Burla Maria Cristina, Carrozzini Benedetta, Cascarano Giovanni Luca, Giacovazzo Carmelo, Polidori Giampiero
Department of Earth Sciences, University of Perugia, 06100 Perugia, Italy.
Acta Crystallogr A. 2011 Sep;67(Pt 5):447-55. doi: 10.1107/S0108767311017843. Epub 2011 Jul 14.
The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst. A 66, 347-361]. New Fourier coefficients were devised which were the basis of a new ab initio method for the solution of the phase problem (i.e. VLD, vive la difference). In this paper we study the joint probability distribution functions P(F, F(p), F(Q)), where F(Q) is the structure factor corresponding to the ideal hybrid Fourier synthesis ρ(Q) = τρ - ωρ(p) and τ and ω are any pair of real numbers. New Fourier coefficients for the calculations of any hybrid synthesis are obtained, and the properties of the corresponding electron-density maps are discussed. The first applications show the correctness of our theoretical approach and suggest possible applications in phasing procedures.
最近，通过联合概率分布函数的方法重新审视了差分电子密度[Burla等人（2010年）。《晶体学报》A辑66卷，347 - 361页]。设计了新的傅里叶系数，这些系数是一种用于解决相位问题的新从头算方法（即VLD，差分万岁）的基础。在本文中，我们研究了联合概率分布函数P(F, F(p), F(Q))，其中F(Q)是对应于理想混合傅里叶合成ρ(Q) = τρ - ωρ(p)的结构因子，τ和ω是任意一对实数。获得了用于计算任何混合合成的新傅里叶系数，并讨论了相应电子密度图的性质。初步应用表明了我们理论方法的正确性，并暗示了在相位确定程序中的可能应用。
