Canonical Approach To Generate Multidimensional Potential Energy Surfaces.

A new force-based canonical approach for the accurate generation of multidimensional potential energy surfaces is demonstrated. Canonical transformations previously developed for diatomic molecules are used to construct accurate approximations to the 3-dimensional potential energy surface of the water molecule from judiciously chosen (adopting the right coordinate system) 1-dimensional planar slices that are shown to have the same canonical shape as the classical Lennard-Jones potential curve. Spline interpolation is then used to piece together the 1-dimensional canonical potential curves, to obtain the full 3-dimensional potential energy surface of a water molecule with a relative error less than 0.01. This work provides an approach to greatly reduce the computational cost of constructing potential energy surfaces in molecules from ab initio calculations. The canonical transformation techniques developed in this work illuminate a pathway to deepening our understanding of chemical bonding.

Is there any fundamental difference between ionic, covalent, and others types of bond? A canonical perspective on the question.

The concept of chemical bonding is normally presented and simplified through two models: the covalent bond and the ionic bond. Expansion of the ideal covalent and ionic models leads chemists to the concepts of electronegativity and polarizability, and thus to the classification of polar and non-polar bonds. In addition, the intermolecular interactions are normally viewed as physical phenomena without direct correlation to the chemical bond in any simplistic model. Contrary to these traditional concepts of chemical bonding, recently developed canonical approaches demonstrate a unified perspective on the nature of binding in pairwise interatomic interactions. This new canonical model, which is a force-based approach with a basis in fundamental molecular quantum mechanics, confirms much earlier assertions that in fact there are no fundamental distinctions among covalent bonds, ionic bonds, and intermolecular interactions including the hydrogen bond, the halogen bond, and van der Waals interactions.

Morse, Lennard-Jones, and Kratzer Potentials: A Canonical Perspective with Applications.

Canonical approaches are applied to classic Morse, Lennard-Jones, and Kratzer potentials. Using the canonical transformation generated for the Morse potential as a reference, inverse transformations allow the accurate generation of the Born-Oppenheimer potential for the H2+ ion, neutral covalently bound H2, van der Waals bound Ar2, and the hydrogen bonded one-dimensional dissociative coordinate in a water dimer. Similar transformations are also generated using the Lennard-Jones and Kratzer potentials as references. Following application of inverse transformations, vibrational eigenvalues generated from the Born-Oppenheimer potentials give significantly improved quantitative comparison with values determined from the original accurately known potentials. In addition, an algorithmic strategy based upon a canonical transformation to the dimensionless form applied to the force distribution associated with a potential is presented. The resulting canonical force distribution is employed to construct an algorithm for deriving accurate estimates for the dissociation energy, the maximum attractive force, and the internuclear separations corresponding to the maximum attractive force and the potential well.

Canonical Force Distributions in Pairwise Interatomic Interactions from the Perspective of the Hellmann-Feynman Theorem.

Force-based canonical approaches have recently given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. Differing molecular categories (covalent, ionic, van der Waals, hydrogen, and halogen bonding) of representative interatomic interactions with binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semiempirical verification to high accuracy. However, the fundamental physical basis expected to provide the inherent characteristics of these canonical transformations has not yet been elucidated. Subsequently, it was shown through direct numerical differentiation of these potentials that their associated force curves have canonical shapes. However, this approach to analyzing force results in inherent loss of accuracy coming from numerical differentiation of the potentials. We now show that this serious obstruction can be avoided by directly demonstrating the canonical nature of force distributions from the perspective of the Hellmann-Feynman theorem. This requires only differentiation of explicitly known Coulombic potentials, and we discuss how this approach to canonical forces can be used to further explain the nature of chemical bonding in pairwise interatomic interactions. All parameter values used in the canonical transformation are determined through explicit physical based algorithms, and it does not require direct consideration of electron correlation effects.

Canonical Approaches to Applications of the Virial Theorem.

Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.

A general transformation to canonical form for potentials in pairwise interatomic interactions.

A generalized formulation of explicit force-based transformations is introduced to investigate the concept of a canonical potential in both fundamental chemical and intermolecular bonding. Different classes of representative ground electronic state pairwise interatomic interactions are referenced to a chosen canonical potential illustrating application of such transformations. Specifically, accurately determined potentials of the diatomic molecules H2, H2(+), HF, LiH, argon dimer, and one-dimensional dissociative coordinates in Ar-HBr, OC-HF, and OC-Cl2 are investigated throughout their bound potentials. Advantages of the current formulation for accurately evaluating equilibrium dissociation energies and a fundamentally different unified perspective on nature of intermolecular interactions will be emphasized. In particular, this canonical approach has significance to previous assertions that there is no very fundamental distinction between van der Waals bonding and covalent bonding or for that matter hydrogen and halogen bonds.

Canonical Potentials and Spectra within the Born-Oppenheimer Approximation.

A generalized formulation of canonical transformations and spectra are used to investigate the concept of a canonical potential strictly within the Born-Oppenheimer approximation. Data for the most accurate available ground electronic state pairwise intermolecular potentials in H2, HD, D2, HeH(+), and LiH are used to rigorously evaluate such transformations. The corresponding potentials are generated explicitly using parameters calculated with algebraic functions from that of the single canonical potential of the simplest molecule, H2(+). The efficacy of this approach is further tested by direct comparison of the predicted eigenvalues of all vibrational states in the selected molecular systems considered with the corresponding most accurately known Born-Oppenheimer eigenvalues currently available. Deviations are demonstrated to be less than 2 cm(-1) for all vibrational states in H2, HD, D2, HeH(+), and LiH, with an average standard deviation of 0.27 cm(-1) for the 87 states considered. The implications of these results for molecular quantum chemistry are discussed.

The Badger-Bauer rule revisited: correlation of proper blue frequency shifts in the OC hydrogen acceptor with morphed hydrogen bond dissociation energies in OC-HX (X = F, Cl, Br, I, CN, CCH).

Potential morphing has been applied to the investigation of proper blue frequency shifts, Δν0 in CO, the hydrogen acceptor complexing in the hydrogen bonded series OC-HX (X= F, Cl, Br, I, CN, CCH). Linear correlations of morphed hydrogen bonded ground dissociation energies D0 with experimentally determined Δν0 free from matrix and solvent effects demonstrate consistency with original tenets of the Badger-Bauer rule (J. Chem. Phys. 1937, 5, 839-51). A model is developed that provides a basis for explaining the observed linear correlations in the range of systems studied. Furthermore, the generated calibration curve enables prediction of dissociation energies for other related but different complexes. The latter include D0 for H2O-CO, H2S-CO, and CH3OH-CO which are predicted by interpolation and found to be 355(13), 171(11), and 377(14) cm(-1) respectively from available experimentally determined proton acceptor shifts. Results from this study will also be discussed in relation to investigations in which CO has been used as a probe of heme protein active sites.

CMM-RS potential for characterization of the properties of the halogen-bonded OC-Cl2 complex, and a comparison with hydrogen-bonded OC-HCl.

Transitions associated with the vibrations ν1, ν1 + ν(b)¹, ν1 + ν5¹, and ν1 + ν5¹ - ν5¹ of the complex OC···Cl2 have been rovibrationally analyzed for several isotopologues involving isotopic substitutions in Cl2. Spectra were recorded using a recently constructed near-infrared (4.34 to 4.56 µm), quantum-cascade laser spectrometer with cw supersonic slit jet expansion. Spectral analysis allowed precise determination of the ν5¹ intermolecular vibration of OC-³5Cl2 to be 25.977637(80) cm⁻¹. These results were incorporated with other previously determined data into a spectroscopic database for generation of a five-dimensional morphed potential energy surface. This compound-model morphed potential with radial shifting (CMM-RS) was then used to make more accurate predictions of properties of the OC-³5Cl2 complex including D(e) = 544(5) cm⁻¹, D0 = 397(5) cm⁻¹, ν3 = 56.43(4) cm⁻¹, and ν(b)¹ = 85.43(4) cm⁻¹. The CMM-RS potential determined for OC-Cl2 was also used to compare quantitatively many of the inherent properties of this non-covalent halogen bonded complex with those of the closely related hydrogen-bonded complex OC-HCl, which has a similar dissociation energy D0. We found that in the ground state, the CO bending amplitude is larger in OC-Cl2 than in OC-HCl.

A four-dimensional compound-model morphed potential for the OC:HBr complex.

A parameterized compound-model morphed intermolecular potential energy surface has been generated for the dimer OC:HBr. This morphed potential is determined by fitting experimentally available gas phase spectroscopic data and found to have a global minimum with a well depth of 564(5) cm(-1) and linear (16)O(12)C-H(79)Br geometry having center of mass to center of mass distance R = 4.525(7) A. The linear isomers (12)C(16)O-H(79)Br and (16)O(12)C-(79)BrH are determined with a corresponding well depth of 273(7) and 269(2) cm(-1) having R = 4.35(4) and 4.24(3) A, respectively. This results in a DeltaE of 293(9) cm(-1) between the global potential energy minimum and the minima in the two higher energy isomers. The generated potential is compared with the corresponding OC:HCl morphed potential. Differences in the morphing parameters are attributed to different contributions to the interaction energy. It is found that the counterpoise method successfully corrected the basis set superposition error in OC:HCl, but was under corrected by 16(7)% in OC:HBr.

A ground state morphed intermolecular potential for the hydrogen bonded and van der Waals isomers in OC:HI and a prediction of an anomalous deuterium isotope effect.

An extended analysis of the noncovalent interaction OC:HI is reported using microwave and infrared supersonic jet spectroscopic techniques. All available spectroscopic data then provide the basis for generating an accurately determined vibrationally complete semiempirical intermolecular potential function using a four-dimensional potential coordinate morphing methodology. These results are consistent with the existence of four bound isomers: OC-HI, OC-IH, CO-HI, and CO-IH. Analysis also leads to unequivocal characterization of the common isotopic ground state as having the OC-HI structure and with the first excited state having the OC-IH structure with an energy of 3.4683(80) cm(-1) above the ground state. The potential is consistent with the following barriers between the pairs of isomers: 382(4) cm(-1) (OC-IH/OC-HI), 294(5) cm(-1) (CO-IH/CO-HI), 324(3) cm(-1) (OC-IH/CO-IH), and 301(2) cm(-1) (OC-HI/CO-HI) defined with respect to each lower minimum. The potential is also determined to have a linear OC-IH van der Waals global equilibrium minimum structure having R(e)=4.180(11) Å, θ(1)=0.00(1)°, and θ(2)=0.00(1)°. This is differentiated from its OC-HI ground state hydrogen bound structure having R(0)=4.895(1) Å, θ(1)=20.48(1)°, and θ(2)=155.213(1)° where the distances are defined between the centers of mass of the monomers and θ(1) and θ(2) as cos(-1)[(1/2)] for i=1 and 2. A fundamentally new molecular phenomenon - ground state isotopic isomerization is proposed based on the generated semiempirical potential. The protonated ground state hydrogen-bonded OC-HI structure is predicted to be converted on deuteration to the corresponding ground state van der Waals OC-ID isomeric structure. This results in a large anomalous isotope effect in which the R(0) center of mass distance between monomeric components changes from 4.895(1) to 4.286(1) Å. Such a proposed isotopic effect is demonstrated to be a consequence of differential zero point energy factors resulting from the shallower nature of hydrogen bonding at a local potential minimum (greater quartic character of the potential) relative to the corresponding van der Waals global minimum. Further consequences of this anomalous deuterium isotope effect are also discussed.

Microwave-based structure and four-dimensional morphed intermolecular potential for HI-CO(2).

(Microwave spectra of the four isotopologue/isotopomers, HI-(12)C(16)O(2), HI-(12)C(18)O(2), HI-(12)C(18)O(16)O, and HI-(12)C(16)O(18)O, have been recorded using pulsed-nozzle Fourier transform microwave spectroscopy. In the last two isotopomers, the heavy oxygen atom tilted toward and away from the HI moiety, respectively. Only b-type Ka = 1 <-- 0 transitions were observed. Spectral analysis provided molecular parameters including rotational, centrifugal distortion, and quadrupole constants for each isotopomer. Then, a four-dimensional intermolecular energy surface of a HI-CO2 complex was generated, morphing the results of ab initio calculations to reproduce the experimental data. The morphed potential of HI-(12)C(16)O(2) had two equivalent global minima with a well depth of 457(14) cm(-1) characterized by a planar quasi-T-shaped structure with the hydrogen atom tilted toward the CO2 moiety, separated by a barrier of 181(17) cm(-1). Also, a secondary minimum is present with a well depth of 405(14) cm(-1) with a planar quasi-T-shaped structure with the hydrogen atom tilted away from the CO2 moiety. The ground state structure of HI-(12)C(16)O(2) was determined to have a planar quasi-T-shaped geometry with R = 3.7717(1) A, thetaOCI = 82.30(1) degrees , thetaCIH = 71.55(1) degrees . The morphed potential obtained is now available for future studies of the dynamics of photoinitiated reactions of this complex.