### Acta Crystallographica Section B

# Structural Science, Crystal Engineering and Materials

### Volume 69, Part 2 (April 2013)

## research papers

*Acta Cryst.* (2013). B**69**, 203-213 [ doi:10.1107/S2052519213004879 ]

### Electron densities by the maximum entropy method (MEM) for various types of prior densities: a case study on three amino acids and a tripeptide

**Abstract:** Dynamic model densities according to Mondal *et al.* [(2012), *Acta Cryst.* A**68**, 568-581] are presented for independent atom models (IAM), IAMs after high-order refinements (IAM-HO), invariom (INV) models and multipole (MP) models of -glycine, DL-serine, L-alanine and Ala-Tyr-Ala at *T* 20 K. Each dynamic model density is used as prior in the calculation of electron density according to the maximum entropy method (MEM). We show that at the bond-critical points (BCPs) of covalent C-C and C-N bonds the IAM-HO and INV priors produce reliable MEM density maps, including reliable values for the density and its Laplacian. The agreement between these MEM density maps and dynamic MP density maps is less good for polar C-O bonds, which is explained by the large spread of values of topological descriptors of C-O bonds in static MP densities. The density and Laplacian at BCPs of hydrogen bonds have similar values in MEM density maps obtained with all four kinds of prior densities. This feature is related to the smaller spatial variation of the densities in these regions, as expressed by small magnitudes of the Laplacians and the densities. It is concluded that the use of the IAM-HO prior instead of the IAM prior leads to improved MEM density maps. This observation shows interesting parallels to MP refinements, where the use of the IAM-HO as an initial model is the accepted procedure for solving MP parameters. A deconvolution of thermal motion and static density that is better than the deconvolution of the IAM appears to be necessary in order to arrive at the best MP models as well as at the best MEM densities.

**Keywords: electron densities; maximum entropy method; prior densities; amino acids; tripeptides; independent atom models; high-order refinements.**

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