Citation
Metzger, Robert Melville (1969) Crystal Coulomb energies: I. Organic donoracceptor complexesa review. II. Classical Ewald calculations of the Coulomb binding energy of four donoracceptor crystals and Wurster's blue perchlorate. III. A rapidconvergence quantummechanical formalism for crystal electronic energies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VD9BK107. https://resolver.caltech.edu/CaltechTHESIS:03172014093730629
Abstract
Chapter I
Theories for organic donoracceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 4650 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε_{1} (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_{o} of ionizing each DA pair, ε_{1} + ε_{o} less than 0, then the lattice is holoionic. The chargetransfer (CT) band in crystals and in solution can be explained, following Mulliken, by a secondorder mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the noninteracting components D and A (or D^{+} and A^{}). The magnetic properties of the DA crystals are discussed.
Chapter II
A computer program, EWALD, was written to calculate by the Ewald fastconvergence method the crystal Coulomb binding energy E_{C} due to classical monopolemonopole interactions for crystals of any symmetry. The precision of E_{C} values obtained is high: the uncertainties, estimated by the effect on E_{C} of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_{C} due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.
E_{C} for Wurster's Blue Perchl orate is 4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_{C} for NMethylphenazinium Tetracyanoquino dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.
EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)(N,N,N',N'Tetramethylpara phenylenediamine: 7,7,8,8Tetracyanoquinodimethan) E_{C} = 4.0 eV while 2ε_{o} = 4.6_{5} eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)(N,N,N',N'Tetramethylpara phenylenediamine:paraChloranil) E_{C} = 4.4 eV, while 2ε_{o} = 5.0 eV: again EC falls short of 2ε_{1}. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)(Hexamethyl benzene:paraChloranil) E_{C} = 4.5 eV, 2ε_{o} = 6.6 eV; for (1:1) (Napthalene:Tetracyanoethylene) E_{C} = 4.3 eV, 2ε_{o} = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.
Chapter III
A rapidconvergence quantummechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecularion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter actions. Previously obtained LCAOMO wavefunctions for the isolated molecule(s) ("unit cell spinorbitals") provide the startingpoint. Bloch's theorem is used to construct "crystal spinorbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^{XT}, direct Coulomb [λλ/λ'λ']^{XT} and exchange Coulomb [λλ'/λ'λ]^{XT} integrals are obtained, and directspace bruteforce expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^{XT}, [λλ/λ'λ']^{XT}, and [λλ/λ'λ]^{XT} with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's twocenter Fourier transform integrals. If the shortrange interactions are calculated by bruteforce integrations in direct space, and the longrange effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^{XT}, [λλ/λ'λ']^{XT} and [λλ'/λ'λ]^{XT}. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^{XT}, etc., where some of the portions contain the Gaussian factor.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Chemistry 
Degree Grantor:  California Institute of Technology 
Division:  Chemistry and Chemical Engineering 
Major Option:  Chemistry 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  24 October 1968 
Record Number:  CaltechTHESIS:03172014093730629 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:03172014093730629 
DOI:  10.7907/VD9BK107 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  8138 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  17 Mar 2014 20:31 
Last Modified:  09 Nov 2022 19:20 
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