Jacek Rychlewski

Sub-microhartree accuracy potential energy surface for H3+ including adiabatic and relativistic effects. I. Calculation of the potential points

Sixty-nine points of the Born–Oppenheimer (BO) potential energy surface (PES) for the ground state of H3+ have been computed using explicitly correlated Gaussian wave functions with optimized nonlinear parameters. The calculated points have an absolute error of about 0.02 cm−1 (0.1 microhartree), i.e., they are by at least one order of magnitude more accurate than ever reported. Similarly accurate adiabatic and relativistic corrections have also been evaluated by means of the Born–Handy formula and by direct perturbation theory (DPT), respectively.

Sub-microhartree accuracy potential energy surface for H3+ including adiabatic and relativistic effects. II. Rovibrational analysis for H3+ and D3+

The 69 potential energy points of H3+ computed by Cencek et al. [J. Chem. Phys., 108, 2831 (1998), preceding paper] have been fitted to an analytical potential energy surface (PES). Rovibrational frequencies have been derived for the symmetric H3+ and D3+ isotopomers. A comparison with experiment shows residual discrepancies of a few tenths of cm−1 which can be ascribed mainly to nonadiabatic effects.

Many‐electron explicitly correlated Gaussian functions. II. Ground state of the helium molecular ion He+2

Explicitly correlated Gaussian functions have been used to compute variationally the Born–Oppenheimer (B–O) potential energy curve for the ground 2Σ+u state of He+2. The energy values are much lower than all previously reported over the whole range of the internuclear distance R. The strict lower bound for the binding energy De amounts to 2.4730 eV and the true value (within the B–O approximation) is estimated to be 2.4742±0.0006 eV.

Factors Affecting Conformation of (R,R)-Tartaric Acid Ester, Amide and Nitrile Derivatives. X-Ray Diffraction, Circular Dichroism, Nuclear Magnetic Resonance and Ab Initio Studies

Abstract Derivatives 2a–15a of (R,R)-tartaric acid (1a) with all combinations of methyl ester, amide, N-methylamide and N,N-dimethylamide groups, as well as the corresponding O,O′-dibenzoyl derivatives 1b–15b and nitriles 16–18 have been synthesized. Their conformations have been studied by the NMR and CD methods in solution as well as by X-ray diffraction in the crystalline state. The preference for planar. T conformation of the four carbon chain is observed under conditions restricting the α-hydroxyacid, ester or amide group to be nearly planar, this conformation being stabilized by intramolecular hydrogen bonds of the S(5) motif and the electrostatic CO/C(β)H and CN/C(β)H coplanar bond interactions. The C=O/C(α)-O bond system tends to be either synplanar (ester, acid), or antiplanar (ester, primary and secondary amide). Ab initio calculations allowed to demonstrate that for the isolated molecules of diamides 10a and 15a there is strong preference for gauche G+(a,a) conformers, the driving force being the formation of the hydrogen bonded six-membered cycles of the S(6) motif joining the OH and C=O groups from two different halves of the molecule. The results compare favourably with the experimental values derived from NMR spectra of 15a in nonpolar solvent. In the absence of intramolecular hydrogen bonding the N,N-dimethylamide group is better accomodated in a gauche G− conformer. This releases the nonbonded interaction due to the amide methyl group anti to the carbonyl group.

(R,R)-Tartaric Acid Dimethyl Diester from X-Ray and Ab Initio Studies: Factors Influencing Its Conformation and Packing

The conformation of dimethyl (R,R)-tartrate has been analyzed on the basis of the single crystal X-ray diffraction method as well as by ab-initio quantum chemical studies. The results showed that the extended T conformation containing two planar hydroxyester moieties predominates in both ab-initio and X-ray studies. The lowest energy conformer in ab-initio calculations has C2 symmetry and hydrogen bonds between a hydroxyl group and the nearest carbonyl oxygen. The second in energetical sequence, with an energy difference of only 1.2 kcal/mol, is the asymmetrical conformer, which differs from the lowest energy form by the rotation of one of the ester groups by 180°. Intramolecular OH...O hydrogen bonds observed in this rotamer again involve only proximal functional groups. This conformer is present in the crystal structure of the studied compound, although its conformation in the solid state is no longer stabilized by intramolecular hydrogen bonds of the type mentioned above. In the crystal, hydroxyl groups are mostly involved in intermolecular hydrogen bonds and form only a weak intramolecular hydrogen bond with each other. The planar arrangement of the α-hydroxyester moieties combined with the extended conformation of the carbon chain seems to be stabilized by the intramolecular hydrogen bonds between neighboring functional groups and by the long range dipole-dipole interactions between two pairs of CO and (β)C-H bonds.

X-ray diffraction and theoretical studies of the methyl ester of (R,R)-tartaric acid monoamide: semiempirical and ab initio calculations of some model compounds

Abstract In its crystal structure, determined by X-ray diffraction, the methyl ester of (R,R)-tartaric acid monoamide crystallizes with two molecules per assymetric unit. Each molecule displays subtle conformational differences effected by 180° rotation by the methyl ester group about the CC∗ bond, whereas the staggered conformation around the central C∗C∗ bond, with a trans arrangement of the ester and amide substituents, and the eclipsed orientation of the amide nitrogen atom with respect to the nearest hydroxyl group, remains the same in both molecules. MNDO and ab initio single-point energies for the two molecules indicate that the lower energy molecule is that with the α-hydroxyl group eclipsed by the carbonyl group rather than the methoxy oxygen atom. Conformers observed in the crystal structure differ from those obtained by full MNDO optimization in the planarity of α-hydroxyester and α-hydroxyamide residues. Ab initio calculations at the 6–31G∗ level on smaller systems, i.e. (2R,3R)-2,3-butanediol and (2R,3R)-2,3-dihydroxybutanedinitrile, suggest different conformational preferences for the two model compounds (gauche vs. trans with respect to the carbon chain), and point to the importance of the intramolecular hydrogen bond in stabilizing the gauche orientation of the vicinal OH groups. A similar hydrogen bond may be present in one of two crystallographically independent molecules of the methyl ester of (R,R)-tartaric acid monoamide, but only as a minor component in a complex system of intermolecular hydrogen bonds.

High-performance Computing in Molecular Sciences

A task which is very common in theoretical chemistry, physics, and engineering — solving the generalized symmetric eigenvalue problem — is discussed. In the considered examples modern quantum chemical methods are applied to solve the Schrodinger equation with a molecular Hamiltonian operator. The solution of the Schrodinger equation is of fundamental importance in quantum chemistry and molecular physics since it gives knowledge of the microscopic world. Two subproblems of completely different character — evaluating matrix elements (a scalar task) and solving the eigenequations (a vector task) are analyzed in terms of the overall computational cost, its scaling with the dimension of the algebraic space and with the size of the molecular system, and of the appropriateness of different computer architectures. The most logical way to achieve a good performance is to use distributed processing on heterogeneous (scalar-vector) systems employing message passing. Experiences in testing one of such systems are discussed and compared with speedups obtained on shared-and distributed-memory homogeneous machines.

Modes of dimerization of the α-hydroxyamide group☆

Abstract An X-ray diffraction and theoretical study on selected dimeric, mostly cyclic, hydrogen-bonded structures occurring in the crystals of several (R,R)-tartaric acid derivatives and involving α-hydroxyamide moieties is presented. The conformational behaviour of the dimers in both isolated and solvated states is considered theoretically with the use of the RHF/6-311 + +G∗∗ method and complete geometry optimization. Solvation effects have been included at the SCRF level and the following models have been employed: Onsager, polarized continuum model, and self-consistent isodensity PCM. All types of dimeric structures observed in the crystals have been obtained as stable local energy minima after complete geometry optimizations.

Gas-phase Conformational Analysis of (R,R)-Tartaric Acid, its Diamide, N,N,N′,N′- Tetramethyldiamide and Model Compounds

Abstract A review over most recent ab initio studies carried out at both RHF and MP2 levels on (R,R)-tartaric acid (TA), its diamide (DA), tetramethyldiamide (TMDA) and on three prototypic model systems (each of them constitutes a half of the respective parental molecule), i.e. 2-hydroxyacetic acid (HA), 2-hydroxyacetamide (HD) and 2-hydroxy-N,N-dimethylacetamide (HMD) is presented. (R,R)-tartaric acid and the derivatives have been completely optimized at RHF/6-31G * level and subsequently single-point energies of all conformers have been calculated with the use of second order perturbation theory according to the scheme: MP2/6-31G * //RHF/6-31G * . In the complete optimization of the model molecules at RHF level we have employed relatively large basis sets, augmented with polarisation and diffuse functions, namely 3-21G, 6-31G * , 6-31++G ** and 6-311++G ** . Electronic correlation has been included with the largest basis set used in this study, i.e. MP2/6-311++G ** //RHF/6-311++G ** single-point energy calculations have been performed. General confomational preferences of tartaric acid derivatives have been analysed as well as an attempt has been made to define main factors affecting the conformational behaviour of these molecules in the isolated state, in particular, the role and stability of intramolecular hydrogen bonding. In the case of the model compounds, our study principally concerned the conformational preferences and hydrogen bonding structure within the α-hydroxy-X moiety, where X=COOH, CONH 2 , CON(CH 3 ) 2 .

Magnetic effects for the hydrogen molecule in excited states: b 3Σ+ u of H2

Using explicitly correlated wavefunctions, ab initio calculations of the magnetizability x and rotational g factor for the lowest triplet state of the hydrogen molecule were carried out. The behaviour of the magnetic properties is discussed in terms of the internal structure of the molecule and the electron density.