Time‐dependent local‐density approximation in real time: Application to conjugated molecules

The time‐dependent local‐density approximation (TDLDA) is applied to the optical response of conjugated carbon molecules in the energy range of 0–30 eV, with calculations given for carbon chains, polyenes, retinal, benzene, and C₆₀. The major feature of the spectra, the collective π–π* transition, is seen at energies ranging from below 2 to 7 eV and is reproduced by the theory to a few tenths of an electron volt with a good account of systematic trends. However, there is some indication that TDLDA predicts too much fragmentation of the strength function in large molecules. Transition strengths are reproduced with a typical accuracy of 20%. The theory also predicts a broad absorption peak in the range of 15–25 eV, and this feature agrees with experiment in the one case where quantitative data is available (benzene). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 55–66, 1999     

A theory of molecules in molecules

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction in the linear configuration of the dimer of FH. The transfer of localized molecular orbitals as well as the majority of the additional approximations introduced to save computational time can be justified and shown to lead to results in good agreement with those of ab initio calculations. An energy analysis of the effect of the hydrogen bond formation on the localized orbitals is given. It is seen that the effect is small, the major contribution to the binding energy is given by a first order perturbation treatment.     

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experi     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

Ab initio theory for treating local electron excitations in molecules and its performance for computing optical properties

In this article, as a first step to develop an efficient approximation for predicting the molecular electronic excited state properties at ab initio level, we propose local excitation approximation (LEA). In the LEA scheme, the only local electron excitations within selected substructure (Chromophore) are treated to calculate the targeted excited state wavefunctions, whereas the other electron excitations (local electron excitations in other substructure and charge‐transfer excitations between different regions) are simply discarded. This concept is realized by using the localized molecular orbitals (LMO) localizing on the chromophore substructure. If the targeted transitions show the strong local character and the adequate substructure is selected as chromophore region, the LEA scheme can provide excited state properties without large loss of accuracy. The fatal slowdown of convergence speed of Davidson's iterative diagonalization due to the use of LMO can be avoided by additional transformation of LMOs. To assess the accuracy and efficiency of the LEA scheme, we performed test calculations using various compounds at configuration interaction single (CIS) and time‐dependent Hartree‐Fock (TDHF) level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Application of self-consistent HMO theory to heteroconjugated molecules

Substantial improvement of the self-consistent HMO theory, as recently developed by one of us, is made in the parametrization for heterobonds. The theory is extensively applied to a large scale of heteroconjugated molecules including rather complicated ones which are biologically important. The calculated molecular geometries and the wavelengths of optical absorption spectra are found to be in good agreement with experimental values. Examining the effect of inclusion of the -technique to this theory, we find that the calculated values of molecular geometries, electronic spectra and ionization potentials are little affected for most molecules. Dependences of the absorption wavelength and the adiabatic potential on the molecular geometry are also investigated.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Quantum mechanical study on plasmon resonances in small ring clusters

The collectivity of the electronic motion in small sodium clusters with ring structure is studied by time‐dependent density functional theory. The formation and development of collective resonances in the absorption spectra were obtained as a function of the ring radius. In small ring clusters, besides the lower‐energy mode and the higher‐energy mode, there is another plasmon resonance mode, that is, the reverse two‐dipole mode. For the reverse two‐dipole mode, the formations of these two dipoles are due to the external field inducement and the shielding effect, although the resonant excitation is mainly due to the coupling effect of the electrons of these two dipoles. © 2012 Wiley Periodicals, Inc.     

Interesting periodic variations in physical and chemical properties of homonuclear diatomic molecules

We carry out a systematic study of various ground state and response properties of homonuclear diatomic molecules (from hydrogen to rubidium, including transition metals) as a function of atomic number of constituent atoms. We perform the ground state and response property calculations by using state of the art density functional theory/time dependent density functional theory. We observe that several properties of homonuclear diatomic molecules show periodic variations along rows and columns of the periodic table. The periodic variations in the ground state properties of diatomic molecules may be explained by the nature and type of the bond that exists between the constituent atoms. Similarly, the periodic variations in the response properties such as static dipole polarizability and strength of the van der Waals interaction between diatomic molecules have been correlated with the variations in metallic/nonmetallic character of the elements along the periodic table. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

On the Pace–Datyner theory of diffusion of small molecules through polymers

The Pace–Datyner theory for diffusion of penetrant molecules in polymers has been analyzed. It has been found that the correct solution of the problem they pose is possible only at 0 K, since then the separation of two chains at x = ∞ is equal to the minimum of the DiBenedetto potential for their interaction. Otherwise the energy of symmetrical separation is infinite. By using the linearization method to solve the differential equation, Pace and Datyner neglected the problem of unnatural boundary conditions at x = ∞ for temperatures above 0 K. The exact numerical solutions of differential equations at temperature 0 K were therefore compared with the results of the Pace–Datyner linear approximation. For temperatures different from 0 K the solution of the problem is possible only when the proper cutoff is imposed. The analytical expression for the coeffients in the DiBenedetto potential has been found, and the potential can be written as     

π-Electron ring currents and magnetic properties of porphyrin molecules in the MO LCAO SCF method

The coupled variant of double-parameter perturbation theory in the MO LCAO SCF method in the London approximation has been used for the calculation of π-electron current distributions in the molecules of porphin and its derivatives. The chemical shifts of¹H-NMR have been computed on the basis of calculations of ring currents and charge distributions. It is shown that π-electron ring currents are responsible for the dominant contribution to the shielding of protons. The theoretical and experimental values of proton chemical shifts are in a good agreement. Chemical shifts of the¹³C and¹⁵N nuclei have also been estimated. Two aromaticity scales are proposed for the compounds under study based on the calculations of the π-electron contribution to the diamagnetic susceptibility and of π-electron currents, respectively.     

The temperature-induced denaturation of small globular proteins as a first-order phase transition of ‘crystal molecules’

A general feature of temperature-induced reversible denaturation of small globular proteins is its all-or-none character. This strong cooperativity leads to think that protein molecules, possessing only two accessible thermodynamic states, the native and the denatured one, resemble ‘crystal molecules’ that melt at raising temperature. An analysis, grounded on mean field theory, allows to conclude that the two-state transition is a first-order phase transition. The implication of this conclusion are briefly discussed.     

A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

New matrix of MALDI-TOF MS for analysis of small molecules

New matrix, metal-phthalocyanine (MPc), of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) was used for analysis of small molecules (usually <500 Da). By using MPcs as matrices, small molecular samples were moved to high mass-to-charge region where there was no interference caused by the traditional matrices. The mass of the target analyte was obtained by simple calculation.     

An approximate diatomics in molecules formulation of generalized valence bond theory

The slow computational speed of the generalized valence bond perfect pairing method (GVB-PP) has been an impediment to its routine use. We have addressed this problem by employing a diatomics in molecules Hamiltonian derived from a second quantization perturbation approach. This results in all three- and four-centered two-electron integrals being dropped from the traditional GVB-PP calculation. For moderate sized molecules, as for example C20 computed with a double zeta + polarization basis, there is on average a fifty-fold decrease in computational times. In this article, we present the theory behind our approach and analyze the accuracy and speed of this approximate GVB-PP method for several cases where density functional methods have produced ambivalent results.     

Adaptive recognition of small molecules by nucleic acid aptamers through a label-free approach

We report a novel label-free method for the investigation of the adaptive recognition of small molecules by nucleic acid aptamers using capillary electrophoresis analysis. Cocaine and argininamide were chosen as model molecules, and the two corresponding DNA aptamers were used. These single-strand DNAs folded into their specific secondary structures, which were mainly responsible for the binding of the target molecules with high affinity and specificity. For molecular recognition, the nucleic acid structures then underwent additional conformational changes, while keeping the target molecules stabilized by intermolecular hydrogen bonds. The intrinsic chemical and physical properties of the target molecules enabled them to act as indicators for adaptive binding. Thus any labeling or modification of the aptamers or target molecules were made obsolete. This label-free method for aptamer-based molecular recognition was also successfully applied to biological fluids and therefore indicates that this approach is a promising tool for bioanalysis.