Philip Coppens

Basic principals of X-Ray charge dnsities analysis and an intro to excitation densities

Atoms in a mol or crystal are not spherical.
The experimental xray charge density minus the charge density of spherical atoms centred at the neutron positions with neutron parameters.
set of nuclear co-ord and detailed map of electron distribution.

Multipoles definition if pseudoatoms

pseudoatom is not so much an atom but something that takes the bonding density of molecules.

Definitions

Multipoles are a complete set of angular functions and the higher you go the more object sets you can represent.
Niels Hansens theory - Charge density refinement program MOLLY, precursor of XD program
Density functions looks like orbitals.
Modifications of pseudoatoms cannot be rigid because of electron-electron repulsion. Atoms that are positive then the same charge density will occur for the same charge density.

X-Ray charge density multipole model

Static Electron Density (ED) is the super position of aspherical pseudoatoms.
Formalism for high order data can show core expansion and contraction of coredeformations

Diff between cd-mulltipoles and atomic orbitals

Spherical Harmonic basis functions.
Normalization of spherical harmonic orbital funcion needs different normalization of density technique.

Electron density in terms of obitals

ONE-electron density - diagonal, atom-centered terms and cross terms, including 2 center terms.
Density functions are products of orbital functions : Y10.Y01 = Y21

Electron Density in terms of orbitals

Mathematical corelation between multipole populations and orbital populations if 2 center terms are neglected.

Total density

Results

Deformation density from multipole refinement : 1. dynamic and static function plots of Static total density.

CONCEPTS:

Bond paths
Bond critical paths
atomic basinsan
Laplacian : charge concentrations - if the peak is big second order derivative is big
An atomic charge is not an atomic charge

Analysis of the toplogy of charge density - quantum theory

Charge density and structural dynamics

Define excitation densities : a laser pump xray probe technique with the BioCARS hutch at APS Argonne.
Definition of Activation difference map: Charge density is hard to discern but the method to calculate the ES (excited state) geometry on GS (ground state) Structure and subtract grids.
Coinage metal compound Ag2Cu2L1

Ag Cu calculation of frontier molecular orbitals - luminous compounds

Piero Macchi

Multipolar Expansion

ED is expanded in multi polar centered atomic functions P is the unknown value rho is the fitting model
There are two kind of functions - radial part and angular part

Choice of radial function

GAussian or Slater functions are used fir ht angular behaviour of Rho to he finite in origin/.

Core orbitals

are a combination of slate functions and when you take a square of the function you get the
spherical valence calculation

Which wave function for core and valence

Roothan-Hartree-Fock calculation on ground state isolated atoms and more relevant ions. Each atonic orbital is expanded in a series of Slater functions

Relativistic atomic wave funtions

Zero order RElativisti approximation DFT calculation on isolated atoms
Scattering factor efrrors with respect to te dirac equation

Deformation valence density (DEFV)

a single slater function will be used for the seta exponet constructed from the single valence orbitals
Satisfy a poisson equation for radial equation the N has to be larger
Valence and core fraction are the largest near the core - to refine the core, then resolution is higher but not from the valence

D orbitals of transition metals - ex 3d orbitals of Fe

Full orbital expansion in the slater function

3d/4s orbital of transition metals

CLose in energy abd far in space

Angular functions and spherical harmonics

Orbitals vs. multipoles

linesr combination of sperical harmonics the xpansion goes maximum for product of two L + L' (l prime) = that mean an approdimation of linear combination of atoms centered - add the odd and even electronic density

Fitting the density of H2

fitting with monopolar functions - but will have spherical atoms with overlap density.
Expand diagonal dipoles but it will not answer
We need dipoles and quadripolar functions to fit the density of two Hydrogen atoms

d-orbitals and metal atoms

make and assumption that the d-orbital and othe atom does not overlap and it allows to get the refinement
Hexadecapole refinement - no overlap among carbon atoms
dipoles and octopoles are very small and only describe 3d product.
TRy refining 3s occupation

Multipolar expansions in the Periodic table - summary

H cannot be described a s monpole
alkaline and noble gases can be described by spherical functions
Hexa/Deca to octapole level or more for lower elements
Mirror Symmetry will force you to reduce the 3m symmetry implying a distorted hybridization models.

Jacob Overgaard

H-atoms

Hydrogen and xrays - in standard xray crystal structure determination, thermal mption is deconvoluted from electronic effects by application of hte Born-Oppenheimer approximation
atomic pdf can be isotropic or anisotropic - H does not have core electrons.

Hydrogen bonding (HB)

H atom is bonded to a more electronegative atom, the donor atom
the positive hydrogen is attracted to negative H partners a. normal and weak HB with double well bonding b. c.
Resonance is non-H structure - with neg. or pos. charge. ```
Use neutron data to obtain unbiased position and adps
obtain anisitropic Hatom adp by TLS analysus if the non Hskeleton and internal vibrational amplitude
Hirshfeld ```

How to combine X and N (neutron) data

Grow the crystal - the bigger, the better but this is really hard to do.

Scaling - UIJXN program

systematic

HB Characterization

module XDPROP can be used to calculate the laplacian distrributuobn - used to studey the nature of the chemical bonding in the hydrogen bond.
Density and laplacian along the O...H bond is interesting

Bond energies

empirically corelate the toological propertios of the HB bcp.

Christian Jelsch

ATOMS 30

ATOM 1 NT ala 1 0.427410 0.050010 0.613830 1.000 1 N ZX CA H2 OCT K1 V0 M0 Q0 UANI 0.012840 0.010190 0.009590 -.000240 0.005260 -.000530

five valence electrons

0. 0. 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.

then the list of atoms til the end

FILT 1.0 (should not be refined - it is fixed)

! scale SELE SCA REFI LS 4 (4 refinement cycles) WRIT RFAC ( write r factorial)

WRIT FOUR

For proteins use a distance restraint for small molecules use a constraint

CONDIS N1 H1 1 1.08 DISTANCE N1 H1 1 1.08 0.01 (<--standard deviation)

after changing values run the program again

GET protein structure file with hydrogen atoms, except water molecules

Mol

xyz 555 01

Tr =0  sign =

655 01   x+1
455 01  x-1 
467 01 x-1 y+1 z+2

xyz 655 02 sym#2 + a'

555 51 -x -y -z

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