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Chapter 1 Scattering of X-rays and Neutrons 3 1.1 Outline of this chapter 3 1.2 Introduction to the theory of X-ray scattering 3 1.2.1 Classical treatment of X-ray scattering 3 1.2.2 Quantum-mechanical treatment: the first Born approximation 5 1.2.3 Scattering by a periodic crystal 7 1.2.4 The structure factor formalism in terms of atomic densities 9 1.3 Resonance scattering of X-rays 11 1.3.1 Classical treatment 11 1.3.2-Quantum-mechanical treatment: the second Born approximation 13 1.3.3 The power series expansion of the scattering operator 15 1.3.4 The optical theorem and the relation between /" and /' 16 1.4 Neutron scattering 18 1.4.1 Properties of neutrons 18 1.4.2 The neutron scattering length 19 Chapter 2 The Effect of Thermal Vibrations on the Intensities of the Diffracted Beams 22 2.1 The normal modes of a crystal 23 2.1.1 Phonons, internal and external modes 23 2.1.2 The frequency of the normal modes 23 2.2 The effect of thermal vibrations on the Bragg intensities 27 2.2.1 The Born-Oppenheimer approximation 27 2.2.2 The harmonic temperature factor 28 viii Contents 2.2.3 Beyond the harmonic approximation 31 2.2.4 Comparison of the anharmonic formalisms 36 2.2.5 Quantum-statistical treatments 37 2.3 The relation between the atomic temperature factors and lattice dynamics 40 2.3.1 General expression 40 2.3.2 The Debye approximation 41 2.3.3 The rigid-body model for molecular crystals 42 2.3.4 The rigid-bond test 48 Chapter 3 Chemical Bonding and the X-ray Scattering Formalism 49 3.1 The breakdown of the independent-atom model 49 3.1.1 Qualitative considerations 49 3.1.2 The electron density and the LCAO formalism 51 3.2 Improved scattering models 55 3.2.1 The spherical atom kappa formalism 55 3.2.2 Modified spherical scattering factor for the hydrogen atom 56 3.2.3 Examples of results obtained with the K-formalism 57 3.2.4 The multipole description of the charge density of aspherical atoms 59 3.2.5 Aspherical atom scattering factors 67 3.2.6 The aspherical density functions of the Hirshfeld formalism 70 Chapter 4 Least-Squares Methods and Their Use in Charge Density Analysis 72 4.1 Least-squares equations 72 4.1.1 Background 72 4.1.2 General formalisms for linear least-squares 72 4.1.3 Explicit expressions for structure factor least-squares 74 4. L4 Variances and covariances of the least-squares parameter estimates 76 4.1.5 Uncorrelated linear combinations of variables 79 4.2 The least-squares parameters in charge density analysis 79 4.2.1 The parameters in a charge density refinement 79 4.2.2 Parameter restrictions imposed by site and local symmetry and chemical equivalence 80 4.2.3 The scale factor 81 4.3 Physical constraints of the electron density 83 4.3.1 The electroneutrality constraint 83 4.3.2 The Hellmann-Feynman constraint 85 4.4 Joint refinement of X-ray and neutron data 86 4.4.1 The use of complementary information 86 4.4.2 Differences in temperature parameters 86 4.4.3 Relative weighting of the X-ray and neutron data 87 4.4.4 Estimate of the goodness of fit 88 Contents xi 9.2.1 The Hohenberg-...

The molecular structure and dynamics of the photoexcited metal-to-ligand-charge-transfer (MLCT) state of [Cu(I)(dmp)(2)](+), where dmp is 2,9-dimethyl-1,10-phenanthroline, in acetonitrile have been investigated by time-domain pump-probe X-ray absorption spectroscopy, femtosecond optical transient spectroscopy, and density functional theory (DFT). The time resolution for the excited state structural determination was 100 ps, provided by single X-ray pulses from a third generation synchrotron source. The copper ion in the thermally equilibrated MLCT state has the same oxidation state as the corresponding copper(II) complex in the ground state and was found to be penta-coordinate with an average nearest neighbor Cu-N distance 0.04 A shorter than that of the ground state [Cu(I)(dmp)(2)](+). The results confirm the previously proposed "exciplex" structure of the MLCT state in Lewis basic solvents. The evolution from the photoexcited Franck-Condon MLCT state to the thermally equilibrated MLCT state was followed by femtosecond optical transient spectroscopy, revealing three time constants of 500-700 fs, 10-20 ps, and 1.6-1.7 ns, likely related to the kinetics for the formation of the triplet MLCT state, structural relaxation, and the MLCT excited-state decay to the ground state, respectively. DFT calculations are used to interpret the spectral shift on structural relaxation and to predict the geometries of the ground state, the tetracoordinate excited state, and the exciplex. The DFT calculations also indicate that the amount of charge transferred from copper to the dmp ligand upon photoexcitation is similar to the charge difference at the copper center between the ground-state copper(I) and copper(II) complexes.

I. Introduction 883 II. Photocrystallography 883 A. Crystallography of Light-Induced Species 883 B. Supporting Techniques 863 III. Metastable Isomers of Transition-Metal Nitrosyl Complexes 863 A. The First Discoveries 863 B. The Nature of the Metastable States of Sodium Nitroprusside 864 1. Sodium Nitroprusside (SNP): Experimental Methods 864 2. Orbital Ordering of the SNP Ground-State Species 866 3. Theoretical Calculation of the Metastable and Excited States and the Mechanism of Photoinduced Interconversion 867 C. Other Small Molecule Complexes 868 1. [NiNO(η 5 -Cp)] 868 2. Ruthenium and Osmium Complexes and the Dependence of the Decay Temperature on Chemical Substitution and Solid-State Environment 869 3. Solid-State Effects 870 4. Theoretical Calculations on Ruthenium Complexes 871 5. Calculated Hyperfine Splittings and Comparison with Results from Mo ¨ssbauer Spectroscopy 874 IV. Heme Systems 875 A. Introduction 875 B. Experimental Evidence for Linkage Isomers of NO Porphyrins and Theoretical Confirmation 875 C. Further Theoretical Studies on NO-Porphyrins 875 V. Linkage Isomerism of Other Di-and Triatomic Ligand Transition-Metal Complexes 876 A. Dinitrogen 876 B. NO 2 878 C. Sulfur-Containing Ligands 879 VI. Concluding Remarks 880 VII. Acknowledgments 880 VIII. Abbreviations 881 IX. Note Added after ASAP Posting 881 X. References 881

The geometries of two known metastable states of sodium nitroprusside dihydrate, Na 2 [Fe(CN) 5 NO]‚2H 2 O, and that of the ground state have been analyzed by X-ray diffraction at 50 K, a temperature at which no decay of metastable-state concentration with time is observed. Data were collected on two laser-excited crystals containing populations of ∼37% of metastable state I (MS 1 ) and ∼10% of metastable state II (MS 2 ), respectively, using imaging plates and a rotating anode source. For MS 1 the apparent geometry changes upon excitation, determined earlier at 138 K (

This book deals with the electron density distribution in molecules and solids as obtained experimentally by X-ray diffraction. It is a comprehensive treatment of the methods involved, and the interpretation of the experimental results in terms of chemical bonding and intermolecular interactions. Inorganic and organic solids, as well as metals, are covered in the chapters dealing with specific systems. As a whole, this monograph is especially appealing because of its broad interface with numerous disciplines. Accurate X-ray diffraction intensities contain fundamental information on the charge distribution in crystals, which can be compared directly with theoretical results, and used to derive other physical properties, such as electrostatic moments, the electrostatic potential and lattice energies, which are accessible by spectroscopic and thermodynamic measurements. Consequently, the work will be of great interest to a broad range of crystallographers and physical scientists.

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The development of a theoretical databank of transferable pseudoatoms for fast prediction of the electron densities and related electronic properties of proteins is described. Chemically unique pseudoatoms identified on the basis of common connectivity and bonding are extracted from ab initio molecular densities of a large number of small molecules using a least-squares projection technique in Fourier transform space. The performance of the databank is evaluated by comparison of the electron densities and electrostatic properties of the amino acids GLN, SER, and LEU and their dimers with those obtained from molecular calculations on the same test compounds. It is found that deformation density bond peaks are reproduced to within 0.02−0.10 e/Å3, whereas electrostatic potentials, bond critical point indices, atomic charges, and molecular moments show differences with results from calculations performed directly on the test molecules which are comparable with or smaller than the spread of the values between different ab initio methods (Hamiltonian, basis set, etc.). The order of intermolecular electrostatic interaction energies for selected dimers of the test compounds are well reproduced, though the results are always smaller, by about 25 kJ/mol on average, than electrostatic energies from Morokuma−Ziegler decomposition of the total interaction energy evaluated with the ADF program. The difference is attributed to the limitations of the Buckingham-type approximation for electrostatic interactions, used in the current study, which assumes nonoverlapping charge densities. The consistency achieved by the pseudoatom databank is much better than that obtained with the AMBER99, CHARMM27, MM3, and MMFF94 force fields, which sometime overestimate, sometimes underestimate, the electrostatic interaction energy. The electrostatic component of the binding energies (directly related to the enthalpy of sublimation) of molecules in crystals, calculated based on the databank parameters, agree within 25−60 kJ/mol with the total binding energies evaluated ab initio at the Density Functional level of theory, even though the exchange−repulsion and dispersion terms have not been taken into account in the databank values.