Mixed quantum-classical simulations of charge transport in organic materials: numerical benchmark of the Su-Schrieffer-Heeger model

The electron-phonon coupling is critical in determining the intrinsic charge carrier and exciton transport properties in organic materials. In this study, we consider a Su-Schrieffer-Heeger (SSH) model for molecular crystals, and perform numerical benchmark studies for different strategies of simulating the mixed quantum-classical dynamics. These methods, which differ in the selection of initial conditions and the representation used to solve the time evolution of the quantum carriers, are shown to yield similar equilibrium diffusion properties. A hybrid approach combining molecular dynamics simulations of nuclear motion and quantum-chemical calculations of the electronic Hamiltonian at each geometric configuration appears as an attractive strategy to model charge dynamics in large size systems "on the fly," yet it relies on the assumption that the quantum carriers do not impact the nuclear dynamics. We find that such an approximation systematically results in overestimated charge-carrier mobilities, with the associated error being negligible when the room-temperature mobility exceeds ～4.8 cm(2)∕Vs (～0.14 cm(2)/Vs) in one-dimensional (two-dimensional) crystals.     

Finite size scaling for the atomic Shannon-information entropy

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.     

Equilibrium and non-equilibrium phase transitions studied by adiabatic calorimetry

An adiabatic calorimetry was used for some investigations of equilibrium and non-equilibrium phase transitions. For one of the substances studied (4,4′-di-n-heptyloxyazoxybenzene) it was possible to determine temperature dependence of an order parameter and number of clusters of high temperature phase in a region of a phase transition. For another substance (liquid 3,4 dimethylpiridine) an anomaly on the specific heat curves was interpreted as being responsible for a decay of molecules’ clusters. Non-equilibrium phase transitions were investigated for some liquid crystal substances. The process of transformation between metastable and stable phases was described quantitatively. The conclusions obtained concern the stability of metastable phases.     

Flying onto global minima on potential energy surfaces: A swarm intelligence guided route to molecular electronic structure

A novel quantum‐classical recipe for locating the global minimum on the potential energy surface of a large molecule and simultaneously predicting the associated electronic charge distribution is developed by interfacing the classical particle swarm optimization with a near optimal unitary evolution scheme for the trial one electron density matrix. The unitary transformation is generated by an antihermitian matrix linked to the molecular electronic Hamiltonian at the instantaneous nuclear configurations discovered by the swarm as it flies. The algorithm is used to predict the extensive reorganization of electronic charge distribution and bond lengths in polythiophene oligomers on doping at various levels.     

Excited state molecular dynamics simulations of nonlinear push–pull chromophores

Julolidinemalononitrile, p-nitroaniline, and julolidinyl-n-N,N^′-diethylthiobarbituric acid are studied with ground and excited state molecular dynamics simulations in conjunction with the collective electronic oscillator formalism and Onsager’s cavity model. Ground and excited state geometries are calculated in the gas phase and four solvents. The results are interpreted in the context of a two-state valence bond model for charge-transfer transitions of conjugated organic molecules, and are compared to recent resonant Raman experimental results. The calculated geometries are qualitatively consistent with both the two-state model and experiment. In addition, calculated transition density matrices are presented to visualize the changes in charge distribution accompanying photoexcitation.     

Origin and Prediction of Highly Specific Bond Cleavage Sites in the Thermal Activation of Intact Protein Ions

Predicting the fragmentation patterns of proteins would be beneficial for the reliable identification of intact proteins by mass spectrometry. However, the ability to accurately make such predictions remains elusive. An approach to predict the specific cleavage sites in whole proteins resulting from collision-induced dissociation by use of an improved electrostatic model for calculating the proton configurations of highly-charged protein ions is reported. Using ubiquitin, cytochrome c, lysozyme and β-lactoglobulin as prototypical proteins, this approach can be used to predict the fragmentation patterns of intact proteins. For sufficiently highly charged proteins, specific cleavages occur near the first low-basicity amino acid residues that are protonated with increasing charge state. Hybrid QM/QM′ (QM=quantum mechanics) and molecular dynamics (MD) simulations and energy-resolved collision-induced dissociation measurements indicated that the barrier to the specific dissociation of the protonated amide backbone bond is significantly lower than competitive charge remote fragmentation. Unlike highly charged peptides, the protons at low-basicity sites in highly charged protein ions can be confined to a limited sequence of low-basicity amino acid residues by electrostatic repulsion, which results in highly specific fragmentation near the site of protonation. This research suggests that the optimal charge states to form specific sequence ions of intact proteins in higher abundances than the use of less specific ion dissociation methods can be predicted a priori.     

Enveloping distribution sampling: a method to calculate free energy differences from a single simulation

The authors present a method to calculate free energy differences between two states A and B "on the fly" from a single molecular dynamics simulation of a reference state R. No computer time has to be spent on the simulation of intermediate states. Only one state is sampled, i.e., the reference state R which is designed such that the subset of phase space important to it is the union of the parts of phase space important to A and B. Therefore, an accurate estimate of the relative free energy can be obtained by construction. The authors applied the method to four test systems (dipole inversion, van der Waals interaction perturbation, charge inversion, and water to methanol conversion) and compared the results to thermodynamic integration estimates. In two cases, the enveloping distribution sampling calculation was straightforward. However, in the charge inversion and the water to methanol conversion, Hamiltonian replica-exchange molecular dynamics of the reference state was necessary to observe transitions in the reference state simulation between the parts of phase space important to A and B, respectively. This can be explained by the total absence of phase space overlap of A and B in these two cases.     

Toward quantitative prediction of molecular fluorescence quantum efficiency: role of duschinsky rotation

It is a highly desirable but difficult task to predict the molecular fluorescence quantum efficiency from first principles. The molecule in the excited state can undergo spontaneous radiation, conversion of electronic energy to nuclear motion, or chemical reaction. For relatively large molecules, it is impossible to obtain the full potential energy surfaces for the ground state and the excited states to study the excited-state dynamics. We show that, under harmonic approximation by considering the Duschinsky rotation effect, the molecular fluorescence properties can be quantitatively calculated from first principles coupled with our correlation function formalism for the internal conversion. In particular, we have explained the peculiar fluorescence behaviors of two isomeric compounds, cis,cis-1,2,3,4-tetraphenyl-1,3-butadiene and 1,1,4,4-tetraphenyl-butadiene, the former being nonemissive in solution and strongly emissive in aggregation or at low temperature, and the latter being strongly emissive in solution. The roles of low-frequency phenyl ring twist motions and their Duschinsky mode mixings are found to be crucial, especially to reveal the temperature dependence. As an independent check, we take a look at the well-established photophysics of 1,4-diphenylbutadiene for its three different conformers. Both the calculated radiative and nonradiative rates are in excellent agreement with the available experimental measurements.     

Rényi entropy of the U(3) vibron model

Rényi entropies and variances are determined in the vibron model. They provide a sharp detector for the quantum (shape) phase transition (from linear to bent) at the critical value ξ _c of a control parameter ξ. Numerical results are complemented and compared with a variational approximation in terms of parity-symmetry-adapted coherent (Schödinger’s catlike) states, which provide a good approximation to describe delocalization properties of the ground state of vibron models across the critical point for N-size molecules.     

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.     

Generalisation of a property of Hamiltonians depending linearly upon a parameter: application to a model of inert gas matrix effect on vibrational spectra

The property that the ground state eigenvalue of a Hamiltonian, depending linearly upon a parameter, is a concave function of this parameter is generalised. It is shown that the concavity or convexity of the nth eigenvalue depends upon the relative weights of the states below the nth state, with respect to those above it, in a weighted sum of transition energies. The result is illustrated on a model of matrix effect on gas phase molecular vibrational spectra. The model is applied to the 2,3-naphthyne molecule.     

Potential energy surfaces and dynamics of Ni2+ ion aqueous solution: molecular dynamics simulation of the electronic absorption spectrum

We develop a model effective Hamiltonian for describing the electronic structures of first-row transition metals in aqueous solutions using a quasidegenerate perturbation theory. All the states consisting of 3d(n) electronic configurations are determined by diagonalizing a small effective Hamiltonian matrix, where various intermolecular interaction terms such as the electrostatic, polarization, exchange, charge transfer, and three-body interactions are effectively incorporated. This model Hamiltonian is applied to constructing the ground and triplet excited states potential energy functions of Ni(2+) in aqueous solution, based on the ab initio multiconfiguration quasidegenerate perturbation theory calculations. We perform molecular dynamics simulation calculations for the ground state of Ni(2+) aqueous solution to calculate the electronic absorption spectral shape as well as the ground state properties. Agreement between the simulation and experimental spectra is satisfactory, indicating that the present model can well describe the Ni(2+) excited state potential surfaces in aqueous solution.     

Charge transfer in photoacids observed by stark spectroscopy

The charge redistribution upon photoexcitation is investigated for a series of pyrene photoacids to better understand the driving force behind excited-state proton-transfer processes. The changes in electric dipole for the lowest two electronic transitions ( (1)L b and (1)L a) are measured by Stark spectroscopy, and the magnitudes of charge transfer of the protonated and deprotonated states are compared. For neutral photoacids studied here, the results show that the amount of charge transfer depends more upon the electronic state that is excited than the protonation state. Transitions from the ground state to the (1)L b state result in a much smaller change in electric dipole than transitions to the (1)L a state. Conversely, for the cationic (ammonium) photoacid studied, photoexcitation of a particular electronic state results in much smaller charge transfer for the protonated state than for the deprotonated state.     

CNDOL: A fast and reliable method for the calculation of electronic properties of very large systems. Applications to retinal binding pocket in rhodopsin and gas phase porphine

Very large molecular systems can be calculated with the so called CNDOL approximate Hamiltonians that have been developed by avoiding oversimplifications and only using a priori parameters and formulas from the simpler NDO methods. A new diagonal monoelectronic term named CNDOL/21 shows great consistency and easier SCF convergence when used together with an appropriate function for charge repulsion energies that is derived from traditional formulas. It is possible to obtain a priori molecular orbitals and electron excitation properties after the configuration interaction of single excited determinants with reliability, maintaining interpretative possibilities even being a simplified Hamiltonian. Tests with some unequivocal gas phase maxima of simple molecules (benzene, furfural, acetaldehyde, hexyl alcohol, methyl amine, 2,5 dimethyl 2,4 hexadiene, and ethyl sulfide) ratify the general quality of this approach in comparison with other methods. The calculation of large systems as porphine in gas phase and a model of the complete retinal binding pocket in rhodopsin with 622 basis functions on 280 atoms at the quantum mechanical level show reliability leading to a resulting first allowed transition in 483 nm, very similar to the known experimental value of 500 nm of "dark state." In this very important case, our model gives a central role in this excitation to a charge transfer from the neighboring Glu(-) counterion to the retinaldehyde polyene chain. Tests with gas phase maxima of some important molecules corroborate the reliability of CNDOL/2 Hamiltonians.     

Quantum charge transport and conformational dynamics of macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a quantum charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder. We argue that collapsing conducting polymers may represent a physical realization of quantum small-world networks with dynamical rewiring probability.     

Formation of negative ions <Emphasis Type="Italic">via</Emphasis> resonant low-energy electron capture by cysteine and cystine methyl esters

The processes of resonance low-energy free electron attachment to methyl esters of some sulfur-containing amino acids were studied. The long-lived molecular negative ions of cystine dimethyl ester formed in the valence state via the Feshbach nuclear excited resonance mechanism were detected by mass spectrometry. The reactions of disulfide bond dissociation were identified in an electron energy range of 0—1 eV. They can be considered as model reactions regarding processes of peptide decomposition due to the resonance interaction with low-energy electrons. Predissociation of short-lived molecular ions of cysteine methyl ester formed by capture of electrons with energies of ~1.6 eV is accompanied by the intra-ionic transfer of negative charge from the carbonyl group to the sulfur atom leading to the elimination from the latter of hydrogen atom.     

The crystal structure and vibrational spectra of two molecules emitting dual fluorescence: 4-(1H-Pyrrol-1-yl)benzonitrile (PBN) and 5-cyano-2-(1pyrrolyl)-pyridine (CPP)

Crystal structures and vibrational spectra are reported for the two title molecules which exhibit dual fluorescence due to the existence of a low lying charge transfer excited state. The data show that in the ground state PBN is twisted whereas CPP is planar, and the crystal structures are quite different. The experimental spectra are in very good agreement with quantum mechanical calculations, which also predict considerable differences between the vibrational spectra of CPP in the ground state and in the charge transfer excited state.     

Spectroscopic consequences of a mixed valence excited state: quantitative treatment of a dihydrazine diradical dication

A model for the quantitative treatment of molecular systems possessing mixed valence excited states is introduced and used to explain observed spectroscopic consequences. The specific example studied in this paper is 1,4-bis(2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl)-2,3,5,6-tetramethylbenzene-1,4-diyl dication. The lowest energy excited state of this molecule arises from a transition from the ground state where one positive charge is associated with each of the hydrazine units, to an excited state where both charges are associated with one of the hydrazine units, that is, a Hy-to-Hy charge transfer. The resulting excited state is a Class II mixed valence molecule. The electronic emission and absorption spectra, and resonance Raman spectra, of this molecule are reported. The lowest energy absorption band is asymmetric with a weak low-energy shoulder and an intense higher energy peak. Emission is observed at low temperature. The details of the absorption and emission spectra are calculated for the coupled surfaces by using the time-dependent theory of spectroscopy. The calculations are carried out in the diabatic basis, but the nuclear kinetic energy is explicitly included and the calculations are exact quantum calculations of the model Hamiltonian. Because the transition involves the transfer of an electron from the hydrazine on one side of the molecule to the hydrazine on the other side and vice versa, the two transitions are antiparallel and the transition dipole moments have opposite signs. Upon transformation to the adiabatic basis, the dipole moment for the transition to the highest energy adiabatic surface is nonzero, but that for the transition to the lowest surface changes sign at the origin. The energy separation between the two components of the absorption spectrum is twice the coupling between the diabatic basis states. The bandwidths of the electronic spectra are caused by progressions in totally symmetric modes as well as progressions in the modes along the coupled coordinate. The totally symmetric modes are modeled as displaced harmonic oscillators; the frequencies and displacements are determined from resonance Raman spectra. The absorption, emission, and Raman spectra are fit simultaneously with one parameter set. The coupling in the excited electronic state H(ab)(ex) is 2000 cm(-1). Excited-state mixed valence is expected to be an important contributor to the electronic spectra of many organic and inorganic compounds. The energy separations and relative intensities enable the excited-state properties to be calculated as shown in this paper, and the spectra provide new information for probing and understanding coupling in mixed valence systems.     

The Jahn-Teller and pseudo-Jahn-Teller effects in the anion photoelectron spectroscopy of B3 cluster

The photodetachment spectroscopy of B3- anion is theoretically studied with the aid of a quantum dynamical approach. The theoretical results are compared with the available experimental photoelectron spectra of B3-. Both B3- and B3 possess D(3h) symmetry at the equilibrium configuration of their electronic ground state. Distortion of B3 along its degenerate vibrational mode nu2 splits the degeneracy of its excited C2E' electronic manifold and exhibits (E [symbol: see text] e)-Jahn-Teller (JT) activity. The components of the JT split potential energy surface form conical intersections, and they can also undergo pseudo-Jahn-Teller (PJT) crossings with the X2A1' electronic ground state of B3 via the degenerate nu2 vibrational mode. The impact of the JT and PJT interactions on the nuclear dynamics of B3 in its X2A1'-C2E' electronic states is examined here by establishing a diabatic model Hamiltonian. The parameters of the electronic part of this Hamiltonian are calculated by performing electronic structure calculations and the nuclear dynamics on it is simulated by solving quantum eigenvalue equation. The theoretical results are in good accord with the experimental data.