Normal Mode Displacements Research Articles

A benchmark dataset for Hydrogen Combustion

The generation of reference data for deep learning models is challenging for reactive systems, and more so for combustion reactions due to the extreme conditions that create radical species and alternative spin states during the combustion process. Here, we extend intrinsic reaction coordinate (IRC) calculations with ab initio MD simulations and normal mode displacement calculations to more extensively cover the potential energy surface for 19 reaction channels for hydrogen combustion. A total of ∼290,000 potential energies and ∼1,270,000 nuclear force vectors are evaluated with a high quality range-separated hybrid density functional, ωB97X-V, to construct the reference data set, including transition state ensembles, for the deep learning models to study hydrogen combustion reaction.

Protein Dynamics to Define and Refine Disordered Protein Ensembles.

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R2 relaxation rates and Lipari-Szabo order parameters (S2 values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

Positive isotope effect in thermally activated delayed fluorescence emitters based on deuterium-substituted donor units

Isotope effect (IE) has been widely applied to probe the kinetics and mechanisms of organic reactions, and hole/electron transport behaviors of semiconductors. The subtle isotope substitution on fluorophores could intrinsically influence their luminescence efficiency and the operational lifetime of organic light-emitting diodes (OLEDs). So far, the IE on the photophysical properties, thermal stabilities and electroluminescence performance of thermally activated delayed fluorescence (TADF) emitters has not been reported. In this work, two deuterium-substituted TADF emitters, TPAAP-D and TPAAQ-D, have been designed and synthesized to investigate the IE in TADF. The comparison study showed that the deuterium substitution led to a decrease in the non-radiative decay rate of S1 (KnrS) and a decrease in the intersystem crossing rate constant (KISC), thus enhancing the luminescence efficiency of deuterated TADF materials. The origin of this positive IE was correlated with the increase in normal-mode displacement (ΔQ) and Huang-Rhys factor (Sj) of deuterated TADF. Furthermore, TPAAP-D and TPAAQ-D exhibited remarkably higher decomposition temperatures than their native counterparts. Importantly, TPAAP-D can sensitize a near infrared (NIR) dye (BF) with the electroluminescence (EL) peak at 760 nm (FWHM = 45 nm) and EQE of 2.8%, which was the best result among the reported fluorophore emitters.

Effect of surface temperature on quantum dynamics of H2 on Cu(111) using a chemically accurate potential energy surface.

The effect of surface atom vibrations on H2 scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose-Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results.

Development of a MATLAB Algorithm for Calculating Reorganization Energy Utilizing Rectilinear Normal Mode Displacements: Investigation of the Effect of Substituents on Electron and Hole Reorganization Energies of Styryl‐Capped Silicon Quantum Dots

We developed a MATLAB algorithm to calculate reorganization energy utilizing rectilinear normal mode displacements. Normal mode‐projected rectilinear displacements and the corresponding angular frequencies, required for evaluating charge transfer reorganization energy within the harmonic oscillator approximation, were obtained from Cartesian coordinates and Cartesian force constant matrices determined with respect to the principal axes. To verify the algorithm developed with MATLAB, we compared the computed charge transfer reorganization energies to those evaluated by the DUSHIN program, and there was no substantial difference, indicating that our algorithm guarantees the numerical accuracy of the calculations. This algorithm was applied to design silicon quantum dots (Si QDs) with low reorganization energies for charge transfer.

First-principles study of large-amplitude dynamic Jahn–Teller effects in vanadium tetrafluoride

Transition metal tetrahalides are a class of highly symmetric molecules for which very few spectroscopic data exist. Exploratory ab initio calculations of electronic potential energy functions indicate that the equilibrium molecular geometries of the vanadium, niobium, and tantalum tetrafluorides (i.e., VF4, NbF4, and TaF4) exhibit strong distortions from the tetrahedral configuration in their electronic ground state (2E) and first excited state (2T2) along the nuclear displacement coordinates of e symmetry. The distortions result from the E × e and T2 × e Jahn-Teller (JT) effects, respectively. In addition, there are weaker distortions in the 2T2 state along the coordinates of t2 symmetry due to the T2 × t2 JT effect. The description of the large-amplitude dynamics induced by these JT effects requires the construction of JT Hamiltonians beyond the standard model of JT theory, which is based on Taylor expansions up to second order in normal-mode displacements. These higher-order JT Hamiltonians were constructed in this work by expansions of the electronic potentials of the title molecule in terms of symmetry invariant polynomials in symmetry-adapted nuclear displacement coordinates for the bending modes of VF4. A multi-configuration electronic structure method was employed to determine the coefficients of these high-order polynomial expansions from first principles. Using these large-amplitude Jahn-Teller Hamiltonians, the vibronic spectra of VF4 were computed. The spectra illustrate the effects of large-amplitude fluxional nonadiabatic dynamics due to exceptionally strong E × e and T2 × e JT couplings. In addition, the vibronic spectrum of the T2 × (e + t2) JT effect, including the bending mode of t2 symmetry, was computed. The spectrum displays strong inter-mode coupling effects exhibiting a vibronic structure, which is substantially different from that predicted by independent-mode approximation. These results represent the first ab initio study of dynamical Jahn-Teller effects in VF4.

Decay dynamics of 6‐azauracil from the light absorbing S2(ππ*) state

AbstractThe initial decay dynamics of 6AU in the S2 state was investigated by using resonance Raman spectroscopy, the time‐dependent wave‐packet theory in a Brownian oscillator model, and complete‐active space self‐consistent field (CASSCF) protocol. The vibrational spectra and the ultraviolet absorption bands were assigned on the basis of the Fourier transform (FT)‐Raman, FT‐infrared measurements, the density‐functional theory computations, and the normal mode analysis. The absorption cross section and the absolute resonance Raman cross sections were simulated simultaneously by using the time‐dependent wave‐packet theory in a Brownian oscillator model. The obtained normal mode displacements of the Franck–Condon active modes were then converted to the short‐time structural dynamics in easy‐to‐visualize internal coordinates. The roles of two pathways via the S2 → S1 internal conversion and the S2 → T3 intersystem crossing were evaluated through the comparison between the short‐time structural dynamics and the CASSCF/CASTP2 calculated structural changes between FC and S2S1 or between FC and S2T3. The results indicate that the structural dynamics in the Franck–Condon region of the S2 state is mostly toward the S2/S1 conical intersection, which supports the conclusion that the S2 → S1 internal conversion dominants the initial decay pathway of 6AU as revealed by the broadband fs TA spectroscopy, whereas the barrierless S2 → T3 intersystem‐crossing process is negligible owing to weak spin‐orbital coupling and unfavorable subsequent T3 → T2 → T1 decay. The reaction coordinates towards the planar S2(ππ*)/S1(nπ*) and severely distorted S2(ππ*)/S0 conical intersection points are proposed respectively, and the solvent effect on the initial decay mechanisms of 6AU, uracil, and thymine is clarified.

The Astrochemistry Implications of Quantum Chemical Normal Modes Vibrational Analysis

Understanding the molecular vibrations underlying each of the unknown infrared emission (UIE) bands (such as those found at 3.3, 3.4, 3.5, 6.2, 6.9, 7.7, 11.3, 15.8, 16.4, 18.9 μ m) observed in or towards astronomical objects is a vital link to uncover the molecular identity of their carriers. This is usually done by customary classifications of normal-mode frequencies such as stretching, deformation, rocking, wagging, skeletal mode, etc. A large literature on this subject exists and since 1952 ambiguities in classifications of normal modes via this empirical approach were pointed out by Morino and Kuchitsu New ways of interpretation and analyzing vibrational spectra were sought within the theoretical framework of quantum chemistry. Many of these methods cannot easily be applied to the large, complex molecular systems which are one of the key research interests of astrochemistry. In considering this demand, a simple and new method of analyzing and classifying the normal mode vibrational motions of molecular systems was introduced. This approach is a fully quantitative method of analysis of normal-mode displacement vector matrices and classification of the characteristic frequencies (fundamentals) underlying the observed IR bands. Outcomes of applying such an approach show some overlap with customary empirical classifications, usually at short wavelengths. It provides a quantitative breakdown of a complex vibration (at longer wavelengths) into the contributed fragments such as their aromatic or aliphatic components. In addition, in molecular systems outside the classical models of chemical bonds and structures where the empirical approach cannot be applied, this quantitative method enables an interpretation of vibrational motion(s) underlying the IR bands. As a result, further modifications in the structures (modeling) and the generation of the IR spectra (simulating) of the UIE carriers, initiated by proposing a PAH model, can be implemented in an efficient way. Here fresh results on the vibrational origin of the spectacular UIE bands based on astrochemistry molecular models, explored through the lens of the quantitative method applied to thousands of different vibrational motion matrices are discussed. These results are important in the context of protoplanetary nebulae and planetary nebulae where various molecular species have been uncovered despite their harsh environments.

VSCF calculations for the intra- and intermolecular vibrational modes of the water dimer and its isotopologs

In this work we show how the VSCF method may be successfully used to describe all fundamental vibrational transitions of several isotopologs of water dimer. By expressing the normal mode displacements in terms of appropriate delocalized internal coordinates we are able to minimize the mode-mode coupling in the PES and thus yield PT2-VSCF frequencies in good agreement with the experiment. The use of curvilinear normal modes is of paramount importance to describe vibrational transitions of the very soft intermolecular modes. Within our approach the maximum calculated error for the (H2O)2 intermolecular frequencies are reduced from 311cm−1 (Cartesian normal modes) to just 56cm−1 (curvilinear normal modes). Plots of the diagonal intermolecular potential and of the vibrational wave function illustrate the remarkable effect of different coordinate systems. In conclusion, our PT2-VSCF calculations provide a fair anharmonic description of the fundamental transitions of water dimers.

Singlet Fission in Quinoidal Oligothiophenes

The electronic properties of quinoidal oligithiophenes make them interesting for applications in semiconductor technology. Because of their very large singlet–triplet splitting, they are promising candidates for singlet fission (SF), a process in which an initially excited singlet state is converted into two triplet excitons. Thus, the efficiency of solar cells could be increased to overcome the Shockley-Queisser limit. Here, we investigate the ability of a quinoidal bithiophene to undergo SF in solution. We calculated the ground state and low-lying excited states using a combined density functional theory and multireference configuration interaction approach including dispersion corrections. Potential energy curves along normal mode displacements were computed to detect avoided crossings between the initially excited bright singlet state and a dark doubly excited state which can be interpreted as a triplet pair overall coupled to a singlet 1(TT). The studied quinoidal bithiophene meets the energetic requ...

Towards a global model of spin-orbit coupling in the halocarbenes.

We report a global analysis of spin-orbit coupling in the mono-halocarbenes, CH(D)X, where X = Cl, Br, and I. These are model systems for examining carbene singlet-triplet energy gaps and spin-orbit coupling. Over the past decade, rich data sets collected using single vibronic level emission spectroscopy and stimulated emission pumping spectroscopy have yielded much information on the ground vibrational level structure and clearly demonstrated the presence of perturbations involving the low-lying triplet state. To model these interactions globally, we compare two approaches. First, we employ a diabatic treatment of the spin-orbit coupling, where the coupling matrix elements are written in terms of a purely electronic spin-orbit matrix element which is independent of nuclear coordinates, and an integral representing the overlap of the singlet and triplet vibrational wavefunctions. In this way, the structures, harmonic frequencies, and normal mode displacements from ab initio calculations were used to calculate the vibrational overlaps of the singlet and triplet state levels, including the full effects of Duschinsky mixing. These calculations have allowed many new assignments to be made, particularly for CHI, and provided spin-orbit coupling parameters and values for the singlet-triplet gaps. In a second approach, we have computed and fit full geometry dependent spin-orbit coupling surfaces and used them to compute matrix elements without the product form approximation. Those matrix elements were used in similar fits varying the anharmonic constants and singlet-triplet gap to reproduce the experimental levels. The derived spin-orbit parameters for carbenes CHX (X = Cl, Br, and I) show an excellent linear correlation with the atomic spin-orbit constant of the corresponding halogen, indicating that the spin-orbit coupling in the carbenes is consistently around 14% of the atomic value.

Formula omitted] Jahn–Teller effect in the [formula omitted] cation and its signatures in the photoelectron spectrum of P4

The Jahn–Teller effect in the electronic ground state of the P4+ radical cation, which is one of the strongest E×e Jahn–Teller effects known in nature, has been revisited in this work with computational methods. The relevance of the Jahn–Teller coupling terms beyond second order in normal-mode displacements has been investigated. An elegant and efficient scheme based on polynomial invariant theory has been employed to expand the E×e potential energy matrix up to arbitrarily high orders in normal mode displacements. Using the state-averaged complete-active-space self-consistent-field method and a correlation consistent double-ζ basis set, an accurate ab initio adiabatic E×e Jahn–Teller potential-energy surface was obtained. It is shown that a polynomial expansion of least up to sixth order is necessary to account for the pronounced anharmonicity of the ab initio potential-energy surface for large amplitude displacements of the Jahn–Teller active vibrational mode. The vibronic structure of the X̃2E band of the photoelectron spectrum of P4 has been computed using a time-dependent wave-packet propagation method. The results reveal the significance of the higher-order Jahn–Teller coupling terms for the high-resolution vibronic spectrum as well as for the low-resolution band shape.

Quantum dynamics of radiationless electronic transitions including normal modes displacements and Duschinsky rotations: a second-order cumulant approach.

An analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and nonequilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

Relative Mechanical Flexibility of Ubiquitin Family Proteins: A Study using Elastic Network Model

The conformational flexibility of biomolecules is essential for their function. Elastic Network Model (ENM) is a class of harmonic models used to computationally describe the flexibility of biomolecules. Despite the simplicity of the underlying potential, ENMs show intriguing abilities to capture functionally relevant conformational changes in proteins, as seen in their crystallographic structures, through their low-frequency normal-mode displacements. We present an ENM based study of the mechanical flexibility of proteins having high structural similarity but low sequence homology.Single-molecule atomic force microscopic (AFM) measurements reveal that ubiquitin requires a higher unfolding force when pulled along N-C termini than the SUMO proteins. The higher mechanical stability of ubiquitin relative to the SUMOs is presumably a sequence effect, as the proteins have identical secondary structures. Our calculations at the atomistic resolution show a strong imprint of the experimentally observed disparity in stabilities of the ubiquitin-like proteins in their flexibilities. Spring constants for normal modes of ubiquitin are higher than that of the SUMOs, implying larger stiffness of ubiquitin over the latter. The residues on the clamp (terminal β-sheets) region of these proteins that govern their stabilities show mobility that is implicated in their flexibilities. We discuss physical considerations for extracting a reduced dimensional basis from ENM for the description of equilibrium flexibility of proteins.The large-amplitude normal modes that represent concerted protein motions additionally reveal the conformational changes taking place when ubiquitin and SUMOs bind with substrates, as observed in the complex crystallographic structures. The flexible SUMO proteins tend to be as stiff as ubiquitin on substrate-binding whereas, there seems to be no considerable enhancement in the rigidity of apo-ubiquitin. We elucidate this feature in our study in the light of spring constants of the slowest normal modes.

Vibrationally specific photoionization cross sections of acrolein leading to the X̃²A' ionic state.

The vibrational branching ratios in the photoionization of acrolein for ionization leading to the X̃²A' ion state were studied. Computed logarithmic derivatives of the cross section and the corresponding experimental data derived from measured vibrational branching ratios for several normal modes (ν9, ν10, ν11, and ν12) were found to be in relatively good agreement, particularly for the lower half of the 11-100 eV photon energy range considered. Two shape resonances have been found near photon energies of 15.5 and 23 eV in the photoionization cross section and have been demonstrated to originate from the partial cross section of the A' scattering symmetry. The wave functions computed at the resonance complex energies are delocalized over the whole molecule. By looking at the dependence of the cross section on the different normal mode displacements together with the wave function at the resonant energy, a qualitative explanation is given for the change of the cross sections with respect to changing geometry.

Comparison of independently calculated ab initio normal-mode displacements for the three C–H stretching vibrations of methanol along the internal rotation path

Graphical displays of normal-mode coefficients from recent quantum chemical projected-frequency calculations are compared with analogous displays constructed after reexamination of results from more extensive higher-level calculations described earlier in the literature. Such comparisons confirm the facts that: (i) no geometrical phase is accumulated in these coefficients when the methyl top undergoes one complete internal-rotation revolution with respect to the frame, and (ii) some of the coefficients, when plotted against the internal rotation angle, exhibit near-cusp-like behavior at one or two angles. The connection between these graphical displays and the magnitude of “Jahn–Teller-like” and “Renner–Teller-like” torsion–vibration interaction terms in a previously reported model Hamiltonian, as well as the connection between the lack of geometric-phase accumulation in these graphs and the number of conical intersections enclosed by one full internal-rotation motion, are briefly discussed.

Jahn-Teller theory beyond the standard model

In the standard model of Jahn-Teller (JT) theory, the spin-free electronic Hamiltonian is expanded up to second order in normal-mode displacements, while the spin-orbit (SO) coupling operator is approximated in zeroth order. In this article, the systematic extension of JT theory beyond the standard model is outlined. For the classic E × e and T2 × t2 JT problems in C3v and Td symmetry, respectively, it is shown how the conventional Taylor expansion of the spin-free Hamiltonian can be replaced by an expansion in invariant polynomials up to arbitrarily high orders. The theory of SO coupling in JT systems is extended beyond the standard model by an expansion of the Breit-Pauli SO-coupling operator up to first order in normal-mode displacements. The spectroscopic relevance of the higher-order electrostatic and the linear relativistic JT coupling terms is illustrated for the vibronic structures of the photoelectron spectra of tetrahedral P4 and Sb4.

Probing the electronic structure of [formula omitted]-fused quinoxalino porphyrins and tetraazaanthracene-bridged bis-porphyrins with resonance Raman spectroscopy and density functional theory

A number of π-extended porphyrins and bis-porphyrins were characterised by resonance Raman spectroscopy and density functional theory (DFT) calculations, using both B3LYP and CAM-B3LYP functionals. Single porphyrin species, incorporating a β,β′-fused quinoxalino unit, and tetraazaanthracene-bridged bis-porphyrins were investigated. Geometry optimisation predicted all species were planar with respect to the porphyrin core(s). Comparison of experimental with simulated vibrational spectra, obtained via DFT calculations [B3LYP/6-31G(d)], verified the modelling; demonstrated by a mean absolute deviation (MAD) between experimental and calculated band positions of less than 10cm−1. Simulated electronic transitions obtained via time-dependent DFT [TD-DFT, B3LYP and CAM-B3LYP/6-31G(d)] lay within 0.4eV of experimental bands and calculations showed perturbation of the frontier molecular orbitals (FMOs) following substitution of the porphyrin core. The nature of transitions that were investigated experimentally via resonance Raman enhancement showed consistency with the character of calculated transitions. A wavepacket analysis of the resonance Raman intensities provided electronic parameters, such as reorganisation energy, as well as normal mode displacements (Δi) that were also consistent with the nature of the specific vibrational modes and probed optical transitions. The largest vibrational reorganisation value obtained was for the Bsh band of compound (1). This result is consistent with the greater electron density shift of the transition found from DFT and resonance Raman and also the less symmetrical nature of (1).

Resonance Raman Spectroscopic and Theoretical Study of Geometry Distortion of Thiourea in 21A State

The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile solution. B3LYP/6-311++G(3df,3pd) and RCIS/6-311++G(3df,3pd) calculations were done to elucidate the ultraviolet electronic transitions, the distorted geometry structure and the saddle point of thiourea in 21A excited state, respectively. The resonance Raman spectra were assigned. The absorption spectrum and resonance Raman intensities were modeled using Heller's time-dependent wavepacket approach to resonance Raman scattering. The results indicate that largest change in the displacement takes place with the C=S stretch mode ν6 (|Δ|=0.95) and noticeable changes appear in the H5N3H6+H8N4H7 wag ν5 (|Δ|=0.19), NCN symmetric stretch+C=S stretch+N3H6+H8N4 wag ν4 (|Δ|=0.18), while the moderate intensities of 2ν15 and 4ν15 are mostly due to the large excited state frequency changes of ν15, but not due to its significant change in the normal mode displacement. The mechanism of the appearance of even overtones of the S=CN2 out of plane deformation is explored. The results indicate that a Franck-Condon region saddle point is the driving force for the quadric phonon mechanism within the standard A-term of resonance Raman scattering, which leads to the pyramidalization of the carbon center and the geometry distortion of thiourea molecule in 21A excited state.

Electron transport properties in fluorinated copper–phthalocyanine films: importance of vibrational reorganization energy and molecular microstructure

Electron transport (ET) properties of a series of fluorinated copper-phthalocyanine (F(16)CuPc) thin films, which were deposited at different substrate temperatures (T(sub)) ranging from 30 to 150 degrees C, have been investigated by quantum mechanical calculations of the reorganization energy (lambda(reorg)), X-ray diffraction (XRD), atomic force microscopy (AFM), and microRaman spectroscopy. Density functional theory calculations were used to predict the vibrational frequencies, normal mode displacement vectors, and electron-vibrational lambda(reorg) for the F(16)CuPc molecule. The electron mobilities (mu(e)) of F(16)CuPc thin films are strongly dependent on the T(sub), and the value of mu(e) increases with increasing T(sub) from 30 to 120 degrees C, at which point it reaches its maximum value. The importance of electron-vibrational coupling and molecular microstructures for ET properties in F(16)CuPc thin films are discussed on the basis of theoretical vibrational lambda(reorg) calculations and experimental observations of resonance Raman spectra. We observed a good correlation between mu(e) and the full-width-at-half-maximum of the vibrational bands, which greatly contributed to lambda(reorg) and/or which reflects the molecular microstructural quality of the active channel. In contrast, the crystal size analysis by XRD and surface grain morphology by AFM did not reveal a clear correlation with the ET behaviours for these different F(16)CuPc thin films. Therefore, we suggest that for organic films with weak intermolecular interactions, such as F(16)CuPc, optimized microscopic molecular-scale parameters are highly important for efficient long-range charge transport in the macroscopic devices.