Chemistry Reference
In-Depth Information
offers. a. reasonable. (mostly. based. on. empirical. corrections). treatment. of. electron.
correlation.at.computational.cost.similar.to.that.of.HF.calculations:
35,40,51-54
.for.this.
reason,.DFT.is.the.most.common.correlated.method.employed.for.investigation.of.
proteins.and.DNA.
35,40,51-54
Fermi.and.Thomas.developed.a.model.in.which.they.suggested.that.the.ground.
state.energy.of.a.system.may.be.connected.to.the.overall.electron.density.of.the.sys-
tem.itself.
71,72
.The.breakthrough.came.with.the.work.of.Hohenberg.and.Kohn.about.
40.years.later.
73
.They.showed.that.the.ground-state.energy.of.a.system.is.
uniquely
.
deined.by.its.overall.electron.density..In.other.words,.the.energy.is.a.unique.
func-
tional
.of.the.electron.density..Shortly.thereafter,.Kohn.and.Sham,.by.replacing.the.
kinetic.energy.of.the.interacting.electrons.with.that.of.a.noninteracting.system,.pro-
posed. the. inal. expression. of. the. ground-state. electronic. energy.
74
. For. a. rigorous.
description.of.DFT.methods.the.reader.is.directed.to.the.following.references.
75,76
One. of. the. most. delicate. points. of. the. DFT. theory. is. the. expression. of. the.
exchange-correlation. functional. in. terms. of. electron. density,. which. if. correctly.
determined.could.lead.to.the.exact.solution.of.the.many-body.problem..To.date,.no.
exact. analytical. form. of. the. exchange-correlation. functional. in. terms. of. the. elec-
tron.density.has.been.formulated..However,.even.very.simple.approximations.to.the.
exchange-correlation.functional.can.give.satisfactory.results..For.instance,.the.sim-
plest.local.density.approximation.(LDA),.which.replaces.the.exchange-correlation.
energy.density.of.the.real.system.with.that.of.an.homogeneous.electron.gas.of.the.
same.density,.is.known.to.yield.excellent.results.for.solids,
40
.but.performs.poorly.for.
molecules..Thus,.when.dealing.with.biological.systems,.more.sophisticated.approxi-
mations.are.required..For.instance,.within.the.gradient-corrected.approximation,.the.
exchange-correlation. functional. depends. on. the. electron. density. as. well. as. on. its.
gradient.. A. typical. example. is. the. exchange. functional. proposed. by. Becke,. used.
in. combination. with. Lee,. Parr,. and. Yang's. correlation. functional,. i.e.,. the. BLYP.
functional.
77,78
. Many. other. functionals. have. been. designed. that. perform. well. for. a.
wide. range. of. chemical. and. biochemical. systems. including. BP,
79,80
. PBE,
81,82
. and.
PW91.
83-85
. However,. a. further. improvement. to. the. accuracy. of. the. exchange. cor-
relation. functional. has. been. achieved. by. combining. the. exchange. functional. with.
HF. exact. exchange.. This. approach. led. to. the. development. of. the. so-called.
hybrid
.
functionals,.such.as.the.very.popular.B3LYP.
77,78
Biological. processes. take. place. in. a. complex. environment. consisting. of. thou-
sands.of.atoms,.and.the.straightforward.application.of.DFT.(or.of.other.QM.meth-
ods).to.DNA.oligonucleotides,.proteins,.and.enzymes.is.dificult.or.impossible..The.
most. commonly. used. approach. to. elude. the. size. limitation. is. the. combination. of.
DFT. (or. other. QM. methods). with. classical. force-ield-based. molecular. mechanics.
in. the. so-called. QM/MM. approaches.
35,36,49,50,86-88
. In. these. methods. the. system. is.
partitioned. in. two. or. more. regions. (or. layers). where. different. levels. of. theory. can.
be.applied..The.chemically.relevant.part.of.the.system.is.often.described.quantum.
mechanically,.whereas.the.remainder.of.the.system.is.treated.with.a.more.eficient.
molecular.mechanics.method..The.choice.of.QM.region.is.not.trivial.as.solvent.mol-
ecules,.counter.ions.and.part.of.protein/DNA.may.be.directly.involved.in.the.process.
of. interest.. In. addition,. a. proper. treatment. of. the. long-range. electrostatic. interac-
tions. between. the. QM. and. MM. atoms. is. crucial. to. obtain. reliable. results.
35,40,50-52
.
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