Multidimensional tunneling dynamics of proton transfer in malonaldehyde molecule and its isotopomers

The twenty-one-dimensional Hamiltonian of malonaldehyde molecule and a number of its isotopomers (H/D, ¹³C/¹²C) was reconstructed in the low-energy region (<3000 cm^–1). Parameters of the Hamiltonian were obtained from quantum-chemical calculations of the energies, equilibrium geometries, and eigenvectors and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and transition state. Despite substantial variation of the barrier height calculated using different quantum-chemical methods (from 2.8 to 10.3 kcal mol^–1), the corresponding potential energy surfaces can be matched with high accuracy by scaling only one parameter (the semiclassical parameter , which defines the scales of potential, energy, and action). Scaling invariance allows optimization of the Hamiltonian in such a way that the calculated ground-state tunneling splitting coincides with the experimental value. The corresponding potential barrier height is estimated at 4.34±0.4 kcal mol^–1. The quantum dynamics problem was solved using the perturbative instanton approach without reducing the number of degrees of freedom. The role of all transverse vibrations in proton tunneling is characterized. Vibration-tunneling spectrum is calculated for the ground state and low-lying excited states and mode-specific isotope effects are predicted.     

Tunneling dynamics of internal rotation in the nitric acid molecule

The Hamiltonian of internal rotation about theC ₂ axis in the HNO₃ molecule and its H/D-, O¹⁸/O¹⁶-, and N¹⁵/N¹⁴-isotopomers was reconstructed using the results of quantumchemical calculations. The Fermi resonance between the torsional (2v₉) and ONO bending (v₅) vibrations is a characteristic feature of the molecule. Tunneling splittings in the ground and excited states were calculated using the perturbative instanton approach. Abnormally large changes in the splittings upon isotope substitution of heavy atoms are predicted. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2052–2060, November, 1999.     

Theoretical prediction on vibrational spectra of [Ar...Ar-H]<Superscript>+</Superscript>

Centrosymmetric linear [Ar-H-Ar]⁺ and asymmetric linear [Ar---Ar-H]⁺ are two stable configurations of [Ar₂H]⁺. Based on the global potential energy surface of [Ar₂H]⁺ provided by our group recently, we calculated the vibrational spectra of [Ar---Ar-H]⁺ with total angular momentum J = 0 by time-dependent quantum mechanical method, and the influence of quantum tunneling effect on vibrational spectra was found. With the help of the observation on the eigenstate functions and the modified potential energy surface, assignments were made to the spectra. The strong coupling between the excited bending mode of [Ar-H-Ar]⁺ and the vibrational states of [Ar---Ar-H]⁺ was discussed.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Potential Energy Surface of Cooperative Proton Tunneling in the C2H+ 3 Cation

The nine-dimensional potential energy surface for proton tunneling in the nonrigid C₂H⁺ ₃ cation was constructed from quantum-chemical data [MP4SDQ(T)/6-311++G(3df,3pd)] on the equilibrium geometry, energy, frequencies, and eigenvectors of the normal vibrations at the stationary points and transition states using the theory of isodynamic symmetry groups along the tunneling path.     

Ab initio energies and tunneling lifetimes of the doubly charged AH2+ (A = Mg—Ar) diatomics

Potential energy curves for the ground and low-lying excited states of the AH²⁺ (A = Mg—Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH²⁺ have low-lying states which support quasi-bound vibrational states. The ArH²⁺ dication has a ²∏_i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.     

Photodeactivation paths in norbornadiene

The first high level ab initio quantum‐chemical calculations of potential energy surfaces (PESs) for low‐lying singlet excited states of norbornadiene in the gas phase are presented. The optimization of the stationary points (minima and conical intersections) and the recalculation of the energies were performed using the multireference configuration interaction with singles (MR‐CIS) and the multiconfigurational second‐order perturbation (CASPT2) methods, respectively. It was shown that the crossing between valence V₂ and Rydberg R₁ states close to the Franck–Condon (FC) point permits an easy population switch between these states. Also, a new deactivation path in which the doubly excited state with (π₃)² configuration (DE) has a prominent role in photodeactivation from the R₁ state due to the R₁/DE and the DE/V₁ conical intersections very close to the R₁ and DE minima, respectively, was proposed. Subsequent deactivation from the V₁ to the ground state goes through an Olivucci–Robb‐type conical intersection that adopts a rhombic distorted geometry. The deactivation path has negligible barriers, thereby making ultrafast radiationless decay to the ground state possible. © 2013 Wiley Periodicals, Inc.     

Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low-lying states of these systems are classified as covalent (CV ) and ionic (IN ) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 2¹A_g state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low-lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 1¹B_u of linear π systems, 1¹B_2g of cyclobutadiene and 1¹B_1U of benzene, are alternating.     

Hydrogen-bonded Intramolecular Charge Transfer Excited State of Dimethylaminobenzophenone using Time Dependent Density FunctionalTheory

Density functional theory and time-dependent density-functional theory have been used to investigate the photophysical properties and relaxation dynamics of dimethylaminobenzophe-none (DMABP) and its hydrogen-bonded DMABP-MeOH dimer. It is found that, in non-polar aprotic solvent, the transitions from S₀ to S₁ and S₂ states of DMABP have both n→π^* and π→π^* characters, with the locally excited feature mainly located on the C=O group and the partial CT one characterized by electron transfer mainly from the dimethylaminophenyl group to the C=O group. But when the intermolecular hydrogen bond C=O…H-O is formed, the highly polar intramolecular charge transfer character switches over to the first excited state of DMABP-MeOH dimer and the energy difference between the two low-lying electronically excited states increases. To gain insight into the relaxation dynamics of DMABP and DMABP-MeOH dimer in the excited state, the potential energy curves for con-formational relaxation are calculated. The formation of twisted intramolecular charge trans-fer state via diffusive twisting motion of the dimethylamino/dimethylaminophenyl groups is found to be the major relaxation process. In addition, the decay of the S1 state of DMABP-MeOH dimer to the ground state, through nonradiative intermolecular hydrogen bond stretching vibrations, is facilitated by the formation of the hydrogen bond between DMABP and alcohols.     

Optical oscillator strengths for lithium

A simple two-parameter analytic potential adjusted so as to reproduce the experimental energy levels is used to generate wave functions for the ground and excited states of the lithium atom. Using these wave functions in conjunction with the Born approximation and the Russell–Saunders LS-coupling scheme, we calculate the optical oscillator strengths for various excitations from the 1s²2s(²S_1/2) ground state. The results are compared to experiment and other calculations.     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

The microwave spectrum of dichlorosilylene (SiCl2) in excited vibrational states

The microwave spectrum of dichlorosilylene in excited vibrational states has been measured in the millimetre- and submillimetre-wave regions. Rotational and centrifugal distortion constants were determined for the ν₁, ν₂, 2ν₂ and ν₃ excited states of the Si³⁵Cl₂ isotopic species and for the ν₂ and 2ν₂ states of Si³⁵Cl³⁷Cl. Analysis of the Coriolis resonance between the ν₁ and ν₃ states of Si³⁵Cl₂ yielded values of the D Coriolis interaction constant with F constrained, of two higher-order terms and also an accurate value [5.402338(95) cm⁻¹] of the energy difference between the two excited vibrational states. The rotational constants of Si³⁵Cl₂ in the first excited states of the three normal vibrations were combined with those of the ground vibrational state reported in a previous paper [M. Tanimoto et al., J. Chem. Phys. 91, 2102 (1989)] to obtain the equilibrium structure, harmonic and cubic/third-order anharmonic potential constants.     

Potential energy surface and highly excited vibrational lines of NO2 via algebraic approach

The algebraic Hamiltonian of NO₂ is optimized using U(4) algebra via fitting to 102 observed vibrational lines. The RMS error of the fitting is 2.39 cm^?1. We calculated highly excited vibrational energy levels using this optimized Hamiltonian, and then obtained the potential energy surface for the electronic ground state by using the classical limit of the U(4) algebraic Hamiltonian. We also calculated the dissociation energies, the force constants etc. Our results are in good agreement with the other theoretical results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Ab initio calculations of the rotationally resolved infrared spectrum of KNa 2 +

Summary Ab initio variational calculations were performed on the rotationally resolved infrared spectrum of KNa ₂ ⁺ . A discrete potential energy surface was generated using the configuration interaction ansatz coupled with the frozen core approximation, from which an analytical representation was obtained using a power series expansion employing a Dunham expansion variable. This force field was embedded in an Eckart-Watson rovibrational Hamiltonian, from which eigenfunctions and eigenenergies were calculated. An SCF dipole moment surface was generated and used to calculate absolute line intensities and square dipole matrix elements between the vibrational ground state and the lowest-lying excited states for some of the most intense transitions within the P, Q and R branches.     

Structure of the 1,3-dinitrobenzene dianion studied by multiconfigurational methods

The structure of the 1,3-dinitrobenzene dianion in the ground and lowest excited electron states was studied by quantum chemical methods. The dianion, unlike the radical anion, is characterized by the symmetrical structure in both the ground triplet (³B₁) and lowest excited singlet (¹A₁) states. The wave function of the singlet state has the biradical character to a great extent. The singlet-triplet splitting calculated by the CASSCF and MRMP2 methods is 6 and 2 kcal mol⁻¹, respectively. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1408–1410, July, 2007.     

Mass-analyzed threshold ionization spectroscopy of pyrimidine: determining the geometry in the first excited and the ionic ground states

Vibrational spectra of the pyrimidine cation in the electronic ground state were measured via several intermediate states of the first excited state (0⁰,16a¹, 16a², 16a⁴, 16b¹, 10b¹, 6b², 6a¹, 1¹, 4¹, 4² and 12¹) by mass-analyzed threshold ionization spectroscopy. For the first time, several vibrational modes could be assigned in the first excited and the ionic ground states. Anharmonic coupling is shown to occur in the first excited state due to Fermi resonance between the 1¹ and the 16a⁴ vibrations. From the results of the measurements and calculations presented here, pyrimidine is predicted to be planar in the first excited and the ionic ground states, and it belongs to the C_2V point group.     

A theoretical study of the vibrational structure in the \documentclass{article}\pagestyle{empty}\begin{document}$\tilde{A}^{2}A_{1} - \tilde{X}^{2}B_{1}$\end{document} transition of PH2

The potential energy curves of the bending mode of PH₂ in the ground ²B₁ and the excited ²A₁ states have been calculated using ab initio SCF -MO wave-functions. The radical is found, in agreement with experiment, to be bent in the two states. The calculated results clarify the interpretations of the anomalous behaviour of observed vibrational intervals, and offer an explanation of the ‘quasilinearity’; of the radical in the ²A₁ state.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998