Quantum molecular dynamics

Electron or ion dynamics are treated using spin‐dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin‐dependent terms, all of which are of order c⁰ in the nonrelativistic regime of particle velocity, where c is the speed of light. The many‐body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time‐dependent Dirac or the time‐dependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

Ab initio quantum chemistry and molecular dynamics simulations studies of LiPF6/poly(ethylene oxide) interactions

Ab initio and molecular mechanics studies of LiPF₆ and the interaction of the salt with the poly(ethylene oxide) (PEO) oligomer dimethylether have been performed. Optimized geometries and energies of Li⁺/PF₆^? complexes obtained from quantum chemistry revealed a preference for C_3V symmetry structures for Li⁺–P separations under 2.8 Å, C_2V symmetry for Li⁺–P in the range of 2.8–3.3 Å and C_4V symmetry for Li⁺–P separations larger than 3.3 Å. Electron correlation effects were found to make an insignificant contribution to binding in the Li⁺/PF₆^? complex. By contrast, analogous studies of PF₆^?/PF₆^? and PF₆^?/dimethyl ether complexes revealed important contributions of electron correlation to the complex interaction energy. A molecular mechanics force field for simulations of PEO/LiPF₆ melts was parameterized to reproduce the geometries and energies of Li⁺/PF₆^?, PF₆^?/PF₆^?, PF₆^?/dimethylether complexes. Molecular dynamics simulations of PEO/LiPF₆ melts were performed to validate this quantum chemistry‐based force field. Accurate reproduction of the increase in solution density with addition of salt was found while the electrical conductivity of PEO/LiPF₆ solutions was found to be within an order of magnitude of the experimental values. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 641–654, 2001     

Spectroscopic constants and molecular properties of the X2Π and a4Σ− electronic states of the SiF radical

The potential energy curves (PECs) of the X²Π and a⁴Σ^? electronic states of the SiF radical have been studied by an ab initio quantum chemical method. The calculations have been made using the complete active space self‐consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation‐consistent basis sets. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third‐order Douglas–Kroll Hamiltonian approximation. The relativistic corrections are made at the level of cc‐pV5Z basis set. The core‐valence correlation corrections are performed using the cc‐pCV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the total‐energy extrapolation scheme. Using these PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs obtained by the MRCI+Q/CV+DK+56 calculations, the vibrational levels, inertial rotation, and centrifugal distortion constants of the first 20 vibrational state of each electronic state are calculated when the rotational quantum number J equals zero. Comparison with the Rydberg‐Klein‐Rees (RKR) data shows that the present results are reliable and accurate. The molecular constants of the X²Π and a⁴Σ^? electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Chemical reaction dynamics of PeCB and TCDD decomposition: A tight‐binding quantum chemical molecular dynamics study with first‐principles parameterization

The decomposition reaction dynamics of 2,3,4,4′,5‐penta‐chlorinated biphenyl (2,3,4,4′,5‐PeCB), 3,3′,4,4′,5‐penta‐chlorinated biphenyl (3,3′,4,4′,5‐PeCB), and 2,3,7,8‐tetra‐chlorinated dibenzo‐p‐dioxin (2,3,7,8‐TCDD) was clarified for the first time at atomic and electronic levels, using our novel tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization. The calculation speed of our new method is over 5000 times faster than that of the conventional first‐principles molecular dynamics method. We confirmed that the structure, energy, and electronic states of the above molecules calculated by our new method are quantitatively consistent with those by first‐principles calculations. After the confirmation of our methodology, we investigated the decomposition reaction dynamics of the above molecules and the calculated dynamic behaviors indicate that the oxidation of the 2,3,4,4′,5‐PeCB, 3,3′,4,4′,5‐PeCB, and 2,3,7,8‐TCDD proceeds through an epoxide intermediate, which is in good agreement with the previous experimental reports and consistent with our static density functional theory calculations. These results proved that our new tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization is an effective tool to clarify the chemical reaction dynamics at reaction temperatures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Pattern recognition in molecular quantum mechanics

It is shown that the classical concept of an open system does not encompass quantal systems but has to be replaced by the non-Boolean notion of an entangled system. Molecular, chemical, or biological phenomena can be considered to be reduced to a fundamental theory like quantum mechanics only if the fundamental and the phenomenological theories are formally and interpretatively connected, and if the classifications used in the empirical sciences are shown to follow from a single set of fundamental dynamical laws. These conditions enforce a non-statistical and ontic interpretation of quantum mechanics, hence a non-Boolean calculus of propositions. In this interpretation the notion of a world state is well-defined, its Schmidt-decomposition defines a background-dependent model state for molecular systems and creates the phenomena we can observe. To any molecular system there is associated in an objective way a nonnegative number which we call the integrity. The integrity measures the inherent fuzziness of the system concept in a holistic theory, and is used to define recognizable molecular patterns.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Polarization and assignment of the two-photon excitation spectrum of benzene vapor

The two-photon excitation (TPE) of benzene fluorescence in the vapor phase at 60 torr is reported for the total-energy region from 38 086 cm^?1 to 42 441 cm^?1 using both circular and linear polarized light from a nitrogen-pumped dye-laser. The theory of the polarization dependence of the vibronic transitions in benzene is briefly reviewed, and it is seen how transitions involving vibrations of b_1u symmetry are expressly forbidden for this type of TPE experiment in which the two photons are identical. Five vibronic origins with distinctive rotational contours and polarization dependence are identified in the TPE spectrum. The υ₁₄(b_2u) vibronic origin at 1570 cm^?1 (above the electronic origin of the ^IB_2u state) stands out very prominently in the linear polarized spectrum, but nearly disappears in the circular polarized spectrum. This striking polarization dependence indicates a significant contribution of A_2u electronic states to the intermediate states of this TPE vibronic transition. The relatively great strength of the υ₁₄ band may be due to vibronic borrowing by the b_2u mode from the ground electronic state (A_1g).     

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band‐gap energies of the , Pc, and structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path‐integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero‐point energy and temperature‐induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band‐gaps substantially, leading to metallization of the and Pc phases via band overlap; the effect on the band‐gap of the structure is less pronounced. Our combined DMC‐PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band‐gap energy and vibron modes. This strong coupling induces a band‐gap reduction of more than 2.46 eV in high‐pressure solid molecular hydrogen. Comparing our DMC‐PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.     

Efficient evaluation of the accuracy of molecular quantum dynamics on an approximate analytical or interpolated ab initio potential energy surface

Ab initio electronic structure methods have reached a satisfactory accuracy for the calculation of static properties, but remain too expensive for quantum dynamical calculations. Recently, an efficient semiclassical method was proposed to evaluate the accuracy of quantum dynamics on an approximate potential without having to perform the expensive quantum dynamics on the accurate potential. Here, this method is applied for the first time to evaluate the accuracy of quantum dynamics on an approximate analytical or interpolated potential in comparison to the quantum dynamics on an accurate potential obtained by an ab initio electronic structure method. Specifically, the vibrational dynamics of H₂ on a Morse potential is compared with that on the full CI potential, and the photodissociation dynamics of CO₂ on a LEPS potential with that on the excited ¹Π surface computed at the EOM‐CCSD/aug‐cc‐pVDZ level of theory. Finally, the effect of discretization of a potential energy surface on the quantum dynamics is evaluated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2426–2435, 2010     

Das Franck‐Condon‐Prinzip

The quantum mechanical model is fully recognized and used for rotational and vibronic transitions in molecules, where according to the model, transitions occur between discrete, the resonance condition matching states, only. It is also accepted that selection rules are implied for rotational and vibronic transitions. Why is it so hard to recognize that this established quantum mechanical model is also valid for vibronic transitions, where the Franck‐Condon principle instead of a selection rule applies to the population of vibronic states in the electronic excitation state? In any case, supposed illustrative and comfortable but wrong explanations, also if they are widely used, must not replace more sophisticated, correct quantum mechanical models. In scientific publications as well as in teaching only the quantum mechanical version of the Franck‐Condon principle should be used. Terms like “Franck‐Condon point” or ”Franck‐Condon region of the photochemical reaction" should be avoided in the future.     

Absolute quantum yield measurements for the formation of oxygen atoms after UV laser excitation of SO2 at 222-4 nm

The dynamics of formation of oxygen atoms after UV photoexcitation of SO₂ in the gas-phase was studied by pulsed laser photolysis-laser-inducedfluorescence ‘pump-and-probe’ technique in a flow reactor. SO₂ at room-temperature was excited at the KrCl excimer laser wavelength (222.4 nm) and O(³P_j) photofragments were detected under collision-free conditions by vacuum ultraviolet laser-induced fluorescence. The use of narrow-band probe laser radiation, generated viaresonant third-order sum-difference frequency conversion of dye laser radiation in Krypton, allowed the measurement of the nascent O(³P_j=2,1,0) fine-structure state distribution:n _j=2/n_j=1/n_j=0 = (0.88 ± 0.02)/(0.10 ± 0.01)/(0.02 ± 0.01). Employing NO₂photolysis as a reference, a value of Φ₀(³P) = 0.13 ± 0.05 for the absolute O(³P) atom quantum yield was determined. The measured O(³P) quantum yield is compared with the results of earlier fluorescence quantum yield measurements. A suitable mechanism is suggested in which the dissociation proceeds via internal conversion from high rotational states of the initially excited SO₂(~C¹B₂ (1, 2, 2) vibronic level to nearby continuum states of the electronic ground state.     

Stark quantum beat spectroscopy of polyatomic molecules

We derive analytical expressions for Stark quantum beat signals of polyatomic molecules and discuss them with regard to molecular and geometrical parameters. The general treatment is specified for near prolate asymmetric rotor molecules and a method for determining rotational constants and all components of the dipole moment of electronically excited polyatomic molecules is presented. The method is tested and illustrated for the vibrationlessS ₁ state of deuterated propynal (HC ≡ CCDO,C _s symmetry) and its lowest frequency non-totally symmetric state 12¹. The results of the vibrationless state are compared with structural data reported in the literature. For the 12¹ state we obtainA=1.5004(43) cm^?1,B=0.16131(34) cm^?1,C=0.14623(34) cm^?1, and the components of the electric dipole moment in the molecular plane μ _a =?0.88(2)D, μ _b =1.03(2)D. Furthermore, it is shown that the modulation depth of Stark quantum beat signals can be utilized to quantify the contribution of the individual components of the transition moment to the total emission.     

Nuclear‐Spin‐Induced Cotton–Mouton Effect in a Strong External Magnetic Field

Novel, high‐sensitivity and high‐resolution spectroscopic methods can provide site‐specific nuclear information by exploiting nuclear magneto‐optic properties. We present a first‐principles electronic structure formulation of the recently proposed nuclear‐spin‐induced Cotton–Mouton effect in a strong external magnetic field (NSCM‐B). In NSCM‐B, ellipticity is induced in a linearly polarized light beam, which can be attributed to both the dependence of the symmetric dynamic polarizability on the external magnetic field and the nuclear magnetic moment, as well as the temperature‐dependent partial alignment of the molecules due to the magnetic fields. Quantum‐chemical calculations of NSCM‐B were conducted for a series of molecular liquids. The overall order of magnitude of the induced ellipticities is predicted to be 10^?11–10^?6 rad T^?1 M ^?1 cm^?1 for fully spin‐polarized nuclei. In particular, liquid‐state heavy‐atom systems should be promising for experiments in the Voigt setup.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Evaluation of molecular integral of Cartesian Gaussian type basis function with complex‐valued center coordinates and exponent via the McMurchie–Davidson recursion formula,and its application to electron dynamics

McMurchie–Davidson recursion formula is extended to derive the ab initio molecular integrals with higher angular quantum number complex Gaussian type basis function which has complex‐valued center coordinates and a complex‐valued exponent. Using the analytical recursion formulae, some calculations of electronic dynamics after beta decay of tritium hydride molecular ion HT⁺ are performed by a quantum wave packet method with thawed Gaussian basis functions of s‐ and p‐type. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The quantum theory of atoms in positronic molecules: A case study on diatomic species

This article presents the first systematic study of a series of diatomic positronic species using the recently proposed regional approach: the quantum theory of atoms in positronic molecules (QTAIPM). This survey includes the LiH,e⁺, NaH,e⁺, LiF,e⁺, NaF,e⁺, BeO,e⁺, MgO,e⁺, CN^?,e⁺, and OH^?,e⁺ species as typical examples. The computational algorithm of the whole analysis is communicated and reviewed in detail. The topological analysis of the joint density distribution reveals topological structures similar to those observed for the purely electronic systems; that is, each system decomposes into two quantum atoms. By considering some of the regional properties of these quantum atoms, it is demonstrated that the positron affects them seriously through two different mechanisms: direct and indirect contributions, the latter refers to electronic and geometric relaxations. The computational results clearly reveal the fact that the regional properties of the quantum atoms of positronic molecules are not deducible from their purely electronic counterparts; thus, an independent analysis is required for each positronic molecule. The positronic population is considered as a typical regional property showing that the attachment of a positron to a purely electronic system enhances the polarization of the electronic distribution. The concept of regional positron affinities is also introduced and discussed as a nonroutine application of the QTAIPM. The results of this article set the stage for further study on the quantum atoms of polyatomic positronic species. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Kinetic Analysis and Structural Interpretation of Competitive Ligand Binding for NO Dioxygenation in Truncated Hemoglobin N

The conversion of nitric oxide (NO) into nitrate (NO₃^?) by dioxygenation protects cells from lethal NO. Starting from NO‐bound heme, the first step in converting NO into benign NO₃^? is the ligand exchange reaction FeNO+O₂→FeO₂+NO, which is still poorly understood at a molecular level. For wild‐type (WT) truncated hemoglobin N (trHbN) and its Y33A mutant, the calculated barriers for the exchange reaction differ by 1.5 kcal mol^?1, compared with 1.7 kcal mol^?1 from experiment. It is directly confirmed that the ligand exchange reaction is rate‐limiting in trHbN and that entropic contributions account for 75 % of the difference between the WT and the mutant. Residues Tyr 33, Phe 46, Val 80, His 81, and Gln 82 surrounding the active site are expected to control the reaction path. By comparison with electronic structure calculations, the transition state separating the two ligand‐bound states was assigned to a ²A state.