Metastable Molecules in Ground and Excited States: Theory Development, Implementation and Applications

1. There are two very different ways of executing linear regression analysis. One is Model I, when the x-values are fixed by the experimenter. The other is Model II, in which the x-values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step-by-step instructions in the Supplementary Information as to how to use loss functions.

This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.

<div class="htmlview paragraph">In this paper methods for the nonlinear dynamic analysis of multibody vehicle systems are presented. A total Lagrangian finite element formulation for deformable bodies of the vehicle systems that undergo large translational and rotational displacements is developed. A set of nonlinear dynamic differential equations are developed in a closed form for each finite element in terms of the reference as well as the nodal elstic coordinates and their time derivatives. These equations are expressed in terms of a set of element invariants that depend on the assumed displacement field. The invariants of the deformable body that undergoes large reference translational and rotational displacements can be obtained by assembling the invariants of its elements using a standard finite element procedure. The nonlinear dynamic equations of the deformable body can then be obtained by assembling the nonlinear element equations. Both the consistent and lumped mass finite element formulations are discussed. The dynamic formulations presented in this paper are exemplified using multibody vehicle systems that consist of interconnected rigid and deformable bodies. Numerical results are obtained using the general purpose computer program <b>DAMS</b> (Dynamic Analysis of Multibody Systems).</div>

The solvation free energy difference, ΔG, and reorganization energy, λ, of the electronic transition between the ground and first excited state of formaldehyde are investigated as a function of the solvent electronic polarizability in aqueous solution. Solvent shifts are difficult to measure experimentally for formaldehyde due to oligomer formation; shifts for acetone, which have been measured experimentally, are used instead for comparison with computational results. Predictions of the Poisson–Boltzmann equation of dielectric continuum theory with molecular shaped cavities and charges on atomic sites calculated from ab initio quantum chemistry are compared with direct molecular dynamics simulations using the fluctuating charge model of polarizable water. The explicit molecule simulations agree with the acetone experimental results, but the continuum dielectric calculations do not agree with explicit solvent or with experiment when the default model cavity is used for both the ground and excited state molecule. Several different algorithms are used to define the size of the molecular cavity in the ground and excited states, but we are unable to find a single set of atomic radii that describe adequately all the data. Quantitative calculations from a continuum model might therefore require charge-dependent solute cavity radii.

Local structural comparison methods can be used to find structural similarities involving functional protein patches such as enzyme active sites and ligand binding sites. The outcome of such analyses is critically dependent on the representation used to describe the structure. Indeed different categories of functional sites may require the comparison program to focus on different characteristics of the protein residues. We have therefore developed superpose3D, a novel structural comparison software that lets users specify, with a powerful and flexible syntax, the structure description most suited to the requirements of their analysis. Input proteins are processed according to the user's directives and the program identifies sets of residues (or groups of atoms) that have a similar 3D position in the two structures. The advantages of using such a general purpose program are demonstrated with several examples. These test cases show that no single representation is appropriate for every analysis, hence the usefulness of having a flexible program that can be tailored to different needs. Moreover we also discuss how to interpret the results of a database screening where a known structural motif is searched against a large ensemble of structures. The software is written in C++ and is released under the open source GPL license. Superpose3D does not require any external library, runs on Linux, Mac OSX, Windows and is available at http://cbm.bio.uniroma2.it/superpose3D.

Spectroscopic determination of vibrational potential energy surfaces in ground and excited electronic states

This thesis is a primarily experimental study of the spectroscopy and dynamics of highly vibrationally excited molecules in the ground and excited electronic states. Linear spectroscopic studies have been performed on CH-stretching overtones of medium and large sized molecules in the gas and solid phases. Also new time-resolved methods based on nonlinear uultiphoton ionization spectroscopy have been applied on the picosecond time-scale to the study of ultrafast intramolecular vibrational-energy redistribution (IVR) in isolated molecules. The first observation of high-energy CH stretching overtones of molecules in low-temperature solids is reported. Spectra of the νCH = 5 transitions of many aromatic molecules at ~2K reveal homogeneously broadened bands which are assigned to inequivalent local modes by studies of same isotopically substituted molecules. Typical linewidths give population lifetimes of ~50 fs for aromatic compared to 100-200 fs for methyl CHs in these large molecules. The polarization ratios of durene CH overtones are in good agreement with those predicted with the localized bond-mode transition moments. Overtone spectra of some gas-phase deuterated methanes and tetramethyl compounds have been studied. Spectra of CHD3 have shown severe vibrational mixing at νCH = 6 and 7 with an apparent tuning of the Fermi-resonance between |νCH> and discrete stretch-bend combination states, e.g., |(ν-1)CH, 2bend>. Nonetheless, the lifetime of the CHD3 overtones must be long (≥5 ps) as evidenced by the narrow resolution limited linewidths. The splitting of the |6,0>± states of CH2D2 is inferred to be Picosecond pump and probe multiphoton ionization is developed for the study of IVR in isolated molecules. Experimental evidence for IVR is presented. Nonexponential decay of vibronic states of S1 trans-stilbene is analyzed in terms of a population rate equation and time-dependent Franck-Condon factor description of IVR. The thermally-averaged IVR time constant is about 2 ps. Also, the excess vibrational energy dependence of the S1 trans-stilbene isomerization rate is determined for total vibrational energy of 2000 to 4500 cm-1 and good agreement is found with calculated thermally averaged rates based on independent results on jet-cooled molecules.

Practical nonlinear inelastic analysis method of composite steel-concrete beams with partial composite action

A complete photophysical characterization of organic molecules designed for use as molecular materials is critical in the design and construction of devices such as organic photovoltaics (OPV). The nature of a molecule's excited state will be altered in molecules employing the same chromophoric units but possessing different molecular architectures. For this reason, we examine the photophysical reactions of two BODIPY-based D-A and A-D-A molecules, where D is the donor and A is the acceptor. A BODIPY (4,4'-difluoro-4-bora-3a,4a-diaza-s-indacene) moiety serves as the A component and is connected through the meso position using a 3-hexylthiophene linker to a N-(2-ethylhexyl)dithieno[3,2-b:2',3'-d]pyrrole (DTP), which serves as the D component. An A-D-A motif is compared to its corresponding D-A dyad counterpart. We show a potential advantage to the A-D-A motif over the D-A motif in creating longer-lived excited states. Transient absorption (TA) spectroscopy is used to characterize the photophysical evolution of each molecule's excited state. Global analysis of TA data using singular value decomposition and target analysis is performed to identify decay-associated difference spectra (DADS). The DADS reveal the spectral features associated with charge-transfer excited states that evolve with different dynamics. A-D-A possess slightly longer excited-state lifetimes, 42 ps nonradiative decay, and 4.64 ns radiative decay compared to those of D-A, 24 ps nonradiative decay, and 3.95 ns radiative decay. A longer lived A-D-A component is observed with microsecond lifetimes, representing a small fraction of the total photophyscial product. Steady-state and time-resolved photoluminescence augment the insights from TA, while electrochemistry and spectroelectrochemistry are employed to identify the nature of the excited state. Density functional theory supports the observed electronic and electrochemical properties of the D-A and A-D-A molecules. These results form a complete picture of the electronic and photophysical properties of D-A and A-D-A and provide contextualization for structure-function relationships between molecules and OPV devices.

Although simple finite elements as truss members and beam members in frames have been used in structural analysis for many years, the general finite element methods of analysis have been developped only recently in parallel with the development of digital computers. It is the use of general matrix methods in high speed digital computers that makes the general finite element methods feasible. At the present time the finite element methods are being used extensively in the analysis and design of flight vehicle structures as well as in other types of structures. Many large general purpose computer programs as well as many specialized programs have been developed for the analysis of structures. These computer programs use various finite elements and usually calculate and assemble the element matrices by one of the three methods of analysis described in previous chapters. Most of the general programs use the displacement method of analysis; a few general programs and many specialized programs use the force method of analysis; a few programs use the mixed method, while some programs use more than one method.

Films of proteins fibrinogen and albumin are exposed to neutral reactive particles in order to study their etching rates in early and late oxygen afterglows of microwave plasma. The etching rates are determined at different pressures between 50 and 400 Pa. The etching rates for both proteins first increase with the increasing pressure, while later they reach a constant value. Furthermore, the etching rates are higher in the early than in the late afterglow. The concentration of all available species in the afterglow, i.e. neutral oxygen atoms in the ground state, neutral molecules in the first excited state, and ozone is determined either by experimental measurements or theoretically using a well-established model. The etching rates are explained by the synergistic effects of atoms and metastable molecules.

Based on the correspondence of the molecular orbital theory and valence bond theory to the description of chemical bonds,the ah imtio valence bond (VB) calculations of the low-lying states of diatomic molecules arc realized.The calculation results for the low-lying states of B2 show that the VB calculation has clear-cut physical significance,and its simulation of the behavior of the potential energy surface about the equilibrium position is superior to that of the molecular orbital theory.The valence bond calculation involving only a few bonded tableaus can correctly re fleet the effect of electronic correlation.

The excitation of lasers based on solutions of complex organic compounds is often effected by single pulses of polarized emission. The irradiation of a solution by a directed polarized emission leads to a spatial anisotropic distribution of the molecules in excited and ground states. As a result, the solution generally becomes optically anisotropic, and the thus-induced amplitude and phase anisotropy of the active medium determines a series of characteristics of the laser emission. The authors studied the induced anisotropy of solutions of technical phthalimides, 3,6-tetramethyldiamino-N-methylphthalimide in ethanol and toluene, and also of 3-mono-methylamino-6-monomethylphthalimide in ethanol. The excitation was effected by emission at a wavelength of 526 nm, while the spectral range of the sounding beam overlapped the absorption and fluorescence bands region, which was attained by generation of a second harmonic of the parametric light generator.

Optical enhancement and control of the nonlinear optical (NLO) properties of organic compounds can be expected at the excited state because of changes in dipole moments and oscillator strength caused by electron density distribution different from that at the ground state. We constructed a novel measurement system of hyperpolarizability β at the excited state of molecules in solutions. The system was based on nanosecond Hyper-Rayleigh Scattering (HRS) method with CW laser excitation. In the HRS technique, a chromophore solution was irradiated by YAG laser beam of various intensities (frequency ω), and the scattered photons at 2ω were detected. The HRS intensity was proportional to the square of the incident laser intensity. The increase of HRS intensity for p-nitroaniline was observed in methanol solutions upon excitation with CW Ar laser at 457.9 nm. The β-value at the excited state was estimated.

The molecular and electronic structure of dysprosium trichloride, DyCl(3), was calculated by high-level quantum chemical methods in order to learn about the effect of the partially filled 4f subshell and of the possible spin-orbit coupling on them. High-temperature electron diffraction studies of DyCl(3) were also carried out so that we could compare the computed geometry with the experimental one, after thermal corrections on the latter. Dysprosium monochloride, DyCl, and the dimer of dysprosium trichloride, Dy(2)Cl(6), were also investigated by computation. We found that the electron configuration of the 4f subshell does not influence the geometry of the trichloride monomer molecule as the ground state and first excited state molecules have the same geometry. Nonetheless, taking the 4f electrons into account in the calculation, together with the 5s and 5p electrons, is important in order to get geometrical parameters consistent with the results from experiment. Based on electron diffraction and different levels of computation, the suggested equilibrium bond length (r(e)) of DyCl(3) is 2.443(14) A, while the thermal average distance (r(g)) from electron diffraction is 2.459(11) A. The molecule is trigonal planar in equilibrium. Although the ground electronic state splits due to spin-orbit coupling, the lowering of the total electronic energy is very small (about 0.025 hartree) and the geometrical parameters are not affected. In contrast with the monomeric trichloride molecule, the bond angles of the dimer seem to be different for different electronic states, indicating the influence of the 4f electronic configuration on their structure. We carried out an anharmonic analysis of the out-of-plane vibration of the trichloride monomer and found that the vibration is considerably anharmonic at 39.5 cm(-1), compared with the 30.5 cm(-1) harmonic value.