Linear Combination Of Molecular Orbitals Research Articles

Size Evolution Dynamics of Gold Nanoclusters at an Atom-Precision Level: Ligand Exchange, Growth Mechanism, Electrochemical, and Photophysical Properties

Interpretation of size evolution is an essential part of nanocluster transformation processes for unraveling the mechanism at an atom-precision level. Here we report the transformation of a non-superatomic Au23 to a superatomic Au36 nanocluster via Au28 cluster formation, activated by the bulky 4-tert-butylbenzenethiol ligand. Time-dependent matrix-assisted laser desorption ionization mass spectrometry data revealed that the conversion proceeds through ligand exchange followed by the size focusing method, ultimately leading to size growth. We also validated this transformation through time-dependent ultraviolet-visible data. Density functional theory calculations predicted that the kernel of the Au28 cluster evolved through a linear combination of molecular orbitals of the fragment of 2e- units (Au42+ and Au3+) from the kernel of the Au23 cluster. Periodic growth of gold cores through continuous growth of Au4 tetrahedral unit leads to the formation of the Au36 cluster from the Au28 cluster. These results reinforce the plausibility of size evolution through the growth mechanism during the transformation process. Differential pulse voltammetry studies showed that the highest occupied molecular orbital-lowest unoccupied molecular orbital gap inversely varies with the kernel size of these clusters. Photophysical experiments support the molecular-like intersystem crossing rather than core-shell relaxation to these clusters. The trends of photoluminescence lifetime were found to be the reverse of those of the energy gap law. The increment of lifetimes for the larger cluster can be mainly due to the contribution of both hot carriers and band-edge carriers.

Trimer effects in fragment molecular orbital-linear combination of molecular orbitals calculation of one-electron orbitals for biomolecules

The fragment molecular orbital (FMO)-linear combination of molecular orbitals (LCMO) method incorporates as an efficient post-process calculation of one-electron orbitals of the whole system after the FMO total energy calculation. A straightforward way to increase the accuracy is inclusion of the trimer effect. Here, we derive a comprehensive formulation called the FMO3-LCMO method. To keep the computational costs of the trimer term low enough, we use a matrix-size reduction technique. We evaluated the accuracy and efficiency of the FMO3-LCMO scheme in model biological systems (alanine oligomer and chignolin). The results show that delocalized electronic orbitals with covalent and hydrogen bonds are better described at the trimer level, and the FMO3-LCMO method is applicable to quantitative evaluations of a wide range of frontier orbitals in large biosystems.

Formation and Characterization of a Molecule–Metal–Molecule Bridge in Real Space

Metal-organic complexes were formed by means of inelastic excitations in a scanning tunneling microscope (STM). The electronic structure of the complex was characterized using STM imaging and spectroscopy. By exploiting the symmetry of the complex, its electronic structure can be rationalized from linear combinations of molecular orbitals. The actual bonding geometry, which cannot be inferred from STM alone, was determined from atomic force microscopy images with atomic resolution. Our study demonstrates that the combination of these techniques enables a direct quantification of the interplay of geometry and electronic coupling in metal-organic complexes in real space.

Origin of the 330 nm absorption band and effect of doping Yb in LiYF 4 crystals

The electronic structures of LiYF 4 (YLF) crystals containing F color center (YLF-F) and Yb doped YLF crystals (Yb 3+:YLF, Yb 2+:YLF) are systematically studied within the framework of the density functional theory. The calculated results indicate that the 330 nm absorption band originates from the F center in YLF crystals. Thus the doping of Yb 3+ can weaken the 330 nm absorption band by competing with F vacancies in capturing free electrons arising after γ-irradiation and change to Yb 2. By analyzing the lattice relaxation and the electronic structure of YLF containing Yb 2+, we can reasonably believe that once Yb 2+ is formed in YLF crystal, its compensating hole will turn out to be shared by two F − nearest to Yb 2+ forming a diatomic fluoride molecular ion ( F 2 − ) perturbed by Yb 2+, or to say V F color center. According to the molecular–orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F 2 − in V F center in LiYF 4 peaks at about 340 nm, which is in agreement with the experimental results.

Molecular orbital calculations on biopolymers. III. conductivity in nucleic-acid base homopolymers

The linear combination of molecular orbitals (LCMO) approximation has been employed to calculate the energy-independent conductivity term for some homopolymers of the bases found in the nucleic acids. The conductivity was assumed to be along the stacked bases; consequently, the sugar-phosphate backbone was neglected. The results are compared to the band-theory results of Ladik and co-workers and to the experimental results of Eley and co-workers. Reasonable agreement with the experimental results was obtained.

Molecular orbital calculation of biomolecules with fragment molecular orbitals

A new method of calculating molecular orbitals and orbital energy levels of biomolecules is proposed based on the fragment molecular orbital method (FMO), in which a huge biomolecule is first divided into ‘fragments’ for feasible calculation. In the present method, called FMO–LCMO, one-electron Hamiltonian of the whole molecule is derived from the output of FMO with little computational cost. The method gives fast and accurate description of the molecular orbitals of the whole system by a linear combination of molecular orbitals (LCMO) of the fragments and provides a good starting point for understanding the electronic structure of biomolecules.

Ab initio lattice relaxation and electronic structures of LiYF4 crystals containing VF color center

Abstract The electronic structures of perfect LiYF4 and the LiYF4 containing lithium vacancy VLi− with the lattice structure optimized are studied within the framework of the density functional theory. By analyzing the lattice relaxation and electronic structure of the LiYF4 containing VLi− we can reasonably believe that once VLi− is formed in LiYF4 crystal, its compensating hole will turn out to be shared by two F− nearest to VLi− forming a diatomic fluoride molecular ion (F2−) perturbed by VLi−, or to say VF color center. According to the molecular-orbital linear combination of atomic orbital (MO-LCAOs) theory, compared to the alkali halides, e.g. LiF, the F2− in VF center in LiYF4 peaks at about 337 nm, which is in agreement with the experimental results.

Electronic structure of the benzene dimer cation

The benzene and benzene dimer cations are studied using the equation-of-motion coupled-cluster model with single and double substitutions for ionized systems. The ten lowest electronic states of the dimer at t-shaped, sandwich, and displaced sandwich configurations are described and cataloged based on the character of the constituent fragment molecular orbitals. The character of the states, bonding patterns, and important features of the electronic spectrum are explained using qualitative dimer molecular orbital linear combination of fragment molecular orbital framework. Relaxed ground state geometries are obtained for all isomers. Calculations reveal that the lowest energy structure of the cation has a displaced sandwich structure and a binding energy of 20 kcal/mol, while the t-shaped isomer is 6 kcal/mol higher. The calculated electronic spectra agree well with experimental gas phase action spectra and femtosecond transient absorption in liquid benzene. Both sandwich and t-shaped structures feature intense charge resonance bands, whose location is very sensitive to the interfragment distance. Change in the electronic state ordering was observed between sigma and piu states, which correlate to the B and C bands of the monomer, suggesting a reassignment of the local excitation peaks in the gas phase experimental spectrum.

Structure and Bonding in B6‐ and B6: Planarity and Antiaromaticity.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Structure and Bonding in B6- and B6: Planarity and Antiaromaticity

The electronic structure and chemical bonding of B6- and B6 were investigated using anion photoelectron spectroscopy and ab initio calculation. Vibrationally resolved photoelectron spectra were obtained for B6- and were compared to calculations performed at various levels of theory. Extensive searches were carried out for the global minimum of B6-, which was found to have a planar D2h structure with a doublet ground state (2B2g). Good agreement was observed between ab initio detachment energies and the experimental spectra, establishing that the ground-state structure of B6- is planar, in contrast to the three-dimensional structures for the valence-isoelectronic Al6- and Al6 species. The chemical bonding in B6- was interpreted in terms of linear combinations of molecular orbitals of two B3- fragments. The antiaromatic nature of chemical bonding was established for B6- and B62-, based on the analysis of orbital contributions to overall paratropic ring currents.

Azabrendanes. III. Synthesis of stereoisomeric exo‐ and endo‐5‐acylaminomethyl‐exo‐2,3‐epoxybicyclo[2.2.1]heptanes and their reduction by lithium aluminum hydride

AbstractA number of stereoisomeric N‐[aryl(alkyl, cycloalkyl)carbonyl]‐exo(endo)‐5‐aminomethylbicyclo[2.2.1]hept‐2‐enes have been synthesized from bicyclo[2.2.1]hept‐2‐en‐exo(endo)‐5‐carbonitrile via reduction of the latter by lithium aluminum hydride and subsequent reactions of the resulting amines with aryl(alkyl, cycloalkyl)carbonyl chlorides and anhydrides. The direction of reaction of amides with peroxy acids does not depend on orientation of substituents in the bicyclic fragment: that is, for both exo‐ and endo‐isomers the epoxidations are completed by the formation of N‐[aryl(alkyl, cycloalkyl)carbonyl]‐exo(endo)‐5‐aminomethyl‐exo‐2,3‐epoxybicyclo[2.2.1] heptanes. The reduction of stereoisomeric epoxides by lithium aluminium hydride proceeds in different directions; that is, isomers with an exo‐oriented amido group form the substituted exo‐5‐alkylaminomethyl‐exo‐2,3‐epoxybicyclo[2.2.1]heptanes and the reactions of epoxides of endo‐amides are accompanied by intramolecular cyclization and completed by the formation of N‐[aryl(alkyl, cycloalkyl)]‐exo‐2‐hydroxy‐4‐azatricyclo[4.2.1.03,7]nonanes. The structures and stereochemical homogenity of the products have been confirmed by the analysis of 1H and 13C NMR spectra, correlation spectroscopy, and nuclear Overhauser enhancement spectroscopy experiments. We discuss the behavior of epoxides and provide an analysis of the coefficients of the atomic orbitals in the molecular orbital–linear combination of atomic orbitals equation (AM1 method). © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:119–130, 2001

Relationship between the Physicochemical Properties of Electrolytes and the Electronic Structure of Solvated Alkali Metal Cations

Group theoretical analysis and linear combinations of molecular orbitals of the cation and solvent are used to establish the nature and stability of bonds and hence the electric mobility of the cation and the viscosity of the electrolyte depending on the type of cation (Li+, Na+, K+, Rb+, Cs+) and molecules (H2O, NH3, H2CO, (CH3)2CO, CH3CN). Solvation effects on the UV photoelectron and intramolecular vibrational IR and NMR spectra are revealed.

Enhanced activation of implanted dopant impurity in hydrogenated crystalline silicon

We propose a physical model for enhanced activation of (implanted) dopant atoms in crystalline Si when the Si vacancy contains atomic hydrogen. Calculations of the potential barriers for inserting the interstitial phosphorus dopant into both hydrogenated and unhydrogenated vacancy sites of the crystalline Si dependent on the charge state of the hydrogenated vacancy, the hydrogen localization, and the transport direction of the interstitial atom to the vacancy are reported using the self-consistent field molecular-orbital linear combination of atomic orbitals technique in the neglect of diatomic differential overlap approach. The results suggest a decrease of the activation temperature for the phosphorus atoms by more than 300 \ifmmode^\circ\else\textdegree\fi{}C.

Collective resonances of the molecule: effects of electron-density profile

Previously, we discussed a purely classical model for analysing surface plasmons of the molecule. The molecule was described as an abrupt spherical shell containing an effective number of or electrons. This simple model was found to be quite applicable for analysis of electron energy loss spectra (EELS), describing the main features of the experimentally observed collective resonances of electrons. In this study we have extended our earlier classical model using spherically averaged radial charge distributions of constructed using different numbers of valence electrons. These charge distributions have been obtained from a self-consistent local density calculation, based on a molecular-orbital linear combination of atomic orbitals (MO-LCAO) approach. Use of this type of smooth charge distribution introduces, together with causality, a natural broadening of the collective resonances.

Quantum chemical studies of propene, ethylene, acetylene and dihydrogen reactivity in the insertion reaction into the titanium‐alkyl bond

AbstractUsing the ab initio method of SCF MO LCAOSCF MO LCAO: Self‐consistent field molecular orbital linear combination of atomic orbitals. in a valency‐splitted basis of the Gaussian functions we have studied the addition of various monomers (C3H8, C2H4, C2H2) and dihydrogen to the titanium‐alkyl bond in the complex H2TiCH3. The structure of transition states in the insertion reaction, heats of π‐complex formation and activation energies for the insertion of the coordinated monomers have been calculated. The calculation results show that the reactivity decreases in the order C2H2 > C2H4 > C3H8 > H2. According to the results obtained, the energy of the π*‐antibonding orbital of monomers can serve as an index of relative reactivity in the insertion reaction into the metal‐alkyl bond.

Nitrogen-containing defects in diamond: experimental data and molecular orbital linear-combination-of-atomic-orbitals

Calculations using the molecular orbital linear combination of atomic orbitals of the probable defect models are presented and calculated data are compared with those obtained by experiment.

Molecular orbital study of the bridging dioxygen ligand in [Al2(CH3)6(O2)

A recent X-ray structure determination of [Al2(CH3)6(O2)]– shows a new bridging co-ordination mode of the dioxygen ligand, with O–O distance and ν(O–O) frequency close to the values observed in solid Na2O2. This could suggest classifying the dinuclear aluminium compound as a peroxo complex. On the basis of results obtained from ab initio molecular orbital–linear combination of atomic orbital calculations, a different description of the electronic structure of the title compound is proposed. Despite the fact that the co-ordinated O2 ligand carries a small negative charge (0.41 electrons), the computed O–O bond length and harmonic frequency are close to the theoretical values expected for the gaseous O2– species. As a consequence, the classification of the dioxygen complex as a peroxo or superoxo complex is of little help in elucidating the real electronic structure of the dioxygen ligand. The electronic mechanism of bonding of the dioxygen to an s–p element like aluminium is markedly different from that occurring in transition-metal compounds, despite some similarities in charge distribution and O–O bond length.

A program for calculating the electronic structure of polyatomic molecules by linear combination of fragment molecular orbitals

The method of linear combination of molecular orbitals (LCMO) is used in approximate quantum-chemical calculations on complicated molecular systems. The molecular orbitals are constructed as in the usual semiempirical methods from the valence orbitals of the atoms, and in LCMO the molecular orbitals for the combined system or complex are constructed from a restricted number of especially selected multicenter fragment orbitals. They have developed the LCMO method in the approximation involving complete neglect of differential overlap. In this publication they describe briefly the program to realize this method.

Origin of the negative shift of half-wave reduction potentials of aromatic polynuclear p-quinones with increasing conjugation.

The half-wave reduction potentials (Ered1/2) of aromatic polynuclear p-quinones are negative shifted with increasing π-electron conjugation, although the Ered1/2 values of usual organic substances are positive shifted with the above structure change. The main reason for this exceptional behavior of the p-quinones has been discussed in detail by applying the composite system method (linear combination of molecular orbitals (LCMO) approximation). For example, after dividing naphthoquinone into benzoquinone and cis-butadiene we consider the mutual interaction between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the former and those of the latter. It was concluded that the interaction between the LUMO of the former and the HOMO of the latter plays an important role. so that the LUMO of benzoquinone is destabilized by going to naphthoquinone, leading to the negative shift of Ered1/2 value.

L2,3MMAuger electron spectrum of the HCl molecule

The high-resolution Auger electron spectrum of HCl has been measured in the gas phase with the use of electron-beam excitation. The fine structure of the spectrum has been interpreted and compared with the calculated line energies. The energies of the initial states in H${\mathrm{Cl}}^{+}$ and the final states in H${\mathrm{Cl}}^{2+}$ have been calculated in the molecular-orbital linear combination of atomic orbitals self-consistent-field approach, with the correlation effects being taken into account in the frame of the configuration-interaction technique. The relative line intensities have been discussed in the light of the analogy to the Auger spectrum of the next-neighbor and isoelectronic element argon.