Maxwell: multipole expansion for condensed phases

Last updated: 11/15/04

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J. C. MaxwellP.P. EwaldE.S. Campbell

The Maxwell package implements the Maxwellian formalism for calculating the interaction energy between charge distributions as represented by the multipole expansion. For crystals, the program implements E. Campbell's formulation of Ewald summation for multipoles of arbitrary order. Other algorithms used in the programs were developed by M. Mezei and E. Campbell.

The Maxwellian formalism extracts scalar multipoles pN and unit vectors (called characteristic directions) sN from the Cartesian moments M(L,M,N,O) from the respective charge distributions and calculates the multipole expansion around a center O of the electrostatic energy of two charge distributions as directional derivatives:

E(1,2,Nmax)=SUM(N=0 to Nmax)SUM(N1+N2=N)
(P1N1*p2N2/N1!N2!) PROD(i=1 to N1)(SiN1.DEL) PROD(i=1 to N2)(SiN2 DEL)
1/(|r2-r1|) at rk=Ok;

The suite of programs in Maxwell includes calculation of the Cartesian multipoles {M(L,M,N,O)} from a single-determinant wave function, optionally partitioning the electron density; calculation of the so-called poles and characteristic directions ({pN}, {sN}) used in the Maxwellian formalism; calculation of interaction energy among a finite set of charge distributions; calculation of interaction energy of an inifinite lattice of multipoles.

See the full documentation for more detail and for references. Some of the papers can be dowloaded from the table below.

The role of the individual programs of the package is summarized below:

Program Input Output MS Copy
MOMENTS Wave function {M(L,M,N,O)} Density partitioning, integrals,
contracting and transforming moments
CHARDIR {M(L,M,N,O)} {pN}, {sN} PDF
MULTIPOL {pN}, {sN}, {xi|i=1,n} E(1,2,...,n,Nmax) Permanent multipole:
Induced multipole:
CRYSCON {xi|i=1,n}, {pN}, {sN} "Crystal constants" Theoretical foundations
Detailed formalism
CRYSTEN "Crystal constants", molecular orientations E(crystal,Nmax)
CRYSPOT {xi|i=1,n}, molecular orientations E(crystal,non-electrostatic)  

List of other programs

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