Extracting effective normal modes from equilibrium dynamics at finite temperature

A general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity time-correlation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal mode analysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio molecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at 20 K in very good agreement with the results of a normal mode analysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initio molecular dynamics simulations of these two systems at 300 K.     

Jumping between protein conformers using normal modes

The relationship between the normal modes of a protein and its functional conformational change has been studied for decades. However, using this relationship in a predictive context remains a challenge. In this work, we demonstrate that, starting from a given protein conformer, it is possible to generate in a single step model conformers that are less than 1 Å (C_α ‐RMSD) from the conformer which is the known endpoint of the conformational change, particularly when the conformational change is collective in nature. Such accurate model conformers can be generated by following either the so‐called robust or the 50 lowest‐frequency modes obtained with various Elastic Network Models (ENMs). Interestingly, the quality of many of these models compares well with actual crystal structures, as assessed by the ROSETTA scoring function and PROCHECK. The most accurate and best quality conformers obtained in the present study were generated by using the 50 lowest‐frequency modes of an all‐atom ENM. However, with less than ten robust modes, which are identified without any prior knowledge of the nature of the conformational change, nearly 90% of the motion described by the 50 lowest‐frequency modes of a protein can be captured. Such results strongly suggest that exploring the robust modes of ENMs may prove efficient for sampling the functionally relevant conformational repertoire of many proteins. © 2017 Wiley Periodicals, Inc.     

Overtone spectrum in terms of normal or of equivalent modes with application to H2O

An algebraic hamiltonian which closely fits the (low and) high stretching vibrational spectrum of H₂O (and of other YXY molecules such as O₃) is shown to correspond to two weakly coupled equivalent modes.     

Infrared intensities of the external modes of crystalline nitrous oxide

The absorption intensities of two infrared active lattice modes of crystalline N₂O have been measured. Both the frequencies and intensities of the external modes of N₂O have been found to be very similar to those of CO₂, and most of the differences between the spectra of CO₂ and N₂O can be explained by the differences in the quadrupole moments.     

Quantum dynamics in macrosystems with several coupled electronic states: hierarchy of effective Hamiltonians

We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multistate conical intersections. The general situation of an arbitrary number of states and arbitrary number of nuclear degrees of freedom (modes) is considered. The macrosystem is decomposed into a system part carrying a few, strongly coupled modes and an environment, comprising the vast number of remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment is constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. By considering the system's Hamiltonian along with a few members of the hierarchy, it is shown mathematically by a moment analysis that the quantum dynamics of the entire macrosystem can be numerically exactly computed on a given time scale. The time scale wanted defines the number of effective Hamiltonians to be included. The contribution of the environment to the quantum dynamics of the macrosystem translates into a sequential coupling of effective modes. The wave function of the macrosystem is known in the full space of modes, allowing for the evaluation of observables such as the time-dependent individual excitation along modes of interest as well as spectra and electronic-population dynamics.     

Connections between perturbation theory and the unitary transformation methods of deriving effective Hamiltonians

The connections between open shell Brillouin–Wigner perturbation theory and the Van Vleck unitary transformation formalisms for generating effective Hamiltonians are explored. An explicit expression is obtained relating the generator ? of the unitary transformation e^i? with the amplitudes to be found from perturbation theory. The “renormalization effects” needed to produce the explicit “orthogonal-Hermitian” form of the effective Hamiltonian in perturbation theory are related directly to the generator of the unitary transformation. The conclusions reached previously by Jørgensen and Brandow regarding the identity of the effective Hamiltonians of the formalisms are explicitly verified for the case that the generator ? satisfied the Kemble condition. The procedure suggests how the powerful techniques of perturbation theory can be used within the unitary transformation framework to guarantee properly renormalized wave functions.     

Bending dynamics of acetylene: new modes born in bifurcations of normal modes

Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C2H2. An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.     

Dispersion of normal modes in cis 1,4 polybutadiene

Among the synthetic polymers of commercial potential, poly-butadiene is an important rubbery material and it encompasses the bulk elastomers in use. To the best of our knowledge, a complete normal coordinate analysis with full phonon dispersion curves for cis 1,4 polybutadiene (CPBD) have not been reported so far. In the present communication, we report a complete normal coordinate analysis with full dispersion curves, density-of-states and calculation of heat capacity. The normal coordinate analysis has been carried out using the Urey-Bradley force field and the Wilson's GF matrix method as modified by Higgs. A comparison has been made with trans 1,4 polybutadiene (TPBD). The prominent features of the dispersion curves like crossing over and regions of zero-slope away from the zone centre are discussed. To check the validity of the force field used and the assignments, normal mode calculations are also performed for unsaturated C-deuterated and fully deuterated CPBD.     

Hydration forces near charged interfaces in terms of effective ion potentials

Experiments and simulations provide detailed information on the structure and interaction of charged interfaces in aqueous solutions. In order to understand this information in terms of general principles it is favourable to use effective potentials, which describe the interaction of ions and surfaces in the presence of solvent. Effective potentials are derived from molecular simulations and are capable of discerning ion-specific behaviour. We argue that short-range interactions in aqueous solutions involve two characteristic lengths, the range of the interaction and the spatial periodicity, both about 2.5 ± 0.5 Å.     

Topological characterization of normal modes in chains and rings

A method for predicting molecular stretching frequencies and normal coordinates for chain and ring pseudomolecules from topological considerations is presented. From previously published hydrocarbon force fields, complete GF product matrices for stretching are calculated for the chain and ring species. It is seen that with little loss of computational accuracy, these GF products can be approximated as GF = E + A, where A is a topological adjacency matrix. Consequently, semi-quantitative calculation of the stretching spectra of the pseudomolecules considered requires only a specification of bond connectivities.     

On-chip electrochemical detection of CdS quantum dots using normal and multiple recycling flow through modes

A flexible hybrid polydimethylsiloxane (PDMS)-polycarbonate (PC) microfluidic chip with integrated screen printed electrodes (SPE) was fabricated and applied for electrochemical quantum dots (QDs) detection. The developed device combines the advantages of flexible microfluidic chips, such as their low cost, the possibility to be disposable and amenable to mass production, with the advantages of electrochemistry for its facility of integration and the possibility to miniaturize the analytical device. Due to the interest in biosensing applications in general and particularly the great demand for labelling alternatives in affinity biosensors, the electrochemistry of cadmium sulfide quantum dots (CdS QDs) is evaluated. Square wave anodic stripping voltammetry (SWASV) is the technique used due to its sensitivity and low detection limits that can be achieved. The electrochemical as well as the microfluidic parameters of the developed system are optimized. The detection of CdS QDs in the range between 50 to 8000 ng mL(-1) with a sensitivity of 0.0009 μA/(ng mL(-1)) has been achieved. In addition to the single in-chip flow through measurements, the design of a recirculation system with the aim of achieving lower detection limits using reduced volumes (25 μL) of sample was proposed as a proof-of-concept.     

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.     

Three-body free-energy terms and effective potentials in polar fluids and ionic solutions

Three-body free-energy terms and corresponding “effective” orientation-independent electrostatic potentials for polar fluids and ionic solutions are given.     

Diabatic ordering of vibrational normal modes in reaction valley studies

Diabatic ordering of the normal model of a reaction complex along the reaction path has several advantages with regard to adiabatic ordering. The method is based on rotations of the vibrational normal modes at one point, s, of the reaction path to maximize overlap with the vibrational modes at a neighboring point. Global rotations precede the rotations of degenerate modes so that changes in the direction of the reaction path and changes in the force constant matrix, which represent the two major effects for changes in mode ordering, can be separated. Overlap criteria identify resolved and unresolved avoided crossings of normal modes of the same symmetry. Diabatic mode ordering (DMO) can be used to resolve the latter by reducing the step size, thus guaranteeing correct ordering of normal modes in dependence of s. DMO is generally applicable to properties of the reaction complex that depend on s such as normal mode frequencies, orbital energies, the energy of excited states, etc. Additional applications are possible using a generalized reaction path vector, which may describe the change in atom masses, geometrical parameters, and/or the force constant matrix. In this way, the vibrational spectra of isotopomers can be investigated or the vibrational frequencies of different molecules correlated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1282–1294, 1997     

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the system's modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.     

Reduced Hamiltonians. II: The size-consistency of reduced Hamiltonians defined in model spaces

The link between the Absar-Coleman and the Valdemoro reduced Hamiltonian has been established. Further, a study of the size-consistency of approximations based on these Hamiltonians has been carried out. It is found that the energies obtained with reduced Hamiltonians that are defined in the full configuration interaction model spaces are not size consistent.