Dylan Jayatilaka

Hirshfeld surface analysis

In the last few years the analysis of molecular crystal structures using tools based on Hirshfeld surfaces has rapidly gained in popularity. This approach represents an attempt to venture beyond the current paradigm—internuclear distances and angles, crystal packing diagrams with molecules represented via various models, and the identification of close contacts deemed to be important—and to view molecules as “organic wholes”, thereby fundamentally altering the discussion of intermolecular interactions through an unbiased identification of all close contacts.

Electrostatic potentials mapped on Hirshfeld surfaces provide direct insight into intermolecular interactions in crystals

Ab initio electrostatic potentials for molecules can readily be mapped onto their Hirshfeld surfaces and displayed within a crystal packing diagram. In this manner the close molecular contacts in the crystal can be rationalized and discussed in terms of the electrostatic complementarity of touching surface patches in adjacent molecules. By way of example a detailed discussion is given of molecular electrostatic potentials for a large number of small, symmetric, cyclic molecules that crystallize in space groupsP41212 or P43212, with a focus on the qualitative insight that can be obtained and the ways in which this complements the intermolecular electrostatic energies recently reported for some of these materials.

Towards quantitative analysis of intermolecular interactions with Hirshfeld surfaces

Enhancements to the properties based on Hirshfeld surfaces enable quantitative comparisons between contributions to crystal packing from various types of intermolecular contacts.

Higher analytic derivatives. IV. Anharmonic effects in the benzene spectrum

This is the fourth in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper we examine anharmonic effects in the infrared and Raman spectra of benzene. The following spectroscopic properties have been calculated; ab initio anharmonic corrections (ω−ν) and estimates of the harmonic frequencies ω for all 30 vibrational modes of C6H6 and C6D6, a complete set of anharmonic constants x and g for C6H6, intensities for the infrared spectrum of C6H6 up to 6148 cm−1, and anharmonic corrections to the Raman scattering factors for the fundamental modes of C6H6. In addition, we have improved on previous calculations of the equilibrium geometry of benzene, using Mo/ller–Plesset perturbation theory and a triple zeta plus double polarization (TZ2P) basis. We have also calculated a zero‐point vibrationally averaged geometry which is in good agreement with the experimental R0 value. All these calculations are based on a Hartree–Fock quartic potential...

Visualisation and characterisation of voids in crystalline materials

We present a simple and more realistic alternative to the conventional approach of mapping void space by rolling a probe sphere of variable radius over a fused-sphere representation of a molecular crystal. Based on isosurfaces of the procrystal electron density, this approach can be used to locate and visualise the void space in crystalline materials, as well as readily compute surface areas and volumes of the voids. The method is quite general, computationally rapid, and capable of locating and characterising all “empty” space, and not just the larger cavities and channels, in molecular crystals, organic, metal–organic and inorganic polymers. Examples elaborate on its application to a variety of crystalline systems where voids have been the subject of recent discussion, including porous dipeptides, metal–organic and covalent organic frameworks. Comparison is made with existing computational methods, as well as with the results from experimental techniques that provide estimates of volumes and surface areas of void space and porosity.

Wavefunctions derived from experiment. I. Motivation and theory

An experimental wavefunction is one that has an assumed form and that is also fitted to experimental measurements according to some well defined procedure. In this paper, the concept of extracting wavefunctions from experimental data is critically examined and past efforts are reviewed. In particular, the importance of scattering experiments for wavefunction fitting schemes is highlighted in relation to the more familiar model, the Hamiltonian paradigm. A general and systematically improvable method for fitting a wavefunction to experimental data is proposed. In this method, the parameters in a model wavefunction are determined according to the variational theorem but subject to an imposed constraint that an agreement statistic between the calculated and observed experimental data has a certain acceptable value. Advantages of the method include the fact that any amount of experimental data can be used in the fitting procedure irrespective of the number of parameters in the model wavefunction, the fact that a unique answer is obtained for a given choice of the model wavefunction, and the fact that the method can be used to model different experiments simultaneously. The wavefunction fitting method is illustrated by developing the theory for extracting a single-determinant wavefunction for a fragment of a molecular crystal, using data obtained from elastic X-ray scattering data. Effects due to thermal motion of the nuclei, secondary extinction of the X-ray scattering and different choices for the crystal fragment are treated.

The prediction of spectroscopic properties from quartic correlated force fields: HCCF, HFCO, SiH+3

Knowledge of a force field expanded through quartic displacements, together with a dipole field expanded through cubic displacements, yields all the harmonic and anharmonic molecular properties of interest to infrared spectroscopists. Such force fields may also explain much of the mechanism behind intramolecular vibrational energy redistribution. The ab initio quantum chemist can now calculate these fields, either at the self‐consistent field level or with the inclusion of electron correlation effects. For accurate predictions, it is important to include electron correlations effects for at least the quadratic part of the force fields. Here we report studies using the second‐order Mo/ller–Plesset method for the full quartic fields. We examine the effects of using large basis sets. The quadratic force constants are calculated analytically; cubic and quartic constants are calculated using central differences of second derivatives in reduced normal coordinates. Three molecules are studied. HCCF, for which a ...

Open‐shell restricted Hartree–Fock perturbation theory: Some considerations and comparisons

A comparative study is presented of the various recently developed open‐shell perturbation theories that are based on a restricted Hartree–Fock reference wave function. Included in this study are issues concerning spin contamination, implementational considerations, and numerical comparisons at the second‐order of perturbation theory for equilibrium geometries, vibrational frequencies, and singlet–triplet energy differences. Based on all of these considerations, it is concluded that the z‐averaged perturbation theory (ZAPT) method is to be preferred over the other recently devised spin–orbital perturbation theories, while the spin‐free OPT2 method possesses some advantages and disadvantages relative to the ZAPT method. In particular, it is shown that OPT2 energies are not invariant to rotations among singly‐occupied degenerate molecular orbitals.

Spin contamination in single-determinant wavefunctions

Abstract Spin contamination in single-determinant wavefunctions is examined by performing unrestricted Hartree—Fock (UHF) calculations which constrain the value using a Lagrange multiplier λ. We call this method spin-constrained unrestricted Hartree—Fock (SUHF). It is shown that as λ→∞, restricted open-shell Hartree—Fock (ROHF) solutions are obtained. Small values of λ can significantly reduce the error, whilst changing the energy only slightly. Calculations are performed with SUHF and its Moller—Plesset counterpart SUMP2. SUMP n calculations with large values of λ appear to be a way to carry out ROHF Moller—Plesset studies. Applications are presented for CN, NH 2 and BH and are compared with UHF and annihilated UHF (AUHF) results.

Wavefunctions derived from experiment. II. A wavefunction for oxalic acid dihydrate

A wavefunction has been derived for the oxalic acid dihydrate molecule using accurate low-temperature X-ray electron-density structure-factor data. The electron density from this constrained theoretical wavefunction is compared to those of unconstrained theoretical wavefunctions. Fitted electron densities around hydrogen atoms show significant deviation compared to Hartree-Fock calculations. In particular, hydrogen bonding appears enhanced in the crystal over theoretical predictions, while the density usually attributed to lone-pair electrons of the oxalic acid oxygen atoms is decreased. The constrained fitting procedure improves the overall agreement of the calculated structure factors even for structure factors that were not used as input to the fitting procedure. The pictures obtained from the constrained fitting procedure are insensitive to random errors introduced into the data. Similarly, the fitting procedure is able to reproduce features that arise from more accurate theoretical calculations. However, we are unable to fit our wavefunction to within the experimentally quoted error bounds without allowing an unreasonably large change in the energy of the constrained wavefunction. Large Hartree-Fock and density functional theory (DFT) cluster calculations involving up to 86 atoms in size also do not show significantly improved agreement with the experimentally observed structure factors. Derived properties from the constrained wavefunction fragments, such as the kinetic energy, electrostatic potential and the electron localization function, are also presented. In general, there are no difficulties in extracting experimental wavefunctions and the associated derived properties from elastic X-ray scattering data for crystal fragments of the order of 20 atoms.