Anisotropic Overlap Research Articles

The interaction-induced dipole of H2-H: New ab initio results and spherical tensor analysis.

We present numerical results for the dipole induced by interactions between a hydrogen molecule and a hydrogen atom, obtained from finite-field calculations in an aug-cc-pV5Z basis at the unrestricted coupled-cluster level including all single and double excitations in the exponential operator applied to a restricted Hartree-Fock reference state, with the triple excitations treated perturbatively, i.e., UCCSD(T) level. The Cartesian components of the dipole have been computed for nine different bond lengths r of H2 ranging from 0.942 a.u. to 2.801 a.u., for 16 different separations R between the centers of mass of H2 and H between 3.0 a.u. and 10.0 a.u., and for 19 angles θ between the H2 bond vector r and the vector R from the H2 center of mass to the nucleus of the H atom, ranging from 0° to 90° in intervals of 5°. We have expanded the interaction-induced dipole as a series in the spherical harmonics of the orientation angles of the H2 bond axis and of the intermolecular vector, with coefficients DλL(r, R). For the geometrical configurations that we have studied in this work, the most important coefficients DλL(r, R) in the series expansion are D01(r, R), D21(r, R), D23(r, R), D43(r, R), and D45(r, R). We show that the ab initio results for D23(r, R) and D45(r, R) converge to the classical induction forms at large R. The convergence of D45(r, R) to the hexadecapolar induction form is demonstrated for the first time. Close agreement between the long-range ab initio values of D01(r0 = 1.449 a.u., R) and the known analytical values due to van der Waals dispersion and back induction is also demonstrated for the first time. At shorter range, D01(r, R) characterizes isotropic overlap and exchange effects, as well as dispersion. The coefficients D21(r, R) and D43(r, R) represent anisotropic overlap effects. Our results for the DλL(r, R) coefficients are useful for calculations of the line shapes for collision-induced absorption and collision-induced emission in the infrared and far-infrared by gas mixtures containing both H2 molecules and H atoms.

Dihedral-angle-corrected registry-dependent interlayer potential for multilayer graphene structures

The structural relaxation of multilayer graphene is essential in describing the interesting electronic properties induced by intentional misalignment of successive layers, including the recently reported superconductivity in twisted bilayer graphene. This is difficult to accomplish without an accurate interatomic potential. Here, we present a new, registry-dependent Kolmogorov-Crespi type interatomic potential to model interlayer interactions in multilayer graphene structures. It consists of two parts representing attractive interaction due to dispersion, and repulsive interaction due to anisotropic overlap of electronic orbitals. An important new feature is a dihedral-angle-dependent term that is added to the repulsive part in order to describe correctly several distinct stacking states that the original Kolmogorov-Crespi potential cannot distinguish. We refer to the new model as the Dihedral-angle-corrected Registry-dependent Interlayer Potential (DRIP). Computations for several test problems show that DRIP correctly reproduces the binding, sliding, and twisting energies and forces obtained from ab initio total-energy calculations based on density functional theory. We use the new potential to study the structural properties of a twisted graphene bilayer and the exfoliation of graphene from graphite. Our potential is available through the OpenKIM interatomic potential repository at https://openkim.org.

Experimental evidence for anisotropic double exchange interaction driven anisotropic transport in manganite heterostructures

An anisotropic double exchange interaction driven giant transport anisotropy is demonstrated in a canonic double exchange system of La2/3Sr1/3MnO3 ultrathin films epitaxially grown on NdGaO3 (110) substrates. The oxygen octahedral coupling at the La2/3Sr1/3MnO3/NdGaO3 interface induces a planar anisotropic Mn-O-Mn bond bending, which causes a significant anisotropic overlap of neighboring Mn orbitals. Due to the anisotropic double exchange interaction, it is found that the conductivity of the La2/3Sr1/3MnO3 film is enhanced when current is applied along the in-plane short crystalline axis. However, the anisotropic behavior is absent in the high temperature paramagnetic phase. Our results demonstrate anisotropic transport in the clean limit where phase separation is absent and the role of anisotropic phase percolation can be excluded.

Structure and magnetic properties of the ionic fullerene salt (TMP+)·(C60˙−)·C6H5CN containing layers of monomeric C60˙− radical anions

The fullerene salt, (TMP+)·(C60˙−)·C6H5CN (1), with a layered structure was obtained as single crystals (TMP+ is the N,N,N′-trimethylpiperazinium cation). The fullerene layers alternating with the TMP+–C6H5CN layers along the c-axis have a honeycomb arrangement of C60˙− in which each fullerene has three neighbors with interfullerene C⋯C contacts in the 3.13–3.38 A range. Despite the dense packing, the fullerene anions showed no intermolecular bond formation, even when down to helium temperatures. The structure of 1 was solved at 120 and 90 K. The fullerene molecules are disordered between three orientations at 120 K. The ordering transition observed in the 100–90 K range is accompanied by the trebling of the unit cell to provide three crystallographically independent fullerenes. The salt shows an asymmetric EPR signal down to 4 K which can be fitted by two Lorentzian lines with g1 = 1.9956 and a linewidth (ΔH) of 2.7 mT and g2 = 1.9815 and ΔH = 5.1 mT at room temperature. The ordering transition results in the abrupt narrowing of both lines in the 100–90 K range. The temperature dependence of the magnetic susceptibility of 1 follows the Curie–Weiss law with a negative Weiss temperature of −11 K, indicating an antiferromagnetic interaction of spins in the fullerene layers. Salt 1 is non-conducting with a room temperature resistivity of 7 × 107 Ω cm, which is probably due to the orientational disorder of the fullerenes and a relatively weak interaction between C60˙− in the layers. Indeed, the AM1 molecular orbital calculations show essentially smaller and more anisotropic overlap integrals between fullerenes than those in the layered metal (MDABCO+)·(C60˙−)·TPC.

ChemInform Abstract: Remote Control of Stereogenicity Transfer by Ring-Generated Anisotropic Orbital Overlap. Stereochemistry of Hydrogen Shift in the Intramolecular Reverse Ene Reaction of a cis-2-Alkyl-1-alkenylcyclopropane.

The thermal rearrangement of cis-2-(2-propyl)-1 (E)-propenylcyclopropane at temperatures near 230°C in the gas phase occurs with activation parameters of E a =35.5±0.6 kcal/mol and log A=12.05±0.5 (A, s −1 ). The optically active isotopically doubly labeled analogue (cis-2(S)-(2(S)-propyl-1-d 3 )-1(S)-(1(E)-propenyl-2-d)cyclopropane 5 was synthesized in 12 steps from dicyclopentadiene. Pyrolysis of 5 gave only 2-methyl-octa-2(Z),5(Z)-diene-1-d 3 -7(S)-d, with high stereospecificity at each of the three sites of sterogenicity. This result is the one predicted if the reaction is controlled by optimal overlap of the reacting C―H and π bond orbitals with the C s symmetric component of the degenerate 3E' highest occupied orbital of the cyclopropane ring

On the Relevance of an Antiferromagnetic Dimer Model for the Spin-Gapped Magnetic Solids Cu(terpy)Mo2O7 and Cu(OH)(p-pyc)H2O

The magnetic solids Cu(terpy)Mo2O7 (terpy = terpyridine) and Cu(OH)(p-pyc)H2O (p-pyc = p-pyridinecarboxylate) have a spin gap and possess chains of Cu2+ ions in which two different Cu...Cu distances alternate. On the basis of their reported crystal structures, the spin-exchange interactions of these compounds were examined by performing spin dimer analysis to determine whether an antiferromagnetic dimer or an alternating antiferromagnetic chain model is appropriate for their magnetic properties. Our analysis shows that an antiferromagnetic dimer model is correct for both compounds because of the anisotropic overlap between the magnetic orbitals of their Cu2+ sites.

Long-range, collision-induced dipoles of Td–D∞h molecule pairs: Theory and numerical results for CH4 or CF4 interacting with H2, N2, CO2, or CS2

Compressed gases and liquids containing molecules of Td and D∞h symmetry absorb far-infrared radiation, due to transient dipole moments induced during molecular collisions. In earlier theoretical work on far-infrared absorption by CH4/N2 mixtures, good agreement was obtained between calculated and experimental spectra at low frequencies, but at higher frequencies—from 250 to 650 cm−1—calculated absorption intensities fell significantly below the experimental values. In this work, we focus on an accurate determination of the long-range, collision-induced dipoles of Td⋯D∞h pairs, including two polarization mechanisms not treated in the earlier line shape analysis: dispersion and nonuniformity in the local field gradient acting on the Td molecule. Since these mechanisms produce transitions with ΔJ=±3 or ±4 for CH4 and ΔJ=0 or ±2 for N2, their inclusion is expected to increase the calculated absorption intensities in the high frequency wings for CH4/N2 mixtures. This should improve agreement with the experimental spectra, and permit more accurate determination of anisotropic overlap terms in the collision-induced dipole. We give numerical values for the long-range dipole coefficients of CH4 or CF4 interacting with H2, N2, CO2, or CS2; the dipole coefficients have been derived with spherical-tensor methods and evaluated using single-molecule moments and susceptibilities from recent ab initio calculations or experiments. The dispersion dipoles are given rigorously in terms of integrals involving the imaginary-frequency polarizability α(iω) and the hyperpolarizabilities β(0;iω,−iω) and B(0;iω,−iω). To obtain numerical estimates for the dispersion dipoles, we have developed constant-ratio approximations that require only the static susceptibilities and C6 van der Waals coefficients.

Far infrared absorption in liquid methane: experiment and theory

The far infrared absorption of liquid methane was measured in the frequency range 30– 550 cm -1 at four temperatures from 91.2 K, near the freezing point, to 122.2 K. The zero, first and second spectral moments were obtained from these measurements and compared with theoretical values. Induction by the octopole and hexadecapole moments of methane was supplemented by an empirical anisotropic overlap induction mechanism. Agreement between theoretical and experimental spectral moments was generally in the range of 10–20%. The computed spectral moments were corrected for quantum effects; with these corrections the agreement with experimental moments improved. The theoretical spectral moments were used to evaluate parameters in an empirical translational line shape in the computation of the overall band shape of the far infrared spectrum. Because the band shape is dominated by the free rotational motion of methane, the exact functional form of the line shape function is not of paramount significance, except at very low frequencies and in the far high frequency wing. The discrepancy between the computed and measured spectra increases with decreasing temperature, with theory increasingly underestimating the experiment. Reasons for discrepancies between theory and experiment are presented.

Far infrared absorption in liquid methane: experiment and theory

The far infrared absorption of liquid methane was measured in the frequency range 30– 550 cm -1 at four temperatures from 91.2 K, near the freezing point, to 122.2 K. The zero, first and second spectral moments were obtained from these measurements and compared with theoretical values. Induction by the octopole and hexadecapole moments of methane was supplemented by an empirical anisotropic overlap induction mechanism. Agreement between theoretical and experimental spectral moments was generally in the range of 10–20%. The computed spectral moments were corrected for quantum effects; with these corrections the agreement with experimental moments improved. The theoretical spectral moments were used to evaluate parameters in an empirical translational line shape in the computation of the overall band shape of the far infrared spectrum. Because the band shape is dominated by the free rotational motion of methane, the exact functional form of the line shape function is not of paramount significance, except at very low frequencies and in the far high frequency wing. The discrepancy between the computed and measured spectra increases with decreasing temperature, with theory increasingly underestimating the experiment. Reasons for discrepancies between theory and experiment are presented.

Collision-induced absorption in gaseous sulphur hexafluoride

The absorption spectrum of gaseous sulphur hexafluoride has been measured in the spectral region from approximately 20 to 140 cm−1 at 339 K. The experiments were performed over a range of densities from 65 to 109.6 amagat (for SF6, 1 amagat = 45.3 mol m−3), using FTIR spectroscopy. From the density dependence of the absorption, the collision-induced spectrum was clearly separated from the strong allowed transitions of vibrational difference bands at 26 and 91 cm−1. Our results for the induced spectrum differ substantially, both in overall magnitude and in shape, from earlier data. We interpret the absorption as due to anisotropic overlap induction; however, a substantial contribution from a hexadecapolar mechanism cannot be ruled out. We can place an upper limit of approximately 7 × 10−42 esu on the hexadecapole moment. The induced line shape is calculated using information theory, based on our knowledge of the zeroth and second moment of the frequency spectrum. Reasonable agreement is found between theory and experiment.

Far infrared absorption of the gaseous CH4–Ar mixture

We present the first measurements of the rototranslational absorption spectrum of the CH4–Ar gaseous system in the far infrared region 40–600 cm−1. Measurements were made at 296, 243, and 195 K at densities as low as possible; the binary absorption spectrum of the CH4–Ar pair was then obtained. We performed a line-shape analysis of these spectra following the procedure previously introduced for pure methane. We find that the experimental data can be described at high frequencies by using ab initio values of the octopole and hexadecapole multipole moments and anisotropic overlap intensities very close to those used for pure methane. At low frequencies, the computed spectrum is significantly lower than the experimental data at any temperature. We thus include in our analysis a low-frequency spectral contribution associated with the isotropic overlap induction mechanism. Good fits of the experimental data are then obtain at each temperature over all the spectral range.

Erratum: Collision-induced rotovibrational spectra of H2-He pairs from first principles

A previous study of the collision-induced dipole moment has treated the ${\mathrm{H}}_{2}$-He complex as a molecule in self-consistent-field and size-consistent coupled-electron-pair approximation [Meyer and Frommhold, Phys. Rev. A 34, 2771 (1986)]. Based on that work, the vibrational dipole transition elements 〈v\ensuremath{\Vert}${A}_{\ensuremath{\lambda}L}$(R,r)\ensuremath{\Vert}v'〉 associated with the fundamental band (v=0\ensuremath{\rightarrow}v'=1) are obtained as functions of separation R of the collisional pair for the isotropic and anisotropic overlap induction components (\ensuremath{\lambda}L=01 and 21), and the quadrupole- and hexadecapole-induced parts (\ensuremath{\lambda}L=23 and 45). From these induced dipole components and Meyer, Hariharan, and Kutzelnigg's isotropic part of the ab initio potential surface, we compute in the (forbidden) fundamental band of hydrogen the collision-induced absorption spectra of the collisional complex of hydrogen (${\mathrm{H}}_{2}$) and helium from an exact quantum formalism. Both the shape of the computed spectral profiles and the theoretical absolute intensity agree closely with existing measurements at temperatures from 18 to 300 K. The fact that these spectra, and presumably the analogous overtone and ``hot'' (v>0) bands of the ${\mathrm{H}}_{2}$-He complex which are not known from measurements, can be accurately obtained from basic principles is significant for research related to the atmospheres of the giant planets and late-type stars.

Intensities of Rv'(0) transitions in solid HD.

Experimental values of the integrated intensity of the zero-phonon ${R}_{2}$(0) and ${R}_{3}$(0) transitions in solid HD are reported. Three distinct dipole components, the allowed dipole and the dipoles induced by the shifted, isotropic and anisotropic overlap mechanisms, in conjunction with their associated interferences, all play an important role in the absorption process. A two-parameter model describing the dependence of the induced dipoles on the internuclear separation is constructed. The parameters in this model are then determined by fitting to the previously observed ${R}_{1}$(0) and the newly measured ${R}_{2}$(0) intensities. The ${R}_{3}$(0) transition intensity predicted by our model agrees well with the experimental value, and the present model also enables us to refine the theoretical calculation of the intensity of the ${R}_{0}$(0) transition published previously.

Analysis of roto-translational absorption spectra induced in low density gases of non polar molecules

We present a new analysis of the roto-translational absorption spectrum of gaseous methane for which experimental data are available at different temperatures. We consider components of the induced dipole associated at long range with induction by the octopole and hexadecapole multipole moments together with components associated with the gradient of both the octopolar and hexadecapolar fields. A satisfactory description of experimental data is obtained only if short range anisotropic overlap is included with the octopolar and hexadecapolar induction. A better description of the experimental absorption bands is obtained if, in addition, the intensity of the double transitions is slightly increased with increasing temperature. This increase is attributed to anisotropic overlap effects on the double transition spectrum, which have not been explicitly taken into account.

Measurements and analysis of rototranslational absorption spectra of low density H2–Ar mixtures

We present new measurements of the rototranslational absorption of H2–Ar mixtures at 195 and 298 K. Measurements were made at densities as low as possible. The first accurate (5% error) rototranslational spectrum of the H2–Ar pair was thus derived. We performed a line-shape analysis of these spectra; as a result, we found a low-frequency component associated with an isotropic overlap induced dipole. We also found an important anisotropic overlap contribution associated with the dominant quadrupolar induction. Through a spectral-moment analysis we determined the intensity of isotropic (λ0 = 2.35 ± 0.15 × 10−3ea0) and anisotropic (λ1 = 0.9 ± 0.1 × 10−3ea0) overlap induced dipoles. The range of the isotropic overlap induced dipole was found to be ρ0 = (0.105 ± 0.010)σ, in very good agreement with the value 0.11 σ frequently assumed in the literature for the range of overlap induced dipoles. Our measurements and the results of our analysis were in good agreement with results of recent computations.

Collision-induced rotovibrational spectra of H2-He pairs from first principles.

A previous study of the collision-induced dipole moment has treated the ${\mathrm{H}}_{2}$-He complex as a molecule in self-consistent-field and size-consistent coupled-electron-pair approximation [Meyer and Frommhold, Phys. Rev. A 34, 2771 (1986)]. Based on that work, the vibrational dipole transition elements 〈v\ensuremath{\Vert}${A}_{\ensuremath{\lambda}L}$(R,r)\ensuremath{\Vert}v'〉 associated with the fundamental band (v=0\ensuremath{\rightarrow}v'=1) are obtained as functions of separation R of the collisional pair for the isotropic and anisotropic overlap induction components (\ensuremath{\lambda}L=01 and 21), and the quadrupole- and hexadecapole-induced parts (\ensuremath{\lambda}L=23 and 45). From these induced dipole components and Meyer, Hariharan, and Kutzelnigg's isotropic part of the ab initio potential surface, we compute in the (forbidden) fundamental band of hydrogen the collision-induced absorption spectra of the collisional complex of hydrogen (${\mathrm{H}}_{2}$) and helium from an exact quantum formalism. Both the shape of the computed spectral profiles and the theoretical absolute intensity agree closely with existing measurements at temperatures from 18 to 300 K. The fact that these spectra, and presumably the analogous overtone and ``hot'' (v>0) bands of the ${\mathrm{H}}_{2}$-He complex which are not known from measurements, can be accurately obtained from basic principles is significant for research related to the atmospheres of the giant planets and late-type stars.

In-crystal ionic polarizabilities derived by combining experimental and ab initio results

It is shown that an empirical model of in-crystal polarizabilities must incorporate the environmentally induced variation of anion polarizabilities. Those of s 2 and p 6 cations can be taken to be constant. Such a model is combined with the ab initio calculation of small cation polarizabilities to extract the polarizabilities of Rb + , Cs + , Tl + , Sr 2+ , Ba 2+ and Pb 2+ from experimental refractive index data. The deficiencies of previous estimates are discussed. The function describing the environmental dependence of halide polarizabilities is found to be transferable between different crystal structures. This does not hold for chalcogenide anions. It is shown that the polarizabilities of d 10 cations are very sensitive to environment. The anisotropy of the purely electrostatic environment increases the polarizability of Ag + in AgF by 4% while model calculations suggest a much larger increase from anisotropic overlap effects. A comparison of the relative merits of an ionic polarizability and a charge-transfer picture of polarization in ionic solids is found to favour the former description.

The translational–rotational absorption spectrum of hydrogen

The collision-induced translational–rotational spectrum of H2 has been accurately measured in the region from about 30 to 2000 cm−1 at 195 and 297 K. A very weak feature due to the hexadecapole-induced dipole, the U0(1) line, has been detected at 195 K in the region around 1622 cm−1. These spectra can be accurately represented by a simple, semi-empirical line shape. The effect of double transitions are considered and explicit expressions for these are given. Spectral integrals proportional to the zero and first moments are determined experimentally and compared with the theoretical moments computed on the basis of quadrupole induction for several potentials. The difference between the experimental and theoretical values, in the order of 20%, is attributed to anisotropic overlap induction, but the inferred magnitude of this component is strongly dependent on the assumed potential.

Collision-induced absorption in a highly symmetric molecule—SF6

The far-infrared absorption spectra of gaseous (298 K) and liquid (273 K, 233 K) SF6 obtained by Rosenberg and Birnbaum [1] are analysed in terms of recent theoretical developments. Analysis of the band shape in the gas and liquid phases indicates that hexadecapole-induced absorption accounts only for the low frequency portion of the collision-induced band. The major part of the absorption can be attributed to a much shorter range mechanism such as anisotropic overlap. The resulting induced dipole which varies very rapidly with intermolecular separation and is consistent with a (7–28) interaction energy gives a good description of the liquid spectra. Collision-induced absorption and depolarized light scattering in SF6 are compared. From a decomposition of the collision-induced gaseous spectrum, the value of the hexadecapolar energy, Φ2/σ9, is 2·7 × 10-24 J (0·20 K) which yields a value of the hexadecapole moment, Φ, of 18 × 10-60 C m4 for σ = 0·468 nm.

Lattice dynamics of solid N2 with an a b i n i t i o intermolecular potential

We have performed harmonic and self-consistent phonon lattice dynamics calculations for α and γ N2 crystals using an intermolecular potential from ab initio calculations. This potential contains electrostatic (multipole) interactions, up to all R−9 terms inclusive, anisotropic dispersion interactions up to all R−10 terms inclusive, and anisotropic overlap interactions caused by charge penetration and exchange between the molecules. The lattice constants, cohesion energy, the frequencies of the translational phonon modes and the Grüneisen parameters for the librational modes are in good agreement with experimental values, confirming the quality of the potential. The frequencies of the librational modes and those of the mixed modes are less well reproduced, especially at temperatures near the α–β phase transition. Probably, the self-consistent phonon method used does not fully account for the anharmonicity in the librations.