Julio C. Facelli

Significant progress in predicting the crystal structures of small organic molecules – a report on the fourth blind test

We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.

Towards crystal structure prediction of complex organic compounds – a report on the fifth blind test

The results of the fifth blind test of crystal structure prediction, which show important success with more challenging large and flexible molecules, are presented and discussed.

Report on the sixth blind test of organic crystal structure prediction methods

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Advances in Theoretical and Physical Aspects of Spin–Spin Coupling Constants

Publisher Summary This chapter discusses advances in the theoretical and physical aspects of spin–spin coupling constants. From both theoretical and experimental points of view, the analysis of high-resolution NMR parameters is an important problem, and its significance for the understanding of molecular electronic structure can hardly be stressed enough. When both approaches are taken together, an excellent example of the Born–Opperheimer approximation is obtained because experimentalists measure transitions among nuclear states that are modified by the interactions among magnetic nuclei, external magnetic field, and electrons, while theoreticians study the way the electronic wave function is modified owing to those interactions. The empirical Hamiltonian describes the way nuclear spin energy levels are modified both by the static magnetic field provided by a spectrometer and by the interactions between magnetic nuclei and electrons belonging to a given molecule.

Intermolecular shielding contributions studied by modeling the 13 C chemical-shift tensors of organic single crystals with plane waves

In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all (13)C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm.

Chemical shift tensors: Theory and application to molecular structural problems

1. The chemical shift tensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 1.1. Symmetry properties of the shielding tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 2. Theory of the magnetic shielding tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 3. Need for shielding calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 4. Algorithms for calculation of shielding tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 4.1. Semiempirical and empirical calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 4.2. Coupled Hartree-Fock perturbation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 4.3. Finite perturbation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.4. Perturbation theory including correlation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.5. Density Functional Theory (DFT) of chemical shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.6. Gauge independent algorithms to calculate shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 5. Intermolecular effects on shielding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5.1. Intermolecular effects in solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5.2. Solid state effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5.2.1. Theoretical methods used to calculate solid state effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.2.2. Shielding calculations using periodic boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6. Software and hardware for quantum mechanical calculations of shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 7. Expected accuracy of quantum mechanics based chemical shift calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 8. Applications of chemical shifts calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.1. Molecular conformation of organic molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.2. Biological molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.3. Disordered systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.4. Nano structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 8.5. Studies in coals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.6. Studies of stereochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.7. NMR crystallography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 9. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Modified genetic algorithm to model crystal structures. I. Benzene, naphthalene and anthracene

This paper describes a new computational scheme to model crystal structures of organic compounds employing a modified genetic algorithm. The method uses real-valued Cartesian coordinates and Euler angles between molecules in a crystal block as variables identifying the genetic parameters, i.e., genes. The model does not make any assumption on the crystallographic group at which the compound belongs nor to the number of molecules in the unit cell. The method has been implemented in the computer package MGAC (Modified Genetic Algorithm for Crystal and Cluster structures) that allows for optimizations using any arbitrary selection function. The examples presented here for the crystalline structures of benzene, naphthalene and anthracene, using an empirical potential energy function as the selection function, show excellent agreement with the experimental ones. While these examples use the “rigid molecule approximation,” the method is quite general and can be extended to take into account any number of intram...

Solid-State Effects on NMR Chemical Shifts

This review presents first a qualitative description of the changes observed in the measured chemical shifts in solid state when compared with those obtained in solution. This qualitative description of the intermolecular interactions that affect the chemical shifts is followed by a comprehensive description of the theoretical methods available to analyze the solid-state effects on the chemical shifts. There are numerous examples of solid-state effects in the literature; here we have selected some of the most notable ones, which are presented as case studies. These case studies are classified by nuclei and by the dominant interaction that defines the solid-state effects. Examples are presented for 13 C, 15/14 N, 1 H, 17 O, 31 P, and 19 F. In addition to the effects discussed for chemical shifts the review also presents examples of the solid-state effects on the quadrupolar constants in the case of non 1/2 spin nuclei.

Modeling NMR chemical shifts: A comparison of charge models for solid state effects on 15N chemical shift tensors

This paper presents results from applying different point charge models to take into account intermolecular interactions to model the solid state effects on the 15N NMR chemical shifts tensors. The DFT approach with the BLYP gradient corrected exchange correlation functional has been used because it can include electron correlation effects at a reasonable cost and is able to reproduce 15N NMR chemical shifts with reasonable accuracy. The results obtained with the point charge models are compared with the experimental data and with results obtained using the cluster model, which includes explicitly neighboring molecular fragments. The results show that the point charge models can take into account solid state effects at a cost much lower than the cluster methods.

Carbon-13 chemical shift tensors of carboxylic acids: GIAO calculations in acetic acid + methylamine dimer

GIAO calculations are presented of the 13C chemical shift tensors of the carboxyl group in the dimer of acetic acid with methylamine. The calculations indicate that the local geometrical parameters describing the carboxyl group are related linearly to the distance between the proton and oxygen atom of the hydroxyl group, which is also a measure of the strength of the hydrogen bond. The individual principal components of the chemical shift tensor exhibit very different dependences on the O-H distance. While δ33 is almost independent of the O-H distance, δ22 varies by more than 70 ppm for O-H distances ranging from 0·8 A to 1·5 A. The calculated values indicate that the difference between the in-plane shielding components, δ11 and δ22, can be used as a measure of the relative delocalization of the π electrons of the carbonyl group, the strength of the hydrogen bond and the local geometry of the carboxyl group.