)=1.1313(10) A. The first excited state is (3)Delta(i), separated from the ground state by 727 cm(-1). Larger dynamical electron correlation energy for the low-spin (3)Phi state than for the high-spin (5)Phi state makes the (3)Phi state to be the ground state, which is discussed in terms of the differences in natural orbitals. A new spin-orbit interaction scheme between the X (3)Phi(i) and 1 (3)Delta(i) states is proposed.

Ab initio calculation of the electronic structures of the 3Phi ground and 5Phi excited states of CoH.

The electronic structures and the spectroscopic constants of the electronic ground 3Phi and low-lying 5Phi electronic excited states of the CoH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI)+Davidson's correction (Q) calculations and size-consistent multireference coupled pair approximation (MRCPA) calculations. Calculations were performed under Cinfinityv symmetry using Slater-type basis functions. The electronic ground state was confirmed to be the 3Phi state. It was found that at least four reference configurations were needed to describe the ground 3Phi state correctly at the MR-SDCI+Q level, while the 5Phi state can be described well by one reference configuration, namely, the Hartree-Fock configuration. Larger dynamical electron correlation for the low-spin 3Phi state than that for the high-spin 5Phi state is discussed. Spectroscopic constants, i.e., equilibrium bond lengths (re), harmonic frequency (omegae), and excitation energy, obtained by the MR-SDCI+Q method showed good correspondence with experimental values. MRCPA calculations gave a slightly shorter value for re than experimental values, but improved omegae and the excitation energy bringing them very close to experimental values.

Theoretical study of the double Renner effect for A2Pi MgNC/MgCN: higher excited rovibrational states.

The authors report here the implementation of a newly developed, highly efficient matrix diagonalization routine in the DR program [T. E. Odaka et al., J. Mol. Struct. 795, 14 (2006)]. The DR program solves the rovibronic Schrodinger equation for a triatomic molecule with a double Renner effect, i.e., with two accessible linear arrangements of the nuclei at which the electronic energy is doubly degenerate. With the new routines, the authors can extend the DR calculations of rovibronic energies for A 2Pi MgNC/MgCN by considering a much larger set of rovibronic states, in particular, states at higher J values, than the authors were able to access previously.

The Renner effect in triatomic molecules with application to CH+, MgNC and NH2.

We have developed a computational procedure, based on the variational method, for the calculation of the rovibronic energies of a triatomic molecule in an electronic state that become degenerate at the linear nuclear configuration. In such an electronic state the coupling caused by the electronic orbital angular momentum is very significant and it is called the Renner effect. We include it, and the effect of spin-orbit coupling, in our program. We have developed the procedure to the point where spectral line intensities can be calculated so that absorption and emission spectra can be simulated. In order to gain insight into the nature of the eigenfunctions, we have introduced and calculated the overall bending probability density function f(p) of the states. By projecting the eigenfunctions onto the Born-Oppenheimer basis, we have determined the probability density functions f+(rho) and f-(rho) associated with the individual Born-Oppenheimer states phi(-)elec and phi(+)elec. At a given temperature the Boltzmann averaged value of the f(p) over all the eigenstates gives the bending probability distribution function F(rho), and this can be related to the result of a Coulomb Explosion Imaging (CEI) experiment. We review our work and apply it to the molecules CH2+, MgNC and NH2, all of which are of astrophysical interest.