Time-dependent Quantum Mechanical Methods Research Articles

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent.

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

Vibronic coupling in the first six electronic states of pentafluorobenzene radical cation: Radiative emission and nonradiative decay

Nuclear dynamics in the first six vibronically coupled electronic states of pentafluorobenzene radical cation is studied with the aid of the standard vibronic coupling theory and quantum dynamical methods. A model 6 × 6 vibronic Hamiltonian is constructed in a diabatic electronic basis using symmetry selection rules and a Taylor expansion of the elements of the electronic Hamiltonian in terms of the normal coordinate of vibrational modes. Extensive ab initio quantum chemistry calculations are carried out for the adiabatic electronic energies to establish the diabatic potential energy surfaces and their coupling surfaces. Both time-independent and time-dependent quantum mechanical methods are employed to perform nuclear dynamics calculations. The vibronic spectrum of the electronic states is calculated, assigned, and compared with the available experimental results. Internal conversion dynamics of electronic states is examined to assess the impact of various couplings on the nuclear dynamics. The impact of increasing fluorination of the parent benzene radical cation on its radiative emission is examined and discussed.

Pyrene radical cation and the diffuse interstellar band at 4430 Å: A theoretical survey

Multistate and multimode vibronic dynamics on the first six coupled (X˜2B1g - A˜2B2g - B˜2B3u - C˜2Au - D˜2B3u - E˜2B3g ) electronic states of pyrene radical cation are investigated with the aid of ab initio electronic structure calculations of potential energy surfaces (PESs) and first principle quantum dynamical methods. Several low-lying conical intersections among various electronic states are found and their impact on the nuclear dynamics is discussed. The simulation of nuclear motion on the underlying coupled electronic states of pyrene radical cation is examined by both time-independent and time-dependent quantum mechanical methods. The combination of time-independent and time-dependent quantum mechanical simulations render a satisfactory explaination of a large part of the complex vibronic spectrum of Py+ which is in very good agreement with the photoelectron spectroscopic data. Furthermore, this study also establishes that polycyclic aromatic hydrocarbons can be the molecular carrier of diffused interstellar bands and ultrafast non-radiative deactivation of their excited electronic states makes them photostable against strong UV irradiation in the interstellar medium.

Renner-Teller and pseudo-Renner-Teller interactions in the electronic ground and excited states of the dicyanoacetylene radical cation: Assignment of vibronic spectrum and elucidation of nonradiative and radiative decay mechanisms

Vibronic interactions in the first five energetically lowest electronic states (X̃2Πu-Ã2Σg+-B̃2Σu+-C̃2Πg-D̃2Πu) of dicyanoacetylene radical cation (C4N2·+) and their effect on the nuclear dynamics are examined in this article. The spectroscopy of C4N2·+ is a subject of outstanding complexity and addressed by the [see, the recent article, J. Chem. Phys. 139, 184304 (2013)]. The energetic ordering of electronic states and the emission mechanism of the states seem to have ambiguity. Here we have undertaken a detailed theoretical study in an attempt to resolve it. A vibronic coupling Hamiltonian of the five electronic states mentioned above is constructed in a diabatic electronic basis and with the aid of ab initio quantum chemistry calculations. Quantum nuclear dynamics studies are carried out by both time-independent and time-dependent quantum mechanical methods. The vibronic spectrum is calculated and the progressions are identified in terms of vibrational modes and compared with experimental slow photoelectron spectroscopy results. Renner-Teller (RT) coupling within the degenerate electronic states (X̃, C̃ and D̃) and the pseudo-Renner-Teller (PRT) coupling among states are examined in detail to elucidate their impact on the vibronic structure of the state and its decay mechanism to the ground (X̃) electronic state. While the dynamics of the X̃ and D̃ states is somewhat simple, the same of the Ã, B̃ and C̃ states is outstandingly complex due to strong RT and PRT interactions.

Molecular Modelling for Reactor Design.

Chemical reactor modelling based on insights and data on a molecular level has become reality over the last few years. Multiscale models describing elementary reaction steps and full microkinetic schemes, pore structures, multicomponent adsorption and diffusion inside pores, and entire reactors have been presented. Quantum mechanical (QM) approaches, molecular simulations (Monte Carlo and molecular dynamics), and continuum equations have been employed for this purpose. Some recent developments in these approaches are presented, in particular time-dependent QM methods, calculation of van der Waals forces, new approaches for force field generation, automatic setup of reaction schemes, and pore modelling. Multiscale simulations are discussed. Applications of these approaches to heterogeneous catalysis are demonstrated for examples that have found growing interest over the last few years, such as metal-support interactions, influence of pore geometry on reactions, noncovalent bonding, reaction dynamics, dynamic changes in catalyst nanoparticle structure, electrocatalysis, solvent effects in catalysis, and multiscale modelling.

Photophysics of phenol and pentafluorophenol: The role of nonadiabaticity in the optical transition to the lowest bright 1ππ* state.

We report multimode vibronic coupling of the energetically low-lying electronic states of phenol and pentafluorophenol in this article. First principles nuclear dynamics calculations are carried out to elucidate the optical absorption spectrum of both of the molecules. This is motivated by the recent experimental measurements [S. Karmakar et al., J. Chem. Phys. 142, 184303 (2015)] on these systems. Diabatic vibronic coupling models are developed with the aid of adiabatic electronic energies calculated ab initio by the equation of motion coupled cluster quantum chemistry method. A nuclear dynamics study on the constructed electronic states is carried out by both the time-independent and time-dependent quantum mechanical methods. It is found that the nature of low-energy πσ* transition changes, and in pentafluorophenol the energy of the first two 1πσ* states, is lowered by about half an eV (vertically, relative to those in phenol), and they become energetically close to the optically bright first excited 1ππ* (S1) state. This results in strong vibronic coupling and multiple multi-state conical intersections among the ππ* and πσ* electronic states of pentafluorophenol. The impact of associated nonadiabatic effects on the vibronic structure and dynamics of the 1ππ* state is examined at length. The structured vibronic band of phenol becomes structureless in pentafluorophenol. The theoretical results are found to be in good accord with the experimental finding at both high energy resolution and low energy resolution.

Theoretical study of photodetachment spectroscopy of hydrogenated boron cluster anion H2B7- and its deuterated isotopomer.

Photodetachment spectroscopy of H2B7- and its deuterated isotopomer probing the energetically low-lying electronic states of the respective neutral cluster is theoretically investigated in this paper. The theoretical methodology is based on detailed quantum chemistry calculations of electronic state energies, construction of a vibronic coupling model in the diabatic electronic basis, and nuclear dynamics calculations from first principles using time-dependent and time-independent quantum mechanical methods. The theoretical model consists of five coupled electronic states and fifteen vibrational modes. Several reduced dimensional calculations are performed to identify the relevant vibrational modes contributing to the vibronic structure of electronic bands and the impact of non-adiabatic coupling on them. The low-energy part of the spectrum of both H2B7 and its deuterated analogue is assigned by examining the vibronic wavefunctions and the results are compared with the experimental findings. The nonadiabatic decay dynamics of the electronic excited states of the neutral clusters is examined at length.

Vibronic Coupling in the X̃2Πg-Ã2Πu Band System of Diacetylene Radical Cation.

Vibronic interactions in the two energetically lowest electronic states (X̃2Πg-Ã2Πu) of the diacetylene radical cation (C4H2•+) are theoretically examined here. The spectroscopy of these two electronic states of C4H2•+ has been a subject of considerable interest and measured in the laboratory by various groups. Inspired by numerous experimental data, we attempt here a detailed investigation of vibronic interactions within and between the doubly degenerate Π electronic states and their impact on the vibronic structure of each state. A vibronic coupling model is constructed in a diabatic electronic basis and with the aid of ab initio quantum chemistry calculations. The vibronic structures of the electronic states are calculated by time-independent and time-dependent quantum mechanical methods. The progression of vibrational modes in the vibronic band is identified, assigned, and compared with the literature data. The nonradiative internal conversion dynamics is also examined and discussed.

Photophysics and photostability of pyrimidine molecule and its radical cation: a theoretical study

ABSTRACTMultistate and multimode vibronic dynamics on first five coupled (S1–S2–S3–S4–S5) electronic states of pyrimidine molecule and first four ( – – –) electronic states of pyrimidine radical cation are investigated with the help of ab initio electronic structure calculations of potential energy surfaces (PESs) and first principle quantum dynamical methods. Excited electronic PESs are generated at the MRCI and Equation of Motion Couple Cluster Single and Double (EOM-CCSD) level of theory. Several low-lying conical intersections among various electronic states are found and their impact on the nuclear dynamics is discussed. The simulation of nuclear motion on the underlying coupled electronic states of pyrimidine molecule and its radical cation is examined by both time-independent and time-dependent quantum mechanical methods. In the latter case, a wave packet propagation-based method within multi-configurational time-dependent Hartree algorithm is employed. The theoretical results are verified with the experimental photoelectron spectroscopy, vacuum ultraviolet spectroscopy and resolved (<10 meV) vibrational energy level spectrum of pyrimidine molecule which has good impact on astrobiology.

In Process Citation

In continuation to our earlier work [Sarkar et al., Mol. Phys. 2015, 113, 3073–3084], we present here the vibronic structure and nonradiative decay dynamics of energetically low-lying electronic states of CH2F2+. Interesting comparison is made with the results obtained for the deuterated isotopomer CD2F2+. The results are compared with both broad band as well as high-resolution experimental spectroscopy data available in the literature. The progression of vibrational modes in the spectra is identified, assigned and discussed in relation to the assignments available in the literature. Both time-independent and time-dependent quantum mechanical methods are used to carry out nuclear dynamics calculations. The underlying potential energy surfaces and their coupling surfaces are constructed by rigorous ab initio quantum chemistry calculations.

Jahn-Teller and pseudo-Jahn-Teller effects in trifluoromethane radical cation

Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) effects in the ground, first and second excited electronic states of the trifluoromethane radical cation are theoretically examined here. Extensive ab initio computation of electronic potential energy surfaces and their coupling surfaces are performed. Full quantum dynamics are obtained by both time-independent and time-dependent quantum mechanical methods. This system belongs to (E+A)⊗e JT-PJT family. Our results compare well with the experimental data. JT interactions are fairly strong in the second excited B˜2E electronic state and the PJT interaction between A˜2A2 - B˜2E electronic states is stronger which cause an increase of the spectral line density of the vibronic spectrum.

Ultrafast dynamics of electronically excited diborane radical cation

Full-dimensional quantum mechanical study is carried out to investigate the vibronic structure and internal conversion dynamics of the energetically low-lying electronic excited states of \( {\text{B}}_{{\text{2}}} {\text{H}}_{6}^{{ \cdot + }} \). A model diabatic electronic Hamiltonian, within the quadratic vibronic coupling approach comprising of five energetically low-lying electronic states, is developed, and the parameters of the Hamiltonian are estimated by performing extensive ab initio electronic structure calculations using the equation-of-motion coupled-cluster singles and doubles method. The nuclear dynamics on the constructed diabatic electronic states is studied by employing both time-independent and time-dependent quantum mechanical methods. Theoretically calculated vibronic structure of the electronic states is found to be in excellent accord with the available experimental results. Extremely strong vibronic interactions among the electronic states result highly overlapping and diffuse vibronic bands and complicate the assignment of vibronic progression. Examination of non-radiative internal conversion dynamics revealed very short lifetime (\(<\)60 fs) of the excited electronic states of \( {\text{B}}_{{\text{2}}} {\text{H}}_{6}^{{ \cdot + }} \).

Time-dependent potential-functional embedding theory

We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods.

Theoretical study of photodetachment processes of anionic boron cluster. III. ${\rm B}_7^-$B7−

Photodetachment spectroscopy of B(7)(-) is theoretically studied in this paper. Calculated photodetachment bands are compared with the available experimental results and assigned to the vibronic structure of the electronic ground and excited states of the neutral B7 cluster. The complex structure of photodetachment bands is found to arise from many stable isomers of B(7)(-) of different symmetry point group. In this study we focus on three most stable isomers of B(7)(-) and examine their photodetachment bands. Extensive quantum chemistry calculations are carried out to establish the potential energy surfaces and the coupling surfaces of the electronic states of neutral B7 originating from each of the three isomers. A diabatic electronic ansatz is employed and the nuclear dynamics is studied both by time-independent and time-dependent quantum mechanical methods. Both agreements and discrepancies of the theoretical results with the experimental findings are discussed.

Theoretical Study on Molecules of Interstellar Interest. I. Radical Cation of Noncompact Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs), in particular, their radical cation (PAH(+)), have long been postulated to be the important molecular species in connection with the spectroscopic observations in the interstellar medium. Motivated by numerous important observations by stellar as well as laboratory spectroscopists, we undertook detailed quantum mechanical studies of the structure and dynamics of electronically excited PAH(+) in an attempt to establish possible synergism with the recorded data. In this paper, we focus on the quantum chemistry and dynamics of the doublet ground (X̃) and low-lying excited (Ã, B̃, and C̃) electronic states of the radical cation of tetracene, pentacene, and hexacene molecule. This study is aimed to unravel photostability, spectroscopy, and time-dependent dynamics of their excited electronic states. In order to proceed with the theoretical investigations, we construct suitable multistate and multimode Hamiltonians for these systems with the aid of extensive ab initio calculations of their electronic energy surfaces. The diabatic coupling surfaces are derived from the calculated adiabatic electronic energies. First principles nuclear dynamics calculations are then carried out employing the constructed Hamiltonians and with the aid of time-independent and time-dependent quantum mechanical methods. The theoretical results obtained in this study are found to be in good accord with those recorded in experiments. The lifetime of excited electronic states is estimated from their time-dependent dynamics and compared with the available data.

Photoabsorption of carbon monoxide: a time-dependent quantum mechanical study

Photoabsorption cross-section values are computed for the A1Π–X1Σ+ transition in 12C16O by a time-dependent quantum mechanical method. The computed oscillator strength values are shown to be in good agreement with the available experimental and theoretical values. The small differences between our computed oscillator strength values and the experimental results could be accounted for by the weak interactions between the A1Π state and triplet states (a′3Σ+, e3Σ− and d3Δ) that cross the PEC of the A state near its minimum. Calculations for different isotopologues of CO (12C17O,12C18O and 13C16O) reveal a mass dependence that becomes more significant for higher vibrational levels.

Water dissociation on Cu (111): Effects of molecular orientation, rotation, and vibration on reactivity

Three-dimensional time-dependent quantum mechanical method has been used to study the influence of orientation, rotation, and vibration on the dissociation of water molecule on Cu(111) surface, using London-Eyring-Polanyi-Sato potential energy surface. Our calculations show that dependency of dissociation probability on the initial orientation of the molecule changes with the vibrational state of the molecule. It has also been found that for v(0) = 0 and 1, where v(0) stands for the vibrational state of the pseudo diatomic HO-H, the rotational excitation of the molecule increases the reactivity, whereas for v(0) = 2, the rotational excitation of the molecule decreases the reactivity. Vibrational excitation of the molecule greatly enhances the dissociation probability.

Emergence of Excited-State Plasmon Modes in Linear Hydrogen Chains from Time-Dependent Quantum Mechanical Methods

Explicitly time-dependent configuration-interaction theory is used to predict a new type of plasmonic behavior in linear hydrogen chains. After an intense ultrashort laser pulse brings the system into a broad superposition of excited states, the electronic dipole of the entire chain oscillates coherently, and the system is predicted to emit radiation at energies significantly lower than the first absorption band. A simple classical model accurately predicts the energy of this plasmon resonance for different hydrogen chain lengths and electron densities, demonstrating that collective, free-electron-like behavior can arise in chains of as few as 20 hydrogen atoms. The excitation mechanism for this plasmonic resonance is a highly nonlinear, multiphoton process, different from the linear excitation of ordinary surface plasmons.

Photophysics of fluorinated benzene. II. Quantum dynamics

Nuclear dynamics in the coupled electronic states of mono-, di-(ortho and meta), and pentafluorobenzene molecules is investigated here. Attempts are specifically made to understand the complexity and broadening of the recorded gas phase electronic absorption spectra of these molecules. Justification is also provided for the low quantum yield of fluorescence emission with increasing number of fluorine substitutions. The nuclear dynamics is simulated from first principles both by time-independent and time-dependent quantum mechanical methods. Potential energy surfaces of the low-lying excited electronic states of these molecules constructed in Paper I [Mondal and Mahapatra, J. Chem. Phys. 133, 084304 (2010)] are employed for the purpose. Theoretical results presented in this paper are compared with the available experimental data and the agreement between the two is found to be excellent. While structured electronic absorption bands are observed for the S(1) state of mono- and difluorobenzene molecules, the same for the pentafluorobenzene is broad and structureless. Occurrence of S(1)-S(2) conical intersections in pentafluorobenzene leads to a nonradiative internal conversion of the S(1) state in approximately 165 fs and contributes to the broadening of the S(1)<--S(0) absorption band and a biexponential decay of its fluorescence emission.

Vibronic dynamics in the low-lying coupled electronic states of methyl cyanide radical cation

Static and dynamic aspects of the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) interactions between the ground and first excited electronic states of the methyl cyanide radical cation are theoretically investigated here. The latter involves construction of a theoretical model by ab initio computation of electronic potential energy surfaces and their coupling surfaces and simulation of the nuclear dynamics employing time-independent and time-dependent quantum mechanical methods. The present system represents yet another example belonging to the ( E + A) ⊗ e JT–PJT family, with common JT and PJT active degenerate (e) vibrational modes. The theoretical results are found to be in very good accord with the recent experimental data revealing that the JT interactions are particularly weak in the ground X ∼ 2 E electronic manifold of methyl cyanide radical cation, On the other hand, the PJT interactions of this ground electronic manifold with the first excited A ∼ 2 A 1 electronic state of the radical cation are stronger which cause an increase of the spectral line density. The effect of deuteration on the JT–PJT dynamics of the methyl cyanide radical cation is also discussed.