Orbital contributions to the molecular charge and energy density distributions in Co2(CO)8

For Co2(CO)8, the representative of a whole class of bridged cobalt complexes, the 18-electron rule predicts a direct metal-metal bond in addition to the metal-bridge bonds. By intuition, this bond should have bent-bond character. However, it is well-known from charge density analyses that no bond critical point exists in the corresponding spatial region. Otherwise, the energy density distribution points to a certain stabilizing contribution of this local area to the total molecular energy. It is shown that a partitioning of the total charge and energy densities into orbital contributions can lead to a deeper insight into complex bonding properties.     

Visualizing molecular wavefunctions using Monte Carlo methods

Using explicitly correlated wavefunctions and variational Monte Carlo we calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree–Fock wavefunction and then comparing these values with our explicitly correlated values. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Effective potential energy curves of H2 molecule evolving in a strong time‐dependent magnetic field

Evolution of hydrogen molecule, starting initially from its field‐free ground state, in a time‐dependent (TD) magnetic field of order 10¹¹ G is presented in a parallel internuclear axis and magnetic field‐axis configuration. Effective potential energy curves (EPECs), in terms of exchange and correlation energy, of the hydrogen molecule as a function of TD magnetic‐field strength, are analyzed through TD density functional computations based on a quantum fluid dynamics approach. The numerical computations are performed for internuclear separation R ranging from 0.1 to 14.0 a.u. The EPECs exhibit field‐dependent significant potential‐well minima both at large internuclear separations and at short internuclear separations with a considerable increase in the exchange and correlation energy of the hydrogen molecule. The results, when compared with the time‐independent (TI) studies involving static TI magnetic fields, reveal TD behavior of field‐dependent crossovers between different spin‐states of hydrogen molecule as indicated by the TI investigations in static magnetic fields. Besides this, present work reveals interesting dynamics in the TD total‐electronic charge‐density distribution of the hydrogen molecule. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An investigation of the two electron chemical bond calculating energy expectation values from density matrix partitionings. II. The heteronuclear case HeH+

Bond energy contributions calculated from first and second order density matrix terms as partitioned by Ruedenberg's procedure have been obtained for HeH⁺ in the ground state and in the first excited 1Σ⁺. For the chemically bonded ground state the full partitioning is investigated for all internuclear distances R. The wavefunctions used for calculating the density matrices are obtained from an SCF calculation at near Hartree-Fock quality, using Slater orbitals with exponents which for each R are optimized simultaneously with the coefficients. For the excited state a limited CI has been performed. The results for promotional, charge transfer, and interference terms for kinetic and potential bond contributions are presented in the form of energy plots E(R). Starting from the promoted atoms and subsequently allowing for charge transfer the importance of the electron interaction is demonstrated by the unusually low quasiclassical electron repulsion curve due to electronic charge transfer, which makes an essential contribution to the decrease in energy during bond formation.     

Continua of interactions between pairs of atoms in molecular crystals

The electron density distributions in crystals of five previously studied DMAN complexes and five Schiff bases (two new ones) have been analysed in terms of various properties of bond critical points (BCPs) found in the pair-wise interactions in their lattices. We analysed the continua of interactions including covalent/ionic bonds as well as hydrogen bonds and all other types of weak interactions for all pairs of interacting atoms. The charge density at BCPs and local kinetic and potential energy densities vary exponentially with internuclear distance (or other measures of separation). The parameters of the dependences appear to be characteristics of particular pairs of atom types. The Laplacian and the total (sum of kinetic and potential) energy density at BCPs show similar behaviour with the dependence being of the Morse type. The components lambda1, lambda2, lambda3 of the Laplacian at BCPs vary systematically with internuclear distance according to the type of atom pair. For lambda1 and lambda2 the distribution is of the exponential type, whereas lambda3 does not seem to follow any simple functional form, consistent with previous theoretical findings. Analytical nonlinear dependences of Laplacian on charge density have been found. They agree reasonably well with those obtained by least square fit of the Laplacian to charge density data. There are four distinct regions of the [symbol: see text]2rho(BCP)/rho(BCP) space, generated by E(BCP) = 0 and G(BCP)/rho(BCP) = 1 conditions. Two regions clearly correspond to the shared-shell and closed-shell interactions and the other two to some intermediate situation.     

Topological analysis of the electron density distribution in perturbed systems. I. Effect of charge on the bond properties of hydrogen fluoride

Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4sigma antibonding orbital of the neutral (F...H) system or the removal of one electron from its pi nonbonding orbitals, leading to (F...H)- and to (F...H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of rho(r). For (F...H), (F...H)-, and (F...H)+, the topological and energetic properties calculated at the F...H bond critical point (BCP) have been related to the 3sigma bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to rho(r) at the interatomic surface. The analysis has been carried out at several F...H internuclear distances, ranging from 0.8 to 3.0 A. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the pi and 4sigma electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F...H), (F...H)-, and (F...H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F-H bond but soften it, giving rise to the stable species (F-H)- and (F-H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F...H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F...H)+ and of the BMO expansion toward both nuclei in (F...H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F...H) (d(eq)0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system rho(d(eq)0), inverted triangle2 rho(d(eq)0), and H(d(eq)0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution.     

外电场对甲醛分子的结构与电子光谱的影响

采用密度泛函理论(DFT)在B3LYP/6-311++G(d,p)基组水平上,计算了不同外加电场(-8.22×10~9~8.22×10~9 V/m)下甲醛分子基态稳定构型、分子键长、电荷分布、能级分布、能隙、红外光谱、拉曼光谱和分子的总能量.在此基础上利用TDDFT/B3LYP/6-311++G(d,p)方法研究了甲醛分子由基态跃迁到前25个激发态的激发能E、谐振强度f、吸收波长λ受外电场的影响.结果表明:随着C=O连线方向外电场的增加,C=O键键长、氢原子电荷、偶极矩和能隙递增;C—H键键长、C,O原子电荷递减,总能量降低.振动频率与红外强度及拉曼强度由于不同振动有不同变化.甲醛分子UV-Vis光谱随外电场的增加,不同的吸收峰发生了不同程度的蓝移或者红移;外电场对甲醛分子的激发能、谐振强度和吸收波长的强度有一定影响,但随电场变化比较复杂.     

The incorporation of hydration forces determined by continuum electrostatics into molecular mechanics simulations

A new technique is presented for incorporating hydration forces into molecular mechanics simulations. The method assumes the classical continuum approximation, where a solvated molecule is represented as a low-dielectric cavity of arbitrary shape embedded in a continuous region of high dielectric constant. Electrostatic effects are computed by first calculating the distribution of polarization charge (induced by the configuration of solute fixed charges) at the molecular surface. The hydration force at a particular atom is then found as the sum of the coulombic interaction with the induced surface charge, plus a purely mechanical contribution that arises from the pressure of the polarized solvent as it is pulled toward the solute. A procedure is developed to use the computed hydration forces in conjunction with the CHARMM molecular mechanics package to carry out energy minimizations in which the effects of solvation are explicitly included. This new technique also allows a detailed analysis of the relative balance of coulombic, hydration, and steric energies as a function of molecular conformation. The method is applied to the test case of a zwitterionic tripeptide (LYS-GLY-GLU), and the computational results suggest that hydration effects can play a significant role in determining a stable conformation for a solvated polar molecule. The future application to larger molecules is discussed.     

Nonequilibrium molecular transport photoinduced by potential energy fluctuations

The mechanism of directed substrate-parallel motion of molecules caused by photoinduced potential energy fluctuations is investigated. Unlike simplistic models (e.g., an on-off ratchet), the approach suggested implies that the necessary asymmetry of the potential energy can arise not only from the asymmetry of the substrate potential but also from an asymmetric distribution of the fluctuating charge density in the molecule. The thus induced asymmetry of the potential energy governs the direction motion and enables, under certain conditions, its reversal at some frequencies of resonant laser pulses or temperature. These inferences are exemplified by the model charge distributions in the molecule and substrate, and the charge density fluctuations which are obtained by quantum chemical calculations for the realistic molecule of a substituted phenylpyrene compound on a model substrate.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

Role of triple bond in 1,2-diphenylacetylene crystal: A combined experimental and theoretical study

We have performed a combined experimental and theoretical study of the molecular system of 1,2-diphenylacetylene. The occurrence of two different geometries of the molecule in the crystal structure, one being planar and the other tilted by approximately 6 degrees , has been investigated in relation to the nature of the acetylenic linker. The experimental charge density analysis shows that the acetylenic linker exhibits a noncylindrical density reminiscent of the strong conjugation present in the molecule. The pi-orbitals of the acetylenic linker derived from density functional theory (DFT) calculations are found to sustain a variety of conjugation lengths between the phenyl rings, thereby giving flexibility to the molecule to arrange itself in various packing conformations in the crystal. It is interesting that the energy involved for such distortions is only kBT, allowing several polymorphic forms of the crystal structure as reported in the literature. The distortions entertained by the molecule and the corresponding changes in the charge density distribution and energy are all relevant to molecular electronics.     

A zero differential overlap study of chemical binding in ammonia-borane and carbony l-borane

A cndo/2D study of the charge distribution obtained through Mulliken population analysis in the ground state of the title compounds shows that the features of charge distribution found by severalab initio calculations are fairly well reproduced by this method. The one-particle density, the interference density at the mid-point of the bond axis and the kinetic part of the interference energy calculated through the deorthogonalized density matrices over a wide range of intermolecular separation between the donor and the acceptor show that the one-particle density and the interference density steadily grow with decreasing internuclear separation, while the kinetic interference energy starts with negative value at large distance, then decreases and passes through a minima near but above the equilibrium distance and then increases rapidly below it conforming to the characteristic general behaviour of the kinetic component of Morse curve. The orbital pairwise interference density and the corresponding kinetic energy components reveal that the orbitals involved in the covalent binding are σ_2p AO of B and 2S and σ_2p AO of N and C atoms in H₃B-NH₃ and H₃B-CO respectively.     

Nonempirical statistical theory for molecular evaporation from nonrigid clusters

We propose a nonempirical statistical theory to give the reaction rate and the kinetic energy distribution of fragments for molecular evaporation from highly nonrigid atomic and van der Waals clusters. To quantify the theory, an efficient and accurate method to evaluate the absolute value of classical density of states (the Thomas-Fermi density in phase space) and the flux at the so-called dividing surface is critically important, and we have devised such an efficient method. The theory and associated methods are verified by numerical comparison with the corresponding molecular dynamics simulation through the study of Ar(2) evaporation from Ar(8) cluster, in which evaporation is strongly coupled with structural isomerization dynamics. It turns out that the nonempirical statistical theory gives quite an accurate reaction rate. We also study the kinetic energy release (KER) arising from these evaporations and its Boltzmann-like distribution both for atomic and diatomic evaporations. This provides a general relation between the KER and temperature of the fragments.     

Probing the weakest bond and the cleavage of p‐chlorobenzaldehyde diperoxide energetic molecule via quantum chemical calculations and theoretical charge density analysis

A high‐level ab initio Hartree‐Fock/Møller‐Plesset 2 and density functional theory quantum chemical calculations were performed on p‐chlorobenzaldehyde diperoxide energetic molecule to understand its bond topological, electrostatic, and energetic properties. The optimized molecular geometry for the basis set 6‐311G** exhibit chair diperoxide ring and planar aromatic side rings. Although the diperoxide ring bear same type of side rings, surprisingly, both the rings are almost perpendicular to each other, and the dihedral angle is 96.1°. The MP2 method predicts the O? O bond distance as ～1.466 Å. The charge density calculation reveals that the C? C bonds of chlorobenzaldehyde ring have rich electron density and the value is ～2.14 e Å^?3. The maximum electron density of the O? O bonds does not lie along the internuclear axes; in view of this, a feeble density is noticed in the ring plane. The high negative values of laplacian of C? C bonds (approximately ?22.4 e Å^?5) indicate the solidarity of these bonds, whereas it is found too small (approximately ?1.8 e Å^?5 for MP2 calculation) in O? O bonds that shows the existence of high degree of bond charge depletion. The energy density in all the C? C bonds are found to be uniform. A high electronegative potential region is found at the diperoxide ring which is expected to be a nucleophilic attack area. Among the bonds, the O? O bond charge is highly depleted and it also has high bond kinetic energy density; in consequence of this, the molecular cleavage is expected to happen across these bonds when the material expose to any external stimuli such as heat or pressure treatment. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Density dependence of the entropy and the solvation shell structure in supercritical water via molecular dynamics simulation

We perform molecular dynamics simulations of supercritical water (SCW) with a wide range of densities along a near critical isotherm using the simple point charge extended (SPC/E) pair potential in order to study the entropy and the solvation shell structure around a central water molecule. It is shown that both the translational and orientational two-particle correlation entropy terms can serve as the metrics of the translational-orientational structural orders in water and it is revealed that the translational structural order is very sensitive to the density variation in the gas-like and liquid-like region, while the orientational structural order is much more dependent upon compression in the medium-density SCW region. The comparison of the magnitudes of the full thermodynamic excess entropy and two-particle correlation entropy confirms the recent findings that the many-body terms other than two-body ones also present significant and non-neglectable contributions to the full excess entropy for the highly anomalous fluids like water. The analysis of entropy terms as a function of intermolecular distance and the orientational distribution functions as well as the three-dimensional spatial distribution functions indicate that the structural order occurs only in a much more diffused first solvation shell due to the elongated hydrogen bonds under supercritical conditions. It is revealed that no obvious second or higher neighbor shells occur in SCW, in contrast with the feature of normal liquid water that the anomalous decrease of translational order upon compression occurs mainly in the second shell.     

Coulomb explosion of nitrogen and oxygen molecules through non-Coulombic states

We have systematically studied Coulomb explosion of nitrogen and oxygen molecules in intense 8 and 24 fs laser pulses. In the experiment, we explicitly separated all explosion pathways through coincident measurements. The high resolution kinetic energy releases (KERs) and the exotic angular distributions of atomic ions provide direct evidence that Coulomb explosion occurs through non-Coulombic states. In the theory, we calculated dissociation potential energy curves (PECs) of nitrogen and oxygen molecules and their multicharged molecular ions using multiconfiguration second-order perturbation theory. The results indicate that Coulomb potentials are close to the accurate PECs of multicharged molecular ions only when the internuclear distance is larger than 3 ?. In comparison with the experimental observations and the theoretical calculations, we determined the internuclear distance when Coulombic explosion occurs. It is near the equilibrium distance of the neutral molecules in the case of 8 fs laser pulses and expands gradually with the increase of the charge state of the molecular ions in the case of 24 fs laser pulses.     

Strategies to model the near-solute solvent molecular density/polarization

The solvent molecular distribution significantly affects the behavior of the solute molecules and is thus important in studying many biological phenomena. It can be described by the solvent molecular density distribution, g, and the solvent electric dipole distribution, p. The g and p can be computed directly by counting the number of solvent molecules/dipoles in a microscopic volume centered at r during a simulation or indirectly from the mean force F and electrostatic field E acting on the solvent molecule at r, respectively. However, it is not clear how the g and p derived from simulations depend on the solvent molecular center or the solute charge and if the g(F) and p(E) computed from the mean force and electric field acting on the solvent molecule, respectively, could reproduce the corresponding g and p obtained by direct counting. Hence, we have computed g, p, g(F), and p(E) using different water centers from simulations of a solute atom of varying charge solvated in TIP3P water. The results show that g(F) and p(E) can reproduce the g and p obtained using a given count center. This implies that rather than solving the coordinates of each water molecule by MD simulations, the distribution of water molecules could be indirectly obtained from analytical formulas for the mean force F and electrostatic field E acting on the solvent molecule at r. Furthermore, the dependence of the g and p distributions on the solute charge revealed provides an estimate of the change in g and p surrounding a biomolecule upon a change in its conformation.     

Vibrational motion in isotopomers of the HeH+ molecular ion: An application of the electron nuclear dynamics method

The importance of isotopic substitution as a tool for elucidation of chemical reaction events originates in the fact that the Coulombic Hamiltonian is isotopically invariant except for the nuclear kinetic energy term. Thus, in theories of isotope effects based on the Born-Oppenheimer scheme, the basic presumption is the invariance of the potential energy surface (PES). We use, however, a fully dynamic approach, called Electron Nuclear Dynamics (END), which does not require a preconstructed PES. Since the END formalism is rather different from commonly used procedures, we study the anharmonic nuclear vibration in isotopic species of the HeH⁺ molecular ion as a model problem. A single time-dependent complex parametrized determinantal wave function is used for the electrons and the nuclei are treated classically. The time evolution of the nuclear and electronic dynamical variables obtained by integration of equations of motion are reported as bond length, nuclear kinetic energy, and Mulliken populations. The molecule vibrates as a classical object. The product of the reduced mass and the square of the vibrational frequency is isotopomer invariant for any common total energy. The difference between the total energy and the nuclear kinetic energy as a function of the internuclear distance is interpreted as the average dynamic potential. © 1997 John Wiley & Sons, Inc.