Some implications of combined X-ray and neutron diffraction studies

Abstract

A survey is made of about ten combined X-ray and neutron diffraction studies. The theory of X-N difference densities is reviewed for both centric and acentric structures. It is concluded that the phase problem has been incorrectly treated in past work on acentric crystals, leading to a systematic underestimate of the difference density. Expressions are given for the average standard deviation in the difference density due to random errors in both the X-ray and neutron measurements. A survey of experimental peak heights indicates that (a) the peaks in lone-pair regions are generally lower than the maxima in the bonds, (b) double bonds may have lower difference densities than either triple or single bonds. The effect of thermal smearing on a theoretical difference density is analyzed and it is shown that the relatively low height of the lone-pair density is a result of molecular vibrations which affect the sharper lone-pair features more strongly than the overlap density. The first-row atom asphericity shifts are reviewed and discussed in terms of scattering factors associated with the difference density features. The size of the shifts varies with data cut-off and thermal amplitude of the atoms, as the lone pair scattering is relatively dominant in the high-order region. Introduction 'Do you feel that you are now using the theory to calibrate the experiment but as you go along to larger and' larger molecules the experiment will play the dominant role in getting out the really chemically interesting information?' Walter C. Hamilton ACA Symposium, Albuquerque (1973).It seems appropriate at this time to discuss how well the experiment has been calibrated by theoretical calculations and to examine information available from very few studies on larger molecules. Survey of structures studiedThe number of compounds that have been studied by the combined X-ray-neutron technique is limited, because the studies are time-consuming and require careful attention to details of both the X-ray and neutron experiments. A listing of published studies is given in Table 1. They fall in three groups: room-temperature studies of centric (1) and acentric (3) crystals and liquid nitrogen temperature studies of centric crystals (2). The resulting X-ray neutron difference density QX-N, which is further defined below represents the redistribution of the electron density when atoms bond to form a molecule. An example is given in Fig. 1, which shows 0X-N in the plane of the tetracyanoethylene molecule (Becker, Coppens & Ross, 1974). Typically, density is accumulated in the bonds between the atoms and in the lone pair at the 'free' side of the * Editorial note:-This paper was presented at a memorial symposium in honour of Walter C. Hamilton, a former Coeditor of Acta Crystallographica, held on 15 June 1973 at Brookhaven National Laboratory, and sponsored jointly by the American Crystallographic Association and the Brookhaven National Laboratory. nitrogen atom. The nitrogen atom and the ethylenic carbon atom are in negative regions indicating ...

Charge density studies below liquid nitrogen temperature: X-ray analysis of p-nitropyridine N-oxide at 30 K

“…An analysis of the positional parameters reveals shifts between 0.007 and 0.013 A for the X-ray positions of N(5), O(1), 0(2) and 0(3), the O atoms being shifted towards the lone-pair density while the nitro-group N is displaced into the C-N bond. The size of these shifts is as observed in other studies (Coppens, 1974) and indicates the dominant effect of low-order reflections even in a refinement including a large number of high-order data. It is of interest that while the shifts are reduced in the high-order refinement (sin0/~.>0.75 A -x, Table 2), systematic discrepancies persist for the four affected atoms, suggesting a persistence of valenceelectron scattering beyond 0.75 A -1.…”

“…Several earlier charge density studies of molecular crystals have clearly indicated the desirability of performing the necessary diffraction experiments at reduced temperatures (Verschoor & Keulen, 1971;Coppens & Vos, 1971;Coppens, 1974). Though the effect of thermal averaging on the density is becoming better understood in a quantitative sense (Coulson & Thomas, 1971;Ruysink & Vos, 1974;Coppens, 1975), reduction of the thermal smearing of the rest density and the corresponding increase in thermal resolution remain of considerable importance.…”

Lithium formate monohydrate: a comparison of the X–N difference density and structural parameters derived from different experiments

“…Since the space group Pna2~ is not centrosymmetric, special attention has to be paid to the phases of the contributions to the difference density. The phases of the amplitudes contributing to the X-N maps were calculated in the way suggested by Coppens (1974). The same procedure was applied by Thomas, Tellgren & Alml6f (1975).…”

Combined X-ray and neutron diffraction studies of normal and deuterated iminodiacetic acid hydrobromide

“…For centrosymmetric structures the average standard deviations in the maps can be approximated by where f~ is the X-ray form factor multiplied by the amplitude of the radiation scattered by one electron and b~ is the scattering length for thermal neutrons (Coppens, 1974). For first row elements (f~) ~ (hi) but for compounds containing heavier elements these two factors will increase the average standard deviation.…”

“…The data for IDAB (X-ray) are taken from Oskarsson (1973). (4) tain information about deviations from spherical symmetry of the electron distribution around the atoms (Coppens, 1974). The quantities Fo.x-F¢,N are used as coefficients in Fourier summations.…”