Control and Prediction of the Organic Solid State

Most of the crystal structure modelling using DMAREL & DMACRYS that has not derived a specific potential for the molecule^1,2 has supplemented the Distributed Multipole electrostatic model with an empirically fitted isotropic atom-atom potential of the form:

where atom i of type i in molecule M is separated by R_ik from atom k of type k in molecule N. Some notes and comments on their use follow, with references to the definitive literature.

WILL01 was derived³ by fitting to a wide range of crystal structures and validated against peptide and nucleoside structures. A key feature is that the hydrogen interaction sites are moved by 0.1 Å into the H-X bond from their neutron or ab initio optimised positions. DMACRYS can perform this foreshortening, which has to also be used in the DMA analysis.

Potential	Atom pair	Description	Aik /kJ mol-1	Bik/Å-1	Cik/kJ mol-1 Å6
WILL01	C(2)···C(2)	C bonded to 2 atoms	103235	3.60	1435.09
WILL01	C(3)···C(3)	C bonded to 3 atoms	270363	3.60	1701.73
WILL01	C(4)···C(4)	C bonded to 4 atoms	131571	3.60	978.36
WILL01	H(1)···H(1)	H bonded to C	12680	3.56	278.37
WILL01	H(2)···H(2)	H in alcoholic group	361.30	3.56	0
WILL01	H(3)···H(3)	H in carboxyl group	115.70	3.56	0
WILL01	H(4)···H(4)	H in N-H group	764.90	3.56	0
WILL01	N(1)···N(1)	N in triple bond	96349	3.48	1407.57
WILL01	N(2)···N(2)	other N with no bonded H	102369	3.48	1398.15
WILL01	N(3)···N(3)	N bonded to 1 H atom	191935	3.48	2376.55
WILL01	N(4)···N(4)	N with 2 bonded H atoms	405341	3.48	5629.82
WILL01	O(1)···O(1)	O bonded to 1 other atom	241042	3.96	1260.73
WILL01	O(2)···O(2)	O bonded to 2 other atoms	284623	3.96	1285.87

This potential was successfully used in a large survey of crystal structure predictions in conjunction with both a point charge⁴ and Distributed Multipole model⁵. However problems have been observed in underestimating hydrogen bond distances when combined with a Distributed Multipole Model, presumably because the electrostatic forces can be stronger than with the point charge model used in Williams' parameterisation. In certain cases,  of (carboxylate)O···H-O  and N···H-O hydrogen bonds the underestimate has led to the hydrogen bonds becoming within the covalent bond range. (An ad hoc fix for the latter⁶ is to replace the purely repulsive, Williams potential between pyridine nitrogen and carboxylic proton (N(2).H(3)) to A=75719.47 kJ/mol and B=5.1765 Å^-1 to model the cocrystal of 4-aminobenzoic acid with 4-nitrophenylacetic acid. This potential is much steeper at unphysically short distances without penalising the lattice energy at typical contacts compared with the original Williams parameterisation.) Graeme Day's group noted noted that O-H(3)···N(2) distances were unreasonably short for the cocrystal in the 2007 blindtest, and found substituting the alcohol H(2) parameters for H(3) in this carboxylic acid produced more reasonable results. We are currently testing the published WILL01 potentials for a range of systems, to establish whether it is worth providing a revision of all the polar hydrogen parameters for use in conjunction with a DMA.

FIT has evolved through using Williams older parameterisations, which had each element in conjunction with C and H only. The H nuclei are used as the interaction sites, although whether Williams corrected for the X-ray foreshortening in these derivations is unclear.

Reference	Atom pair	Description	Aik /kJ mol-1	Bik/Å-1	Cik/kJ mol-1 Å6
7	C···C	Any C atom	369743	3.60	2439.8
7	H···H	H bonded to C	11971	3.74	136.4
8	HN···HN	H bonded to N	5029.68	4.66	21.50
9	HO···HO	H bonded to O	2263.3	4.66	21.50
7	N···N	Any N atom	254529	3.78	1378.4
10	O···O	Any O atom	230064.1	c=3.96	1123.59
11	F···F	Any F atom	363725	4.16	844
12	Cl···Cl	Any Cl Atom	924675	c=3.51	7740.48
Other parameters that have been used in conjunction with FIT for a few applications
16	S···S	S atoms in blind tests (for thiol and thioether)	401033.7336	3.30	5790.656
17	S···S	S atoms in sulfoxides	236501.5221	2.90	8397.1147
17	O···O	O atoms in sulfoxides	202983.6471	3.96	640.8628309

Note that NEIGHBOURS does not distinguish between H-O and H-N and so many papers have use the H_N (=H_p) parameters for any polar hydrogen, including in hydrates and ice.¹³ NEIGHCRYS will automatically provide the Williams typing and can allow a user specified typing, allowing the ability of DMACRYS to use more atomic types for a given atom to be applied without manual editing of the input file. The extent to which the parameters in combination have been tested beyond⁸ is limited, though there has been some validation for the F parameters in Ashley Hulme's thesis and for the isotropic chlorine in situations without close Cl···Cl contacts.¹⁴ There are various failures: problems in stacking of some rigid aromatics differences led Tom Lewis to reduce the C parameters by 25% in his studies (thesis + ¹⁵ ).

It is important to note that both these empirically fitted potentials are effectively modelling the total intermolecular potential with the electrostatic component removed, as well as it is sampled in the crystal structures used for fitting and validation. It is not surprising that the results can be sensitive to the quality of the electrostatic model used, and may be very poor for atypical short contacts. Since they are empirically based, the choice of which to use can only be made by empirical testing for related crystal structures.

Reference List