DMol

B       Glossary

Table 2. Symbols used in equations

symbol	definition (page)
ij	Lagrangian multipliers
xc []	exchange-correlation energy per particle in a uniform electron gas
	shift parameter
l	Lagrange multipliers
µxc	exchange-correlation potential
	orbital density, number of particles
a	partition function, atomic charge density, molecular charge density
(r)	molecular charge density
d	deformation density
i	occupied molecular orbitals
µ	atomic basis function, atomic orbital
	wavefunction
a	perturbation
b	eigenvalues
C	constraint
Ciµ	molecular orbital expansion coefficients, LCAO-MO coefficients
Cx	correlation contribution
d	damping factor, mixing coefficient
e	error vector
EHF or Eta	Hellmann-Feynman energy term
Et	total energy
Exc[]	exchange and correlation energy
g	partition function for numerical integration
g	gradient vector
H	Hessian matrix
l	number of shells
m	atomic mass, number of constraints
M	number of multipolar functions
N	number of atomic orbitals, number of atoms
N	number of angular integration points
No	number of occupied atomic orbitals
NR	number of radial integration points
P	number of integration points
r	numerical integration point
R	set of coordinates
T[]	kinetic energy of system of noninteracting particles of density
u	eigenvectors
U[]	electrostatic energy due to Coulombic interactions
V	attractive and repulsive electrostatic forces, Coulombic potential
w(r)	integration weights for mesh points
x	geometry

Table 3. Definitions of terms

term	page
alpha electrons	spin-up electrons
AO	atomic orbital
beta electrons	spin-down electrons
BFGS	Broydon-Fletcher-Goldfarb-Shanno minimizer
Bohr	0.532 Å
DN	double-numerical basis set
DND	like DNP, but without p functions for hydrogen
DFT	density-functional theory
DNP	double-numerical plus polarization basis set
EF	eigenvector-following
HOMO	highest occupied molecular orbital
LDF	local density functional method
LUMO	lowest unoccupied molecular orbital
MO	molecular orbital
SCF	self-consistent field method
SO	symmetry orbital
spin density	the amount of excess alpha over beta spin
spin-restricted	use same i for alpha and beta electrons
spin-unrestricted	use different i for alpha and beta electrons
UHF	spin-unrestricted Hartree-Fock calculation