Long-range dispersion interactions involving excited atoms; The H(1s)–H(2s) interaction

The dispersion interaction between two nonoverlapping atoms (or molecules) is expressed in terms of single-atom “polarizabilities.” The formulation is valid even if one atom (or both) is in an excited state. To illustrate the procedure, the dispersion interaction between a 1s and a 2s hydrogen atom is computed accurately through order R^?10 (R = internuclear separation).     

Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third- and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R^?1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H? H⁺ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R^?1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R^?1 expansion is analyzed to see why it works as well as it does.     

Asymptotic behavior of the primitive function of different “symmetry-adapted” perturbation schemes for the H ground state

The leading terms in the asymptotic 1/R expansion of the wave functions and energies of various “symmetry-adapted” perturbation schemes for intermolecular forces, as well as for the “polarization approximation” (PA ) are derived for the H ground state, both exactly (i.e., to infinite order in λ) and in the first two orders of the λ expansion. It is pointed out that only in the PA and the Hirschfelder–Silbey scheme is the formal primitive function Φ genuinely primitive, whereas Φ in the other schemes is asymmetric in a rather strange way. In this lack of genuine primitivity lies the reason why in these schemes the leading term of the 1/R expansion is only recovered to infinite order in λ and requires knowledge of the R^?4 term of the wave function, provided that one uses the “internal” energy expression. Four different energy expressions are compared that behave differently in the different schemes. The results obtained here are basis independent, but the implications of the basis completeness problem are discussed as well.     

Note on the atomic correlation energy

In the introductory section, we compare the total, kinetic, nuclear-electron, Coulomb, exchange, and correlation energies of ground-state atoms. From the analyses of the data, one can conclude that the Hartree-Fock (HF) model is notably good and might require only a small perturbation to become essentially an “accurate” model. For this reason and considering past literature, we present a semiempirical extension of the HF model. We start with a calibration of three independent models, each one with an effective Hamiltonian, which introduces a small perturbation on the kinetic, the nuclear-electron, or the Coulomb HF operators. The perturbations are expressed as very simple functions of products of orbital probability density. The three perturbations yield very equivalent results and the computed ground-state energies are reasonably near to the accurate nonrelativistic energies recently provided by E. Davidson and his collaborators for the 2–18 electron systems and the estimates by Clementi and his collaborators for the 19–54 electron systems. The first ionization potentials from He to Cs, the second ionization potentials from Li to Zn, and excitation energies for npⁿ, 3dⁿ, and 4s¹3dⁿ configurations are used as additional verification and validation. The above three effective Hamiltonians are then combined in order to redistribute the correlation energy correction in a way which exactly satisfies the virial theorem and maintains the HF energy ratios between kinetic, nuclear-electron, and electron-electron interaction energies; the resulting effective Hamiltonian, named “virial constrained,” yields good quality data comparable to those obtained from the three independent effective operators. Concerning excitation energies, these effective Hamiltonians yield values only in modest agreement with experimental data, even if definitively superior to HF computations. To further improve the computed excitation energies, we applied an empirical scaling in the vector coupling coefficient; this correction yields very reasonable excitations for all the configurations that we have considered. We conclude that the use of effective potentials to introduce small perturbations density-dependent onto the HF model constitutes a broad class of practical and reliable semiempirical solutions to atomic many-electron problems, can provide an alternative to popular proposals from density functional theory, and should prepare the ground for “generalized HF models.” © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 571–591, 1997     

Long-range interaction between 1s and 2s or 2p hydrogen atoms

Long-range interaction energy between two hydrogen atoms has been computed in the second order of the perturbation theory. All states of the system arising when one of the atoms is in the 1s and the other in the 2s or 2p state have been considered. The energy represented by a series expansion in inverse powers of the internuclear distance, R, has been computed up to the terms in R^?8. The results are believed to give reliable interaction energies for R > 15 a.u. Accurate interaction energy for two ground-state hydrogen atoms has also been obtained up to the terms in R^?10. Results for the B′ ¹∑ state are employed to discuss the experimental ground-state dissociation energy of H₂, D₂, and HD. For H₂ all values of the dissociation energy obtained from various experimental absorption limits, by using the computed potential energy curve to separate off the effect of rotation, are shown to be satisfactorily consistent. The resulting total energy of H₂ is, however, higher than the most accurate theoretical value.     

A reversible fluorescence “ON–OFF–ON” sensor for sequential detection of F− and Cu2+ ions and its application as a molecular-scale logic device and security keypad lock

A new azoimine receptor, R₁, was synthesized by Schiff base condensation of 4-(4-butylphenyl) azophenol and 2,6-diaminopyridine and acts as a colorimetric and fluorometric chemosensor for F^? and also toward Cu²⁺ ions in aqueous environment. UV–Vis absorption and fluorescent emission spectra were employed to study the sensing process. Emission study was performed to examine the dual sensing ability of the obtained probe with sequential addition of F^? followed by Cu²⁺ and vice versa. The receptor is an efficient “ON–OFF” fluorescent probe for the fluoride ion. Also, R₁ + F^? operated as an “OFF–ON” fluorescent sensor for Cu²⁺ ions. Considering emission intensity and absorption wavelength for F^? and Cu²⁺ ions, a molecular system was developed with the ability to mimic the functions of XNOR logic gating on the molecular level. In addition, R₁ behaved as a molecular security keypad lock with F^? and Cu²⁺ inputs. The keypad lock operation is particularly important, as the output of the system depends not only on the proper combination but also on the order of input signals, creating the correct password that can be used to “open” this molecular keypad lock through strong fluorescence emission at 460?nm.     

Recognition Polymers

From the universe of polymeric materials which appear in biology and medicine we select for discussion that set whose principal function is to recognize and respond appropriately to specific substances in their environment. They may be 1.2, 2.2, or 3 dimensional shapes such as messenger RNA, cellulose acetate membranes, or artificial esophagi. They may function by recognizing the difference between right and wrong chemical species and responding by binding the correct ones and rejecting the wrong ones, e.g., enzymes and their substrates, codons and their anticodons. What happens after recognition and response is not of interest at the moment, e.g., the catalytic effect of the enzyme on the bound substrate or the codonanticodon binding effect on protein synthesis.

Another example is in the chemical senses where there is sketchy evidence that proteins are involved in recognizing tastants. This could be done by having a protein on the tongue bind all tastants (rather close contact is required to make fine distinctions) and then recognize them by very intimate contacts and sending signals to the brain for conscious recognition. Alternatively, each taste modality may have a protein that excludes all but one type and generates only one signal for the CNS.

Another important class are antibodies that recognize their own antigens out of about 10⁴ different ones and complex with them and exclude the others. A model for antigen-antibody interaction must account for the non-binding of nonantigens as well as the much simpler case of the binding of the antigen.

Another class are the permselective membranes that recognize some species and let them pass while recognizing others and not let them pass. A final class to be discussed will be implant polymers which have an un-desired ability to recognize and bind platelets.

The question we are asking is whether it is possible to establish general principles in chemical physics that govern these different types of molecular recognition so that the principles could be incorporated into polymer design. Recent advances in “intermolecular” force theory suggests that this goal is achievable in the foreseeable future. Intermolecular has been put in quotes because when two molecules are in sufficiently close contact to recognize one another they probably have an appreciable exchange term and are therefore not two molecules but one.

The recent advances referred to involve computer simulation of complex formation using the new 1-4-6-12 potential forms corresponding to a long range (R^?1) coulombic electrostatic interaction, a medium range (R^?4) electrostatic-induced dipole attraction, a short range (R^?6) dispersive attraction, and a very short range (R^?12) orbital overlap repulsion. In the cases of interest, e.g., in an aqueous environment, all four terms are important and statements such as “the binding is purely electrostatic,” i.e., all R^?1, are misleading as well as wrong (since even ions need the R^?12 repulsion to keep them at their equilibrium distance). Discussions of permeability in terms of “pore sizes” is equally limiting for it implies that only the R^?12repulsion is appreciable. The fallacy of using competitive equilibria to determine the relative contributions of terms will be discussed. The im: portant use in biology of “other contacts” within the system to give a variable base line so that the typical binding-no binding discrimination can be made with attraction-less attraction rather than the more awkward attraction-repulsion potentials will also be discussed.     

Statistical representation of atomic systems structure. II. classification of the representation; entropy dependence of the total energy for isoelectronic series

The energies of the ground states of the mononuclear atomic systems, until now determined merely by approximate methods, turn out to exhibit some almost exact interdependencies. A simple statistical functional of the electronic structure (the “γ representation”) turns out to be decisive for the system energy. In this paper that interdependence is further traced for the N-electron systems in isoelectronic series (with constant N and varying Z). The resulting “combinatorial formula” reproduces the experimental data with the errors at least ten times smaller than those of the conventional Hartree–Fock approximation. The reason why there is such an exact formula for the ground-state energy remains to be clarified. The limiting behavior of our energy formula for large Z exhibits consistency with the Thomas–Fermi and the Z^?1perturbation expansion models.     

Long range interaction energies using Gaussian basis sets and a one center method

A one center method, based on the work of Karplus and Kolker, is discussed and used to calculate the induction energy, through O(R^?8), for the H(ls) – H⁺ interaction employing two types of Gaussian basis sets constructed from functions of the form {r^je^?αr2}. The effective hydrogen atom excitation energies and transition multipole moment matrix elements generated in these calculations are used to calculate the dispersion energy for the H(ls) – H(ls) interaction, through O(R^?10), and the R^?9 triple dipole energy corresponding to the interaction of three H(ls) atoms. The results indicate that Gaussian functions can form good basis sets for obtaining long range forces for a variety of multipole interaction energies.     

Electrochemical investigation of the chemical diffusion,partial ionic conductivities,and other kinetic parameters in Li3Sb and Li3Bi

The galvanostatic intermittent titration technique (GITT) has been used to electrochemically determine the chemical and component diffusion coefficients, the electrical and general lithium mobilities, the partial lithium ionic conductivity, the parabolic tarnishing rate constant, and the thermodynamic enhancement factor in “Li₃Sb” and “Li₃Bi” as a function of stoichiometry in the temperature range from 360 to 600°C. LiCl, KCl eutectic mixtures were used as molten salt electrolytes and Al, “LiAl” two-phase mixtures as solid reference and counterelectrodes. The stoichiometric range of the antimony compound is rather small, 7 × 10^?3 at 360°C, whereas the bismuth compound has a range of 0.22 (380°C), mostly on the lithium deficit side of the ideal composition. The thermodynamic enhancement factor in “Li₃Sb” depends strongly on the stoichiometry, and has a peak value of nearly 70 000; for “Li₃Bi” it rises more smoothly to a maximum of 360. The chemical diffusion coefficient for “Li₃Sb” is 2 × 10^?5 cm² sec^?1 at negative deviations from the ideal stoichiometry and increases by about an order of magnitude in the presence of excess lithium at 360°C. The corresponding value for “Li₃Bi” is 10^?4 cm² sec^?1 with high lithium deficit, and increases markedly when approaching ideal stoichiometry. The activation energies are small, 0.1–0.3 eV, depending on the stoichiometry, in both phases. The mobility of lithium in “Li₃Bi” is about 500 times greater than in “Li₃Sb” with a lithium deficit. The ionic conductivity in “Li₃Sb” increases from about 10^?4 Ω^?1 cm^?1 in the vacancy transport region to about 2 × 10^?3 where transport is probably by interstial motion at 360°C. For “Li₃Bi” a practically constant value of nearly 10^?1 Ω^?1 cm^?1 is found at 380°C. The parabolic tarnishing rate constant shows a sharp increase at higher lithium activities in “Li₃Sb” whereas in “Li₃Bi” it has a roughly linear dependence upon the logarithm of the lithium activity. The tarnishing process is about 2 orders of magnitude slower for “Li₃Sb” than for “Li₃Bi.” Because of the fast ionic transport in these mixed conducting materials, “Li₃Sb” and “Li₃Bi” may be called “fast electrodes.”     

A crossed molecular beam study of the chemiluminescent reaction Xe(3P2,0) + BrCN → Xe(1S0) + Br + CN(B2Σ+)

The chemiluminescent interaction of Xe(³P_2,0) and BrCN has been studied under crosscd-beam conditions at collision energies ranging up to 70 kj mol^?1. The CN(B → X) fluorescence spectrum, the excitation function for its production and the fluorescence polarisation - or rather its absence - have been determined. The results can be explained by a two-stage harpooning mechanism involving an inert-gas cyanide (Xe⁺CN^?)¹ intermediate but not by a “sensitisation” mechanism proceeding through electronic energy transfer.     

The decomposition of chemically activated n–butane,isopentane, neohexane,and n–pentane and the correlation of their decomposition rates with radical recombination rates.

The total decomposition rates of the chemically activated alkanes n-butane, n-pentane, isopentane, and neohexane were measured using an internal comparison technique. Chemical activation was by the C? H insertion reaction of excited singlet-state methylene radicals. A total of ten rate constants ranging from 4.6 × 10⁵ to 2.3 × 10⁷ sec^?1 were measured for these alkanes at different excitation energies. These rates correlate via RRKM theory calculations with thermal A-factors in the range of 10^16.1 to 10^17.1 sec^?1 for free rotoractivated complex models and in the range of 10^16.4 to 10^17.8 sec^?1 for vibrator-activated complex models. It was found that high critical energies for decomposition, “tight” radical models, and activated complex models with free internal rotations were required to correlate the decomposition rates of these alkanes with estimated alkyl radical recombination rates. The correlation is just barely possible even for these favorable extremes, indicating that there may be a basic discrepancy between the recombination rate and decomposition rate data for alkanes.     

Intermolecular Interactions in Weak Donor–Acceptor Complexes from Symmetry‐Adapted Perturbation and Coupled‐Cluster Theory: Tetracyanoethylene–Benzene and Tetracyanoethylene–p‐Xylene

The interactions in the complexes of tetracyanothylene (TCNE) with benzene and p‐xylene, often classified as weak electron donor–acceptor (EDA) complexes, are investigated by a range of quantum chemical methods including intermolecular perturbation theory at the DFT‐SAPT (symmetry‐adapted perturbation theory combined with density functional theory) level and explicitly correlated coupled‐cluster theory at the CCSD(T)‐F12 level. The DFT‐SAPT interaction energies for TCNE–benzene and TCNE–p‐xylene are estimated to be ?35.7 and ?44.9 kJ mol^?1, respectively, at the complete basis set limit. The best estimates for the CCSD(T) interaction energy are ?37.5 and ?46.0 kJ mol^?1, respectively. It is shown that the second‐order dispersion term provides the most important attractive contribution to the interaction energy, followed by the first‐order electrostatic term. The sum of second‐ and higher‐order induction and exchange–induction energies is found to provide nearly 40 % of the total interaction energy. After addition of vibrational, rigid‐rotor, and translational contributions, the computed internal energy changes on complex formation approach results from gas‐phase spectrophotometry at elevated temperatures within experimental uncertainties, while the corresponding entropy changes differ substantially.     

Invariance properties of the multipole expansion

The calculations of long-range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σ C_kR^?k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.     

On the mechanism of interaction between copper (I) and O2

The mechanism of the interaction of Cu⁺-α,α-dipyridyl complex (Cu⁺L₂) with O₂ in both neutral and acid media was studied by the stopped-flow method. The dependence of the mechanism on the acidity of the medium was established. In an acid medium H⁺ participated in a direct O₂ reduction to HO₂ by interaction with an oxygen adduct L₂Cu⁺O₂ formed without displacement of ligand molecules. In a neutral medium the reaction rate was limited by inner sphere charge transfer from Cu⁺ to O₂ to form an oxygen “charge transfer” complex L₂CuO⁺₂. The latter interacted either with the second ion Cu⁺L₂ or with the free ligand, or else it dissociated, reversibly or irreversibly, to form a radical anion O^?₂. The bimolecular rate constants of the oxygen “adduct” and “charge transfer” complex formation appeared to be k_bi = (1.0 ± 0.1) × 10⁵ and (1.5 ± 0.2) × 10⁴M^?1?sec^?1, respectively. The effective termolecular rate constants of O₂ reduction to HO₂ in an acid medium (with contribution from H⁺) and to O^?₂ in a neutral medium (with contribution from α,α-dipyridyl) were k_ter = 2.7 × 10⁸ and 10⁷M^?2?sec^?1. The rate constants of the elementary steps were estimated. The auto-oxidation mechanism of the aquoion and complexes of Cu⁺ is discussed in terms of the results obtained.     

六、七、八元瓜环与苯胺系列衍生物的相互作用

利用紫外吸收光谱、荧光光谱以及¹H NMR方法详细考察了六、七、八元瓜环(Q[6], Q[7], Q[8])与苯胺系列衍生物客体的相互作用和体系pH对其作用的影响. 实验结果表明, 3种瓜环与苯胺系列衍生物客体的相互作用强弱、作用比例以及作用模式与体系的酸度密切相关: 在“高”或“低”pH条件下, 未观察到瓜环与这些客体的明显作用; 在介于“高”与“较高”或“低”与“较低”的pH范围, 瓜环与这些客体发生相互作用, 形成1∶1的包结配合物; 而在介于“较高”与“较低”的pH范围, 瓜环与这些客体发生相互作用, 可形成1∶2的包结配合物. 对于不同的瓜环-客体作用体系, 相应的pH范围各不相同. 本文利用简便的实验方法, 测试了这些pH值及其范围. 根据测定的结果, 结合瓜环以及客体的结构特征, 对体系主客体在不同的酸度区域表现出的不同作用模式进行了探讨.     

Second order charge overlap effects and damping functions for isotropic atomic and molecular interactions

Second order charge overlap effects and the related dispersion energy damping functions have been evaluated for the H-(1s)-H(1s) interaction through partial wave indices l_a+l_b such that (l_a+l_b) ? 13. These results are a substantial improvement on, or addition to, previous literature results and are important since they can be used, following several available scaling approaches, to construct damping functions for other interactions. They also indicate that the “spherical” energies are not an insignificant part of the total second order Coulomb energy until R becomes reasonably large. The various approaches for evaluating the non-expanded second order Coulomb energy are compared and the difficulties associated with the accurate determination of these energies, and the related damping functions, for general interactions are discussed in some detail.     

Parallel ab initio and molecular mechanics investigation of polycoordinated Zn(II) complexes with model hard and soft ligands: Variations of binding energy and of its components with number and charges of ligands

In this study we compare the binding energies of polycoordinated complexes of Zn²⁺ within cavities composed of model “hard” (H₂O, OH⁻) or “soft” (CH₃SH, CH₃S⁻) ligands. Ab initio supermolecule computations are performed at the HF and MP2 levels using extended basis sets to determine the binding energies and their components as a function of: the number of ligands, ranging from three to six; the net charge of the cavity; and the “hard” versus “soft” character of the ligands. These ab initio computations are used to test the reliability of the SIBFA molecular mechanics procedure, originally formulated and calibrated on the basis of ab initio computations, for such charged systems. The SIBFA intermolecular interaction energies match the corresponding ab initio values using a coreless effective potential split‐valence basis set with a relative error of ≤3%. Extensions to binuclear Zn²⁺ complexes, such as those that occur in the Zn‐binding sites of Gal4 and β‐lactamase proteins, are performed to test the applicability of the methodology for such systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1011–1039, 2000     

The elements of Flatland: Hartree-Fock atomic ground states in two dimensions for Z = 1–24

The Hartree–Fock problem in two dimensions (2D) has been solved for 1 ≤ Z ≤ 24 using a Gaussian basis and assuming r^?1 Coulomb interactions. The order of occupation of the one-electron states is like in the 3D case. The 1s shell is found to be particularly small and strongly bound, making the 2D hydrogen a “superhalogen” and the 2D He a “superinert gas.” In contrast to 3D, 4s¹3d² and 4s²3d³ configurations are preferred for the 2D “Sc” and “Cu,” respectively. The six first 2D atoms have stronger and the later ones weaker valence-bonding energies than do their 3D analogs. It is noted that the 2D Dirac energy expression for a hydrogenlike atom for m_j = l + 1/2 agrees with the 3D Klein–Gordon one.     

Theoretical study in [C2H4–Tl]+ and [C2H2–Tl]+ complexes

We studied the attraction between [C₂H_n] and Tl(I) in the hypothetical [C₂H_n–Tl]⁺ complexes (n = 2,4) using ab initio methodology. We found that the changes around the equilibrium distance C–Tl and in the interaction energies are sensitive to the electron correlation potential. We evaluated these effects using several levels of theory, including Hartree–Fock (HF), second‐order Møller–Plesset (MP2), MP4, coupled cluster singles and doubles CCSD(T), and local density approximation augmented by nonlocal corrections for exchange and correlation due to Becke and Perdew (LDA/BP). The obtained interaction energies differences at the equilibrium distance R_e (C–Tl) range from 33 and 46 kJ/mol at the different levels used. These results indicate that the interaction between olefinic systems and Tl(I) are a real minimum on the potential energy surfaces (PES). We can predict that these new complexes are viable for synthesizing. At long distances, the behavior of the [C₂H_n]–Tl⁺ interaction may be related mainly to charge‐induced dipole and dispersion terms, both involving the individual properties of the olefinic π‐system and thallium ion. However, the charge‐induced dipole term (R^?4) is found as the principal contribution in the stability at long and short distances. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007