Intramolecular Degrees Of Freedom Research Articles

Two-Step Machine Learning Approach for Charge-Transfer Coupling with Structurally Diverse Data.

Electronic coupling is important in determining charge-transfer rates and dynamics. Coupling strength is sensitive to both intermolecular, e.g., orientation or distance, and intramolecular degrees of freedom. Hence, it is challenging to build an accurate machine learning model to predict electronic coupling of molecular pairs, especially for those derived from the amorphous phase, for which intermolecular configurations are much more diverse than those derived from crystals. In this work, we devise a new prediction algorithm that employs two consecutive KRR models. The first model predicts molecular orbitals (MOs) from structural variation for each fragment, and coupling is further predicted by using the overlap integral included in a second model. With our two-step procedure, we achieved mean absolute errors of 0.27 meV for an ethylene dimer and 1.99 meV for a naphthalene pair, much improved accuracy amounting to 14-fold and 3-fold error reductions, respectively. In addition, MOs from the first model can also be the starting point to obtain other quantum chemical properties from atomistic structures. This approach is also compatible with a MO predictor with sufficient accuracy.

Comparison between longitudinal viscoelastic relaxation and sound dispersion of molecular liquids on the molecular scale.

Molecular dynamics simulation on some molecular liquids was performed to study sound dispersion on the molecular scale. The sound velocity was determined from the intermediate scattering function, and the relation between the longitudinal modulus and frequency was compared with the frequency-dependent longitudinal modulus in the q = 0 limit evaluated by the Kubo-Green theory. The sound dispersion of a monoatomic liquid up to qσ ≅ 2 was almost quantitatively explained by the viscoelasticity in the q = 0 limit when the wavenumber dependence of the heat capacity ratio was taken into account. The situation was similar for a polyatomic molecular liquid for which the intramolecular degrees of freedom were fixed. For a polyatomic liquid with intramolecular degrees of freedom, the sound dispersion on the molecular scale was connected to the high-frequency limit of the ultrasonic relaxation mode assigned to the vibrational energy relaxation. After subtracting the contribution of the vibrational energy relaxation, both the longitudinal viscoelasticity and the sound dispersion depended little on the presence of intramolecular degrees of freedom.

Temperature-dependent dynamic structure factors for liquid water inferred from inelastic neutron scattering measurements.

Temperature-dependent dynamic structure factors S(Q, ω) for liquid water have been calculated using a composite model, which is based on the decoupling approximation of the mean square displacement of the water molecules into diffusion and solid-like vibrational parts. The solid-like vibrational part Svib(Q, ω) is calculated with the phonon expansion method established in the framework of the incoherent Gaussian approximation. The diffusion part Sdiff(Q, ω) relies on the Egelstaff-Schofield translational diffusion model corrected for jump diffusions and rotational diffusions with the Singwi-Sjölander random model and Sears expansion, respectively. Systematics of the model parameters as a function of temperature were deduced from quasi-elastic neutron scattering data analysis reported in the literature and from molecular dynamics (MD) simulations relying on the TIP4P/2005f model. The resulting S(Q, ω) values are confronted by means of Monte Carlo simulations to inelastic neutron scattering data measured with IN4, IN5, and IN6 time-of-flight spectrometers of the Institut Laue-Langevin (ILL) (Grenoble, France). A modest range of temperatures (283-494K) has been investigated with neutron wavelengths corresponding to incident neutron energies ranging from 0.57 to 67.6 meV. The neutron-weighted multiphonon spectra deduced from the ILL data indicate a slight overestimation by the MD simulations of the frequency shift and broadening of the librational band. The descriptive power of the composite model was suited for improving the comparison to experiments via Bayesian updating of prior model parameters inferred from MD simulations. The reported posterior temperature-dependent densities of state of hydrogen in H2O would represent valuable insights for studying the collective coupling interactions in the water molecule between the inter- and intramolecular degrees of freedom.

Theoretical investigation of the vibrational structure of the Ar–CO2 complex

We develop a new flexible-monomer two-body ab initio potential energy surface (PES) for the Ar−CO2 complex. The accuracy of this new potential function is validated by its agreement in the vibrational spectrum of the complex. Vibrational self-consistent field theory (VSCF) and vibrational configuration interaction (VCI) theory were employed to solve the complete vibrational Hamiltonian, including both intermolecular and intramolecular degrees of freedom. We observe excellent agreement with theoretical and experimental results for the vibrational energy levels in the Terahertz region. In the intramolecular region, we confirm the slight splitting of the bending modes of the CO2 monomer, where the in-plane bend is 0.83 cm−1 less energetic than the out-of-plane mode. We also explore the combination bands in the asymmetric stretching region of the CO2 monomer that involve the intermolecular motions, and show that these results compare favorably to the fundamental intermolecular vibrational energy levels.

Nonstationary Theory of Excited State Charge Transfer Symmetry Breaking Driven by Polar Solvent.

A consistent theory of electron transfer symmetry breaking (SB) dynamics in excited quadrupolar molecules in polar solvents is developed. The interaction of the electronic subsystem of the molecule with intramolecular degrees of freedom and solvent polarization is taken into account and is divided into interaction with inertial and inertialess degrees of freedom. A strong influence of the inertialess polarization of the solvent on the extent of symmetry breaking is revealed. The theory is nonlinear due to the equilibration of inertialess degrees of freedom to the solute electronic state. The interaction of a molecule with the inertial solvent polarization is described in terms of a single variable-the reaction coordinate, for which a rigorous definition is given. The free energy of the system is derived, and the motion of the system along the reaction coordinate is modeled by the Smoluchowski equation. The theory is adapted to describe the dynamics of SB in real solvents characterized by several relaxation time scales. Conditions for the applicability of a much simpler stationary SB model are formulated. The role of thermal fluctuations in the solvent polarization is clarified. Instead of the magnitude of the dissymmetry parameter, a distribution function of molecules over this parameter is introduced. An analysis of the Franck-Condon state created by a short pump pulse shows that it has distinct features of a state with broken symmetry for a wide range of parameters. Thermal fluctuations of the solvent polarization are shown to crucially affect SB.

Direct Observation of Molecular Orbitals Using Synchrotron X-ray Diffraction

The physical properties of molecular crystals are governed by the frontier orbitals of molecules. A molecular orbital, which is formed by superposing the atomic orbitals of constituent elements, has complicated degrees of freedom in the crystal because of the influence of electron correlation and crystal field. Therefore, in general, it is difficult to experimentally observe the whole picture of a frontier orbital. Here, we introduce a new method called “core differential Fourier synthesis” (CDFS) using synchrotron X-ray diffraction to observe the valence electron density in materials. By observing the valence electrons occupied in molecular orbitals, the orbital state can be directly determined in a real space. In this study, we applied the CDFS method to molecular materials such as diamond, C60 fullerene, (MV)I2, and (TMTTF)2X. Our results not only demonstrate the typical orbital states in some materials, but also provide a new method for studying intramolecular degrees of freedom.

Entropy Scaling of Viscosity - II: Predictive Scheme for Normal Alkanes.

In this work, a residual entropy value 6/10 of the way between the critical point and a value of -2/3 of Boltzmann's constant is shown to collapse the scaled viscosity for the family of normal alkanes. Based on this approach, a nearly universal correlation is proposed that can reproduce 95% of the experimental data for normal alkanes within ±18% (without removal of clearly erroneous data). This universal correlation has no new fluid-specific empirical parameters and is based on experimentally accessible values. This collapse is shown to be valid to a residual entropy half way between the critical point and the triple point, beyond which the macroscopically-scaled viscosity has a super-exponential dependence on residual entropy, terminating at the triple point. A key outcome of this study is a better understanding of entropy scaling for fluids with intramolecular degrees of freedom. A study of the transport and thermodynamic properties at the triple point rounds out the analysis.

Alchemical free energy calculations via metadynamics: Application to the theophylline-RNA aptamer complex.

We propose a computational workflow for robust and accurate prediction of both binding poses and their affinities at early stage in designing drug candidates. Small, rigid ligands with few intramolecular degrees of freedom, for example, fragment-like molecules, have multiple binding poses, even at a single binding site, and their affinities are often close to each other. We explore various structures of ligand binding to a target through metadynamics using a small number of collective variables, followed by reweighting to obtain the atomic coordinates. After identifying each binding pose by cluster analysis, we perform alchemical free energy calculations on each structure to obtain the overall value. We applied this protocol in computing free energy of binding for the theophylline-RNA aptamer complex. Of the six (meta)stable structures found, the most favorable binding structure is consistent with the structure obtained by NMR. The overall free energy of binding reproduces the experimental values very well.

Алгоритмы численного моделирования сверхбыстрого фотоиндуцированного межмолекулярного переноса заряда в жидкостях

Предложены подходы к численному решению систем уравнений, описывающих кинетику двухстадийной фотохимической реакции в вязком полярном растворителе. Математическая модель построена на основе расширенной интегральной теории встреч и учитывает диффузионную подвижность молекул-реагентов в жидкости, неравновесность среды и внутримолекулярных степеней свободы, удаленный перенос электрона в донорно-акцепторных парах, разделенных растворителем. В рамках метода броуновского моделирования разработаны алгоритмы расчета безреакционных стохастических траекторий частиц на поверхностях свободной энергии, соответствующих различным состояниям реагентов и продуктов, схемы детектирования реакционных событий и генерации электронных прыжков, а также алгоритмы расчета нестационарных потоков частиц между электронными состояниями и вычисления интегральных ядер кинетических уравнений. Представлены результаты тестовых расчетов, демонстрирующие корректность численного решения и воспроизводящие известные особенности реакций электронного переноса в полярных жидкостях. Efficient approaches to the numerical solution of equations describing the kinetics of two-stage photochemical reactions in a viscous polar solvent are proposed. The mathematical model is based on the extended integral encounter theory and takes into account diffusive mobility of reactants in solution, nonequilibrium of solvent and intramolecular degrees of freedom, and remote electron transfer in solvent-separated donor-acceptor pairs. In the framework of the Brownian simulation technique, a number of numerical algorithms for calculating unreactive stochastic trajectories of particles on free energy surfaces corresponding to different electronic states of reactants and products are suggested, some computational schemes for the detection of reaction events and the generation of electronic hops are developed, and algorithms for calculating the time-dependent reaction fluxes between the electronic states and integral kernels of the kinetic equations are implemented. The results of test simulations demonstrating the validity of the numerical solutions and reproducing well-known features of electron transfer reactions in polar solvents are discussed.

A 3‐D bonding perspective of the factors influencing the relative stability of the S1/S0 conical intersections of the penta‐2,4‐dieniminium cation (PSB3)

AbstractA balanced treatment of the covalent and ionic contributions to the ground and excited states originating from torsion about double bonds is known to be strongly dependent on the presence of dynamic electron correlation. We undertake an analysis of the minimum energy pathways corresponding to deactivation of the first excited singlet state of PSB3. In doing so we consider torsion about the three double bonds including other intramolecular degrees of freedom, such as the bond length alternation. The 3‐D bond‐path analysis provides a new ‘bond‐localized orbital‐like’ directional interpretation of bonding. Therefore, we present a more sophisticated method of determination of the degree of covalent and ionic contributions known to be responsible for altering the relative stability of the S1/S0 conical intersections. The results presented suggest that the commonly used simplified multi‐reference methodologies that often result in incorrect predictions for the excited state deactivation reaction mechanism.

Developing Local Order Parameters for Order–Disorder Transitions From Particles to Block Copolymers: Application to Macromolecular Systems

In part 1 of this two-paper series, a local order parameter framework was put forth that could track the changes occurring when block copolymer-like mesophases formed from a disordered state. The framework was developed using a two-particle model and involved identifying the local symmetries and geometric motifs that were unique to a given mesophase. In this paper, this framework is suitably modified to track the mesophase formation of standard coarse-grained bead–spring simulation models of polymers and oligomers. In particular, a mesoscale chain model typically employed with dissipative-particle dynamics is used to study the ordering transition of a linear symmetric diblock copolymer into a lamellar phase, and a more detailed bead–spring model of branched bolaamphiphile molecules is used to track the formation of a single diamond phase. These applications illustrate the robustness of the method in handling molecules with intramolecular degrees of freedom (including multiple chemical blocks and branched ...

Challenging structure determination from powder diffraction data: two pharmaceutical salts and one cocrystal with Z′ = 2

Abstract Structure solution of molecular crystals from powder diffraction data by real-space methods becomes challenging when the total number of degrees of freedom (DoF) for molecular position, orientation and intramolecular torsions exceeds a value of 20. Here we describe the structure determination from powder diffraction data of three pharmaceutical salts or cocrystals, each with four molecules per asymmetric unit on general position: Lamivudine camphorsulfonate (1, P 21, Z=4, Z′=2; 31 DoF), Theophylline benzamide (2, P 41, Z=8, Z′=2; 23 DoF) and Aminoglutethimide camphorsulfonate hemihydrate [3, P 21, Z=4, Z′=2; 31 DoF (if the H2O molecule is ignored)]. In the salts 1 and 3 the cations and anions have two intramolecular DoF each. The molecules in the cocrystal 2 are rigid. The structures of 1 and 2 could be solved without major problems by DASH using simulated annealing. For compound 3, indexing, space group determination and Pawley fit proceeded without problems, but the structure could not be solved by the real-space method, despite extensive trials. By chance, a single crystal of 3 was obtained and the structure was determined by single-crystal X-ray diffraction. A post-analysis revealed that the failure of the real-space method could neither be explained by common sources of error such as incorrect indexing, wrong space group, phase impurities, preferred orientation, spottiness or wrong assumptions on the molecular geometry or other user errors, nor by the real-space method itself. Finally, is turned out that the structure solution failed because of problems in the extraction of the integrated reflection intensities in the Pawley fit. With suitable extracted reflection intensities the structure of 3 could be determined in a routine way.

Tensor network simulation of polaron-polaritons in organic microcavities

In the regime of strong coupling between molecular excitons and confined optical modes, the intramolecular degrees of freedom are profoundly affected, leading to a reduced vibrational dressing of polaritons compared to bare electronically excited states. However, existing models only describe a single vibrational mode in each molecule, while actual molecules possess a large number of vibrational degrees of freedom and additionally interact with a continuous bath of phononic modes in the host medium in typical experiments. In this work, we investigate a small ensemble of molecules with an arbitrary number of vibrational degrees of freedom under strong coupling to a microcavity mode. We demonstrate that reduced vibrational dressing is still present in this case, and show that the influence of the phononic environment on most electronic and photonic observables in the lowest excited state can be predicted from just two collective parameters of the vibrational modes. Besides, we explore vibrational features that can be addressed exclusively by our extended model and could be experimentally tested. Our findings indicate that vibronic coupling is more efficiently suppressed for environments characterized by low-frequency (sub-Ohmic) modes.

Next‐generation quantum theory of atoms in molecules for the ground and excited states of fulvene

AbstractA vector‐based representation of the chemical bond is introduced, which we refer to as the bond‐path framework set B = {p, q, r}, where p, q, and r represent 3 eigenvector‐following paths with corresponding lengths H*, H, and the familiar quantum theory of atoms in molecules (QTAIM) bond‐path length (BPL). The intended application of B is for molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions θ, or normal modes of vibration. The lengths H* and H of the eigenvector‐following paths are constructed using the e 1 and e 2 Hessian eigenvectors, respectively, along the bond path, these corresponding to the least and most preferred directions of charge density accumulation. In particular, the paths p and q provide a vector representation of the scalar QTAIM ellipticity ε. The bond‐path framework set B is applied to the excited state deactivation of fulvene that involves distortions along various intramolecular degrees of freedom, such as the bond stretching/compression of bond‐length alternation and bond torsion distortions. We find that the H* and H lengths can differentiate between the ground and excited electronic states, in contrast to the QTAIM BPL. Five unique paths were presented for B = {(p0,p1), (q0,q1), r} for the ground and first excited states where the profile of the scaling factor, the ellipticity ε, reveals a large unexpected asymmetry for the excited state.

Contributions of different degrees of freedom to thermal transport in the C60 molecular crystal

Three models of the ${\mathrm{C}}_{60}$ molecular crystal are studied using molecular dynamics simulations to resolve the roles played by intermolecular and intramolecular degrees of freedom (DOF) in its structural, mechanical, and thermal properties at temperatures between 35 and 400 K. In the full DOF model, all DOF are active. In the rigid body model, the intramolecular DOF are frozen, such that only center of mass (COM) translations and molecular rotations/librations are active. In the point mass model, the molecule is replaced by a point mass, such that only COM translations are active. The zero-pressure lattice constants and bulk moduli predicted from the three models fall within ranges of 0.15 and 20%. The thermal conductivity of the point mass model is the largest across the temperature range, showing a crystal-like temperature dependence (i.e., it decreases with increasing temperature) due to the presence of phonon modes associated with the COM translations. The rigid body model thermal conductivity is the smallest and follows two distinct regimes. It is crystal-like at low temperatures and becomes temperature invariant at high temperatures. The latter is typical of the behavior of an amorphous material. By calculating the rotational diffusion coefficient, the transition between the two regimes is found to occur at the temperature where the molecules begin to rotate freely. Above this temperature, phonons related to COM translations are scattered by the rotational DOF. The full DOF model thermal conductivity is larger than that of the rigid body model, indicating that intramolecular DOF contribute to thermal transport.

Polarons in endohedral Li+@C60- dimers and in 1D and 2D crystals

The electron charge distribution and polaron formation on the carbon sites of dimer clusters Li+@C60- and of 1D or 2D Li+@C60- periodic systems are studied with the use of the generalized Su–Schrieffer–Heeger model with respect to the intermolecular and intramolecular degrees of freedom. The charge distributions over the molecular surface and Jahn–Teller bond distortions of carbon atoms are calculated using the self-consistent iterative methods. Polarons formed in periodic 1D and 2D systems (chains and planar layers) as well as in dimer cluster system are examined. In the periodic systems polaron formation may be described by the cooperative Jahn–Teller effect. Orientation of the polarons on the molecule surface depends on the doping of the system, moreover, electron doping changes the energy levels in the system.

Communication: Pseudoisomorphs in liquids with intramolecular degrees of freedom.

Computer simulations show that liquids of molecules with harmonic intramolecular bonds may have "pseudoisomorphic" lines of approximately invariant dynamics in the thermodynamic phase diagram. We demonstrate that these lines can be identified by requiring scale invariance of the inherent-structure reduced-unit low-frequency vibrational spectrum evaluated for a single equilibrium configuration. This rationalizes why generalized excess-entropy scaling, density scaling, and isochronal superposition apply for many liquids with internal degrees of freedom.

Characteristics of energy exchange between inter- and intramolecular degrees of freedom in crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) with implications for coarse-grained simulations of shock waves in polyatomic molecular crystals.

In this report, we characterize the kinetics and dynamics of energy exchange between intramolecular and intermolecular degrees of freedom (DoF) in crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). All-atom molecular dynamics (MD) simulations are used to obtain predictions for relaxation from certain limiting initial distributions of energy between the intra- and intermolecular DoF. The results are used to parameterize a coarse-grained Dissipative Particle Dynamics at constant Energy (DPDE) model for TATB. Each TATB molecule in the DPDE model is represented as an all-atom, rigid-molecule mesoparticle, with explicit external (molecular translational and rotational) DoF and coarse-grained implicit internal (vibrational) DoF. In addition to conserving linear and angular momentum, the DPDE equations of motion conserve the total system energy provided that particles can exchange energy between their external and internal DoF. The internal temperature of a TATB molecule is calculated using an internal equation of state, which we develop here, and the temperatures of the external and internal DoF are coupled using a fluctuation-dissipation relation. The DPDE force expression requires specification of the input parameter σ that determines the rate at which energy is exchanged between external and internal DoF. We adjusted σ based on the predictions for relaxation processes obtained from MD simulations. The parameterized DPDE model was employed in large-scale simulations of shock compression of TATB. We show that the rate of energy exchange governed by σ can significantly influence the transient behavior of the system behind the shock.

Do Intra-Molecular Degrees of Freedom Determine the Electronic State?

Novel type of electronic phase transition driven by the electric dipoles of counter anions has been clarified by nuclear magnetic resonance (NMR) investigation.

Vibrational relaxation and energy migration of N-methylacetamide in water: the role of nonbonded interactions.

Nonequilibrium molecular dynamics (MD) simulations together with physics-based force fields are used to follow energy flow between vibrationally excited N-methylacetamide (NMA) and water. The simulations are carried out with a previously validated force field for NMA, based on a multipolar representation of the electrostatics, and with a new fluctuating point charge model. For the water solvent, a flexible and a rigid model was employed to distinguish between the role of inter- and intramolecular degrees of freedom. On a 10 ps time scale about 90% of the available energy goes into the solvent. The remaining energy resides within internal NMA-degrees of freedom from where energy flow takes place on longer time scales. The total amount of energy transferred to the solvent on the 10 ps time scale does not depend on whether the water molecules are rigid or flexible during the simulations. Vibrational energy relaxation time scales include two regimes: one on the several 100 fs time scale and a longer one, ranging from 6 to 10 ps. This longer time scale agrees with previous simulations but overestimates the experimentally determined relaxation time by a factor of 2, which can be explained by the classical treatment of the vibrations. Including a previously determined quantum correction factor brings the long time scale into quite favorable agreement with experiment. Coupling to the bending vibration of the water molecules in H-bonding contact with the excited C═O chromophore is substantial. The equilibrium and nonequilibrium distribution of the bending angles of the water molecules in contact with the local oscillator are non-Gaussian, and one approaches the other on the subpicosecond time scale. Analysis of the water velocity distribution suggests that the C═O vibrational energy relaxes into the solvent water shells in an impulsive fashion on a picosecond time scale.