Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 276

originally.as.distributed.version,.which.was.later.on.superceded.by.the.2.3.1.release..
Besides.the.standard.LCGTO-DFT.implementation.of.previous.deMon.versions,.the.
2.2.6. release. contained. the. irst. stable. implementation. of. auxiliary. density. func-
tional. theory. (ADFT). [34]. that. permits. calculations. of. large. systems. with. modest.
computational.resources..With.the.2.3.1.release,.a.parallel.ADFT.SCF.module.was.
realized.on.the.basis.of.MPI.[35]..This.version.is.now.used.in.several.research.labo-
ratories.all.around.the.world.and.has.served.as.a.development.platform.over.the.last.
3.years..Today,.ADFT.is.accepted.as.a.stable.and.eficient.alternative.to.conventional.
Kohn-Sham. DFT. calculations. due. to. the. increasing. number. of. deMon2k. ADFT.
calculations.
In.February.2009,.the.ninth.deMon.developers.workshop.was.held.in.Pune,.India..
At.this.workshop,.the.new.3.0.release.of.deMon2k.was.presented..It.is.a.systematic.
further. development. of. the. 2.3.1. version.. Major. improvements. are. the. implementa-
tion.of.an.iterative.solution.for.the.itting.equations.[36],.of.auxiliary.density.pertur-
bation. theory. (ADPT). [37],. of. a. hierarchical. transition. state. inder. [38],. and. of. an.
extended.Born-Oppenheimer.molecular.dynamics.(BOMD).module.[39,40]..Based.on.
the.demand.from.the.deMon2k.user.community,.we.have.also.extended.the.molecu-
lar.property.section.of.the.program..The.new.version.contains.internal.modules.for.
TD-DFT.calculations.from.the.group.of.M.E..Casida.[41],.nuclear.magnetic.resonance.
shielding.tensor.calculations.employing.gauge.invariant.atomic.orbital.basis.sets.and.
polarizability. as. well. as. hyperpolarizability. calculations.. The. electronic. structure.
analysis.module.has.also.been.extended,.including.atoms.in.molecules.[42].and.natural.
bond.orbital.[43].analysis.tools..A.standardized.interface.to.CHARMM.for.Quantum.
Mechanical/Molecular.Mechanical.(QM/MM).[44].calculations.is.available.

9.2.5 de m on 2 k
An. essential. feature. of. all. deMon. programs. is. the. use. of. auxiliary. functions. to.
enhance. computational. eficiency.. In. deMon2k,. primitive. Hermite. Gaussian. aux-
iliary.functions.are.employed..Because.the.recurrence.relations.for.the.calculation.
of. three-center. ERIs. are. formulated. over. Hermite. Gaussians,. the. use. of. Hermite.
Gaussian.auxiliary.functions.considerably.improves.the.eficiency.of.the.ERI.calcu-
lations.[17,45]..The.primitive.Hermite.Gaussian.auxiliary.functions.are.indicated.by.
a.bar..An.(unnormalized).Hermite.Gaussian.auxiliary.function.centered.at.the.atom.
K .with.exponent.ζ k .has.the.form

k

k k

Y

x

⎛ ⎞

z

⎛
⎜

⎞
⎟

⎛
⎜

⎞
⎟

∂ ∂ ∂

2

− ς ( r K − )

k ( ) r = e (9.20)

⎜ ⎟

k

∂ K ∂ K ∂ K

⎝ ⎠

x y z

. .

Here,. k ‾ x ,. k ‾ y ,. and. k ‾ z . denote. the. angular. indices. of. the. auxiliary. functions.. As. in.
earlier.deMon.versions,.the.Hermite.Gaussian.auxiliary.functions.are.grouped.into.
sets.with.common.exponents.in.deMon2k..The.default.auxiliary.function.set.A2.[46].
possesses. s .and. d .sets..An. s .set.contains.only.one.s-type.auxiliary.function.whereas.
a. d .set.contains.one.s-,.three.p-,.and.six.d-type.auxiliary.functions..More.recently,.
the.automatic.generation.of.auxiliary.function.sets.was.introduced.in.deMon2k..In.