Charge, atomic Hirshfeld

The Mulliken and Hirshfeld atomic charges shown in the curves below are quite resembling, both indicating polarization of the nickel cluster and electron transfer to the hydrogen molecule. This latter result is opposite to that yielded by our SCF calculations (Fig. 8, lower left), which may be attributed to the fact that SCF neglects electron correlation while DFT tends to overestimate it, the charge distribution being very sensitive to the amount of electron correlation introduced [25]. 

Fig. 9. Calculated total energies (upper row), molecular bond lengths (middle row), and Mulliken and Hirshfeld atomic charges (lower two rows) for the EE-type (left column) and N-type (right column) approaches of the H2 molecule to the Ni4 cluster, using a DFTprocedure.

The Hirshfeld functions give an excellent fit to the density, as illustrated for tetrafluoroterephthalonitrile in chapter 5 (see Fig. 5.12). But, because they are less localized than the spherical harmonic functions, net atomic charges are less well defined. A comparison of the two formalisms has been made in the refinement of pyridinium dicyanomethylide (Baert et al. 1982). While both models fit the data equally well, the Hirshfeld model leads to a much larger value of the molecular dipole moment obtained by summation over the atomic functions using the equations described in chapter 7. The multipole results appear in better agreement with other experimental and theoretical values, which suggests that the latter are preferable when electrostatic properties are to be evaluated directly from the least-squares results. When the evaluation is based on the density predicted by the model, both formalisms should perform well. 

Hirshfeld s stockholder partitioning applied to a theoretical density of hydrogen cyanide, HCN, gives the following values for the atomic charges, dipole moments, and second moments /i ... 

E. R. Davidson and S. Chakravorty, Theor. Chim. Acta, 83, 319 (1992). A Test of the Hirshfeld Definition of Atomic Charges and Moments. 

Another defmition of atomic charges, which is implemented in the Biosym package we have used in our DFT calculations, is that resulting from Hirshfeld s partitioning... 

In addition to Mulliken charge analysis, ADF calculates several atomic charges that do not share the flaws of Mulliken (strong basis set dependence). These charge analysis methods ( Voronoy deformation density and Hirshfeld provide atomic charges that agree well with chemical intuition. 

Another method to find atomic charges is the Hirshfeld method. Here, atomic charges are obtained by distributing the molecular electronic probability density at each point in space among the atoms in the molecule according to the formula... 

An assessment of several atomic charge methods applied to gas-phase polypeptide conformers found that the Hirshfeld-I method performed best overall in reproducing MP2-calculated electric dipole moments and in being transferable from one conformer of a molecule to another [T. Verstraelen et al., J. Chem. Theory Comput., 8,661 (2012)]. Also, Hirshfeld-I charges reproduce the molecular electrostatic potential with good accuracy. 

New theoretical and experimental work on the uncertainty principle (Section 5.1). The CM5 and Hirshfeld-I methods for atomic charges (Section 15.7). 

De Profit F, Alsenoy CV, Peelers A, Langenaeker W, Geerlings P. Atomic charges, dipole moments, and Fukui functions using Hirshfeld partitioning of the electron density. J Corn-put Chem. 2002 23 1198-209. 

Davidson, E.R. Chakravorty, S. A test of the hirshfeld definition of atomic charges and moments. Theor. Chim. Acta 1992,83, 319. 

Several other definitions of atomic charges have been published in the chemical literature. Among those, two methods have gained some popularity. Hirshfeld partitioning is based upon the stockholder principle . According to that principle, p(r) at each point is partitioned into atomic contributions, called densities of bonded. atoms , that are given by... 

The Hirshfeld procedure produces atomic charges that possess rather small magnitudes. At the HF/6-31 IG level of theory, the values of Qa are 0.14 for C in CO and 0.63 fw Li in LiF. The near-Hartree-Fock-limit charges of the Li atoms in LiH and LiF equal 0.414 and 0.624, respectively, being much smaller than their AIM counterparts of 0.911 and 0.937. The Hirshfeld chaiges of atoms in Li2BeF4 derived from the experimentally determined p(r) amount to only 0.11, 0.16, and —0.09 for Li, Be, and F. These examples reveal substantial underestimation of bond ionicities in strongly ionic compounds. 

The sum i runs over all nnmerical integration points in the molecule and the sum over j over all atoms. We designate this type of atomic charge as q and will refer to this as the Hirshfeld charge thronghont the paper. 

Tab. 1.3 Comparison between different sets of atomic point charges for a zwitterionic Gly-Ala dipeptide in aqueous solution. D-RESP electrostatic potential derived charges [12] fitted to all 36 configurations. Hirshfeld average value of the Hirshfeld charges [89c] along the full trajectory, Amber AMBER 1995 force field [86], Gromos GROMOS96 force field [85], The charges of equivalent atoms are imposed to be equal.

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