Intermolecular Potential Surface Research Articles

Spectroscopic determination of the water dimer intermolecular potential-energy surface

Two polarizable six-dimensional water dimer intermolecular potential surfaces have been determined by fitting the distributed multipole ASP (anisotropic site potential) potential form to microwave, terahertz, and midinfrared cavity ringdown (D2O)2 spectra via a rigorous calculation of the water dimer eigenstates with the PSSH (pseudo-spectral split Hamiltonian) method. The fitted potentials accurately reproduce most ground-state vibration-rotation-tunneling spectra and yield excellent second virial coefficients for both H2O and D2O. The calculated dimer structure and dipole moment are close to those determined from microwave spectroscopy and high level ab initio calculations, except that the O–O distance (2.952 Å) is significantly shorter than the currently accepted experimental value. The dimer binding energy (4.85 kcal/mol) is considerably smaller than the accepted experimental result, but in excellent agreement with recent theoretical results, as are the acceptor switching and donor–acceptor interchange tunneling barriers and the cyclic water trimer and tetramer structures and binding energies.

Intermolecular perturbation theory applied to an exactly solvable model

AbstractIt is remarkable that application of intermolecular perturbation theory to a simple, exactly solvable model of diatomic molecules reproduces the basic problems encountered when that theory is applied to real systems. For real systems it took over 50 years to recognize fully the consequences of choosing products of atomic/molecular functions as unperturbed wave functions. The primary consequence is that the physical ground state energy is generally buried in a continuum of unphysical state energies, i.e., energies of states which violate the Pauli Exclusion Principle. This makes the simplest perturbation theory incapable of predicting even the ground state energy of most systems when summed to infinite order. The model reveals clearly why and how unphysical solutions arise in intermolecular perturbation theory. The model neglects the interaction between electrons, reducing the N‐electron problem to that of the one‐electron molecular ion. Because the model can be solved exactly, it is suggested that it could be useful in testing new perturbation theories for the calculation of intermolecular potential surfaces. The traditional test systems, H2+ and H2, provide no real test because they have no unphysical solutions. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002

Semiclassical modeling of infrared pressure-broadened linewidths: A comparative analysis in CO2–Ar at various temperatures

A novel semiclassical approach, which makes use of the exact trajectory implemented within the Robert–Bonamy formalism, is employed for modeling infrared pressure-broadened linewidths. As a prototype, the carbon dioxide molecule perturbed by argon is examined in the temperature range 160–760 K, for which various measurements and computations are available. For a meaningful comparison with previous theoretical works done with both semiclassical and quantum approaches, the ab initio intermolecular potential surface of Parker et al. [J. Chem. Phys. 64, 1668 (1976)] is used. Our values are found to be in agreement with up-to-date experimental data at all temperatures studied.

Classical analysis of intermolecular potentials for Ar–CO2 rotational collisions

Classical trajectory calculations have been performed for four potential energy functions to describe Ar–CO2 collisions. A comparison is given between classical cross sections calculated using the two most recent potential surfaces and two older intermolecular potential surfaces based on the electron gas model. The two-dimensional atom ellipsoid model has also been applied for the study of multiple collisions. The model was able to predict such a phenomenon in agreement with quantum scattering results previously published for an ab initio potential surface in the region of very low collision energy. On the other hand, the two older potentials showed multiple collision effects at very high energies. The comparison of the cross sections showed some deviations from the experimental data. By introducing two parameters, a modified surface is proposed by changing the most recent intermolecular potential. In this case the agreement with experimental measurements and theoretical scattering cross sections was considerably improved. It is concluded that global potential surfaces for describing Ar–CO2 interaction are not well established. To achieve the requirement of reproducing all properties of this system, the present work suggests that one needs further experimental and theoretical investigations. Key words: classical trajectories, dynamics, cross sections, Ar–CO2 collisions, potentials.

Electron Density as a Descriptor of Thermal Molecular Size

A quantitative relationship is developed between repulsive intermolecular potential surfaces and molecular electron density contours, using the helium atom as a probe. For a variety of small neutral molecules and anions, the molecular surface consistent with approach of a helium atom at a temperature of 298 K is identified with the electron density contour at 0.0033 ± 0.0005 au. This gives a prescription for molecular size and shape that is expected to be useful for cavities in solution and other applications.

The dependence of intermolecular interactions upon valence coordinate excitation: The υHF=4 levels of ArHF

The valence state dependence of the Ar–HF interaction potential is extended to υHF=4. Three new ArHF (υHF=4) states, (4000), (4100), and (4110), are observed between 14 780 and 14 880 cm−1 using intracavity laser induced fluorescence. The term values and rotational constants of these states are the following: (4000) ν0=14 783.603 23(30) cm−1, B=0.103 606 8(68) cm−1; (4100) ν0=14 867.419 06(70) cm−1, B=0.102 612(27) cm−1; and (4110) ν0=14 875.048 30(39) cm−1, B=0.103 217(19) cm−1, respectively. The spectral red shifts of ArHF (υ000) dramatically increase from 9.654 cm−1 at υ=1 to 48.024 cm−1 at υ=4. The rotational constant of ArHF(4000) increases essentially linearly with HF valence excitation, becoming 1.3% (40 MHz) greater than that observed at υ=0. At υ=4, the outer classical turning point of HF is extended by 0.4 Å from re, and there is no evidence for Ar–H repulsion. The spectral red shift for linear hydrogen bonded Ar–HF(υ000) indicates a strong enhancement of binding energy upon HF valence bond excitation, while the rotational constant reveals an almost surprising decrease in heavy atom separation. Both the T-shaped ArHF(υ110) and antilinear Ar–FH(υ100), however, show very little dependence of binding energy upon υHF valence excitation. These observations are in good accord with the ab initio intermolecular potential surface.

Weak bond stretching for three orientations of Ar–HF at vHF=3

Three new ArHF (vHF=3) states, (3001), (3101), and (3111), have been observed between 11 350 and 11 420 cm−1 by the hot band transitions from (0001) using intracavity laser induced fluorescence. The term values and rotational constants of these levels are: (3001) ν0=11 385.928 98(28) cm−1, B=0.095 546(32) cm−1; (3101) ν0=11 444.258 12(68) cm−1, B=0.090 617(37) cm−1; and (3111) ν0=11 456.076 51(36) cm−1, B=0.091 863(14) cm−1. Observation of the ArHF (3001) state provides the van der Waals stretching frequency for ArHF at v=3, namely 46.8945(4) cm−1=(3001)–(3000). This value shows an increase of 8.208 cm−1 (21%) upon HF v=3←0 valence excitation. The stretching frequency for the T shaped ArHF is (3111)–(3110)=33.7055(5) cm−1. This value is only 7% greater than that observed at v=1. The (vHF101) Σ bend-stretch combination state, corresponding to (νs=1) of the Ar–FH configuration, has not been observed at vHF=0–2. The stretching frequency here is (3101)–(3100)=31.8178(8) cm−1. The soft-mode frequencies reveal strong bend-stretch coupling in the complex. Excellent agreement (within 0.3 cm−1) is found between experiment and prediction from Hutson’s H6(4, 3, 2) potential [J. Chem. Phys. 99, 9337 (1993)], for the three new levels. Large basis set coupled cluster calculations [CCSD(T)] of the Ar–HF intermolecular potential surface, V(R,θ,r), are presented for r=0.6–2.0 Å and θ=0–180° on a grid with 15° spacing. This is an enlargement of the HF valence coordinate of more than double the equilibrium value. The dependence of the intermolecular potential upon the HF valence coordinate, r, is very anisotropic, being maximal for θ=0° and becoming essentially independent of r for θ⩾45°.

Ab initio study of the intermolecular potential surface of He–NH3

The intermolecular potential surface for the van der Waals complex He–NH3 is studied by ab initio calculation using fourth-order Møller–Plesset perturbation theory (MP4) with a bond function basis set. The calculation gives a global minimum at R=3.26 Å, θ=89°, φ=60° (in a Jacobi coordinate system) with a well depth of De=32.96 cm−1, along with barriers of 23.09 and 20.86 cm−1 for in-plane rotations at θ=0° and 180°, respectively, and a barrier of 10.45 cm−1 for out-of-plane rotation at θ=89°, φ=0°. The potential energy surface of He–NH3 is compared to those of Ar–NH3 and He–H2O, respectively.

Experimental and theoretical study of line mixing in methane spectra. I. The N2-broadened ν3 band at room temperature

Line-mixing effects have been studied in the ν3 band of CH4 perturbed by N2 at room temperature. New measurements have been made and a model is proposed which is not, for the first time, strictly empirical. Three different experimental set ups have been used in order to measure absorption in the 2800–3200 cm−1 spectral region for total pressures in the 0.25–2 and 25–80 atm ranges. Analysis of the spectra demonstrates the significant influence of line mixing on the shape of the Q branch and of the P and R manifolds. A model is proposed which is based on state-to-state collisional transfer rates calculated from the intermolecular potential surface with a semiclassical approach. The line-coupling relaxation matrix is constructed from these data and two additional parameters which are fitted on measured absorption. Comparisons between measurements and spectra computed accounting for and neglecting line mixing are made. They prove the quality of the approach which satisfactory accounts for the effects of pressure and of rotational quantum numbers on the spectral shape under conditions where modifications introduced by line mixing are important. For high rotational quantum number lines, the main features induced by collisions are predicted but some discrepancies remain; the latter may be due to improper line-coupling elements but there is strong evidence that the use of inaccurate line broadening parameters also contributes to errors in calculated spectra.

Determination of an ethane intermolecular potential model for use in molecular simulations from ab initio calculations

Counterpoise-corrected, supermolecule, ab initio energies obtained at the MP2/6-311+G(2df,2pd) level were computed for 22 different relative orientations of two ethane molecules as a function of the separation distance between the molecular centers. These energies were used to regress the parameters in several simple, analytical, interatomic or site–site models that can be used for implementation in molecular simulations. Sensitivity analysis indicates that the intermolecular potential surface is insensitive to C–C interactions and that the parameters in the C–C model are coupled and unobtainable from the dimer energies. Representation of the potential surface can be made in terms of C–H and H–H interatomic potentials if the C–C interactions are treated as shielded. Simple Lennard-Jones and exp-6 models do not adequately represent the potential surface using these shielded models, nor do they produce the anticipated physics for the interatomic potentials. The exp-6 model with a damping function and the modified-Morse interatomic potentials both reproduce the intermolecular potential surface well with physically realistic intersite potentials suitable for use in molecular dynamics simulations.

The intermolecular potential between an inert gas and a halogen: Prediction and observation of transitions between the linear and T-shaped isomers of HeClF

The intermolecular potential surface of He and ClF is calculated with a large basis at the fourth-order Mo/ller–Plesset level. The rotation–vibration levels calculated from the intermolecular potential surface serve as an excellent guide for finding the experimental spectra. Pure rotational transitions are observed for the lowest linear Σ0 state and for an excited T-shaped K=0 Σ1 state of He35ClF and He37ClF. Direct transitions between the linear ground state and the T-shaped state are observed for He35ClF. The observed energy difference between the J=0 level of the linear state and the J=0 level of the T-shaped state is 2.320 cm−1. In addition, transitions into the two J=1 levels and one J=2 level of the K=1 T-shaped state, Π1, are observed for He35ClF. The He–ClF complex is highly nonrigid, undergoing large amplitude oscillation in both angular and radial coordinates. The effect of zero-point oscillation is seen in the large difference, 22.9 cm−1, between the calculated potential energy minima of −58.1 (linear) and −35.2 cm−1 (T-shaped) and the measured value (including zero-point energy) of 2.320 cm−1. The potential surface is poorly represented as a sum of spherical atom–atom interactions. At both minima the He–Cl distance is shorter than the sum of van der Waals radii. The ab initio potential is too shallow since an appreciably better fit of the spectral transitions is obtained by uniformly increasing the magnitude of the interaction potential by 10%. Bound states calculated for a potential with the T-shaped minimum removed show significant differences from experiment, indicating that the T-shaped minimum does indeed exist. Spectroscopic constants for He35ClF are obtained in a fit to experimental data. For the ground state, Σ0, B=5586.8312(34), D=1.6595(10) MHz, H=36.472(93) kHz, μa=0.8780(14) D, and eqeff Q(J=1)=−133.659(18) MHz. For the T-shaped state, Σ1, ν=69 565.023(35), B=7056.161(17), D=6.9523(24) MHz, μa=0.620(12) D, and eqeff Q(J=1)=−39.936(92) MHz. For the T-shaped Π state, Π1, ν=100 302.239(46), B=7430.338(32), ql=1380.622(46) MHz, μa=0.5621(99) D, and eqeff Q(Π1−J=1)=−45.15(87) MHz. The large change in geometry between the Σ0 and Σ1 states is evidenced by the difference in rotational constants, dipole moments, and quadrupole coupling constants for each state. In addition, these values are consistent with a T-shaped Σ1 state rather than an antilinear Σ1 state.

Hydrogen bonding properties of oxygen and nitrogen acceptors in aromatic heterocycles

The directionality and relative strengths of hydrogen bonds to monocyclic aromatic heterocycles were investigated using crystal structure data and theoretical calculations. Surveys of the Cambridge Structural Database for hydrogen bonds between C(sp3)(SINGLE BOND)O(SINGLE BOND)H and aromatic fragments containing one or more nitrogen and/or oxygen heteroatoms showed that hydrogen bonds to nitrogen atoms are much more abundant than to oxygen. Distinct preferred orientations were also revealed in these surveys. Theoretical calculations were performed on the interaction of methanol with pyridine, pyrimidine, pyrazine, pyridazine, oxazole, isoxazole, 1,2,4-oxadiazole, and furan as models for the heterocyclic fragments. The intermolecular potential surface was thoroughly scanned using a model potential that accurately described the electrostatic forces (derived from distributed multipole analysis) with empirical parameters for the repulsion and dispersion terms. Minima on this surface agreed well with the observed orientations in the data base and they were typically deeper for nitrogen than for oxygen acceptors, although the hydrogen bond strength and geometry was influenced by other heteroatoms in the ring. These results were confirmed by highly accurate intermolecular perturbation theory calculations, which also estimated the deviations from hydrogen bonding in the traditional nitrogen lone pair direction that could occur with negligible reduction in the interaction energy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 2060–2074, 1997

Hydrogen bonding properties of oxygen and nitrogen acceptors in aromatic heterocycles

The directionality and relative strengths of hydrogen bonds to monocyclic aromatic heterocycles were investigated using crystal structure data and theoretical calculations. Surveys of the Cambridge Structural Database for hydrogen bonds between C(sp3)(SINGLE BOND)O(SINGLE BOND)H and aromatic fragments containing one or more nitrogen and/or oxygen heteroatoms showed that hydrogen bonds to nitrogen atoms are much more abundant than to oxygen. Distinct preferred orientations were also revealed in these surveys. Theoretical calculations were performed on the interaction of methanol with pyridine, pyrimidine, pyrazine, pyridazine, oxazole, isoxazole, 1,2,4-oxadiazole, and furan as models for the heterocyclic fragments. The intermolecular potential surface was thoroughly scanned using a model potential that accurately described the electrostatic forces (derived from distributed multipole analysis) with empirical parameters for the repulsion and dispersion terms. Minima on this surface agreed well with the observed orientations in the data base and they were typically deeper for nitrogen than for oxygen acceptors, although the hydrogen bond strength and geometry was influenced by other heteroatoms in the ring. These results were confirmed by highly accurate intermolecular perturbation theory calculations, which also estimated the deviations from hydrogen bonding in the traditional nitrogen lone pair direction that could occur with negligible reduction in the interaction energy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 2060–2074, 1997

A density functional water dimer potential surface

A full six-dimensional intermolecular potential surface for the water dimer is obtained using density functional theory. The surface was evaluated at 20 480 numerical quadrature points using a hybrid functional. It was then fitted to products of rotational functions. The equilibrium geometry and the transition states on the surface were located and their features are in agreement with previous ab initio studies. The binding energy and the barrier heights are slightly underestimated. We believe that the surface faithfully represents many of the important features of the water dimer potential.

An ab initio study of the intermolecular potential surfaces of HeCH 4 and NeCH 4

The intermolecular potential surfaces for the Van der Waals complexes HeCH 4 and NeCH 4 are studied by ab initio theory using complete fourth-order Møller-Plesset perturbation theory (MP4) with an efficient basis set containing bond functions. For HeCH 4, the global minimum occurs at R = 3.4 A ̊ , θ = 180°, φ = 0° (in a Jacobi coordinate system) with a minimum energy D e = −26.2 cm −1. For NeCH 4, the global minimum occurs at R = 3.5 A ̊ , θ = 180°, φ = 0° with a minimum energy D e = −59.0 cm −1. Two saddle points were found for each of the systems. The potential energy surfaces are compared with the semiempirical surfaces and recent ab initio results on the same systems.

Anharmonic and harmonic intermolecular vibrational modes of the DNA base pairs

Intermolecular vibrational modes of the H-bonded adenine…thymine Watson–Crick (AT) base pair were studied for the first time using multidimensional nonharmonic treatment. Relying on a Born–Oppenheimer–like separation of the fast and slow vibrational motions, the complete multidimensional vibrational problem is reduced to a six-dimensional subproblem in which all rearrangements between the pair fragments (i.e., adenine and thymine) can be described. Following the Hougen–Bunker–Johns approach and using appropriate vibrational coordinates, a nonrigid reference is defined which covers all motions on the low-lying part of the intermolecular potential surface and which facilitates the derivation of a suitable model Hamiltonian. The potential energy surface is determined at the ab initio Hartree–Fock level with minimal basis set (HF/MINI-1) and an analytic potential energy function is obtained by fitting to the ab initio data. This function is used to calculate vibrational energy levels and effective geometries within the framework of the model Hamiltonian, disregarding the role of the kinematic and potential (in-plane)–(out-of-plane) interactions. The calculations are in reasonable agreement with the normal coordinate analysis (harmonic treatment) thus indicating physical correctness of this standard approach for an approximate description of the lowest vibrational states of the AT base pair. In addition, to get a deeper insight, harmonic vibrational frequencies of the AT pair and 28 other base pairs are evaluated at the same and higher levels of theory [ab initio Hartree–Fock level with split-valence basis set (HF/6-31G**)]. The HF/MINI-1 and HF/6-31G** intermolecular harmonic vibrational frequencies differ by less than 30%. For all the base pairs, the buckle and propeller vibrational modes [for definition and nomenclature see R. E. Dickerson et al., EMBO J. 8, 1 (1989)] are the lowest ones, all being in the narrow interval (from 4 to 30 cm−1 in the harmonic approximation). Although most of the evaluated harmonic frequencies are qualitatively correct approximations to the genuine vibrational frequencies, in some cases due to a strong nonharmonic behavior of the buckle motion, they become physically meaningless. To get physically correct results in such cases, apparently, the standard harmonic oscillator approach should be replaced by a more adequate approach, for instance, by the approach we used in the case of the adenine…thymine pair.

Intermolecular potential for Ar-HBr ( ν1 = 1) studied by high resolution near infrared spectroscopy

The fundamental ν 1, combinations ν 1 + 2 ν 2 0, ν 1 + ν 2 1, ν 1 + ν 3, ν 1 + 2 ν 2 0 + ν 3, hot band ν 1 + 2 ν 2 0 − 2 ν 2 0, and difference band ν 1 − 2 ν 2 0 have been rovibrationally for both 79Br and 81Br isotopomers in Ar-HBr. The bands involving 2 ν 2 0 directly sample the second minimum of the intermolecular potential surface of the complex, corresponding to the isomeric structure Ar-BrH. Nuclear quadrupole structure has also been partially resolved in the Q branch transitions of the ν 1 + ν 2 1 band. In addition, a strong Coriolis perturbation between the ν 1 + ν 2 1 e and ν 1 + ν 3 states was investigated. A model potential surface for Ar-HBr (HBr ν 1 = 1) was derived and compared with the H4 intermolecular potential for Ar-HBr (HBr ν 1 = 0).

An accurate ab initio potential energy surface of HeH 2O

We present an accurate calculation of the intermolecular potential surface for the van der Waals complex HeH 2O using complete fourth-order Møller-Plesset perturbation theory (MP4) with an efficient basis set containing bond functions. The calculation gives a global minimum at R=3.15 A ̊ , θ=105°, φ=0° (in a Jacobi coordinate system) with a minimum energy D e=31.8 cm −1, along with barriers of 13.4 and 12.6 cm −1 for in-plane rotation at θ=0° and 180°, respectively, and a barrier of 20.0 cm −1 for out-of-plane rotation at θ=105°, φ=90°. The potential energy surface is compared with previously published surfaces for HeH 2O, and with the potential energy surface for ArH 2O.

Ab Initio Molecular Orbital Analysis of Dimers of cis-Formic Acid. Implications for Condensed Phases

The gas phase structure of cis-formic acid dimers is investigated by high-level correlated ab initio molecular orbital methods using large basis sets augmented with both polarization and diffuse functions (up to MP2/D95++(d,p) level). Seven stable dimer structures were located on the potential energy hypersurface of the dimer configurational space with two H-bonding interactions. No stable dimer with only one H-bond was found. The heat of dimerization (10.7−11.3 kcal/mol) of the most stable, C2h cyclic dimer is in excellent agreement with more recent experimental measurements. Beside the dimer with two equivalent O−H···OC H-bonds, there exist two local minima with significant stabilization from C−H···O interactions. The three weakest of the seven complexes contain exclusively C−H···O H-bonding interactions. The dimers can interconvert to each other by rotation, disrupting one of their H-bonds. The saddle points and the local minima are anticipated not to play important roles in the gas phase but can have dominant influence on liquid dynamics. The interaction energies of the complexes allow us to assess the relative importance and approximate energetic contributions of the individual H-bonds to the overall stability of the dimers. It is illustrated that, in addition to the inferred stabilization of two separate O−H···OC H-bonds, the most stable C2h complex is stabilized by about 0.4−0.6 kcal/mol internal cooperative effect, less than in the similar acetic acid dimer. The C−H H-bonding dimers display contraction of the C−H bond lengths and positive frequency shift of the ν(C−H) stretching modes relative to the noninteracting monomer. We also show that the effect of BSSE on the intermolecular potential surface of the dimers and, in particular, on the location of the true potential minimum only negligibly influences the interaction energy, but significantly distorts the intermolecular equilibrium geometry.

Observation of strong Coriolis coupling in the infrared spectrum of Ar-CO

Using a continuous two-dimensional jet expansion in combination with a computer controlled diode laser spectrometer, the rotation-vibration spectrum of the Ar-CO van der Waals complex has been studied in the 2157 cm-1 region. 47 new lines of the parallel transition from the K a = 1 (νCO = 0) ground state to the combination band of the CO fundamental vibration (νCO = 1) and the excited bending K a = 1 (j = 2) state were assigned. The lower state is identical to that found by McKellar et al. (1992, J. Molec. Spectrosc., 153, 475). The excited bending K a = 1 state is located at an energy of 14·63 cm-1 with respect to the K a = 1 (νCO = 1, j = 1) state. Due to a strong Coriolis interaction with a nearby K a = 0 state, this new band shows unusually large asymmetry splittings. Using the results of a perturbative analysis of the Coriolis coupling, the nature of the K a = 0 state could be assigned as containing both j = 2 (doubly excited bending) and j = 0 (van der Waals stretching mode) contributions. These experimental results provide a sensitive test of the depth and the anisotropic part of the intermolecular potential surface of Ar-CO and will be of great value for future ab initio calculations.