1.

1Comput
ati
onal
Chemi
str
y

Thewor
dcomput
ati
onalchemi
str
yisdescr
ibedast
hemat
hemat
icaldescr
ipt
ionoft
he
chemi
str
y.Thi
swor
dcanal
sobeappl
i
edaf
terdev
elopi
ngt
hemat
hemat
icalmet
hods,
t
hei
rimpl
i
cat
ionandex
ecut
ionbyusi
ngcomput
ers.Thequal
i
tat
iveandquant
it
ati
ve
aspect
sofchemi
str
ycanbecomput
edal
thoughv
erysmal
lnumber
soff
act
sexact
ly
expl
ainbutev
eryaspect
sofchemi
str
ycanbedesi
gnat
ed.Thecomput
ati
onalchemi
str
y
i
sassi
mpl
east
heguessofdr
ivi
ngt
imebet
weent
woci
ti
esandascompl
exast
he
guessofweat
hercondi
ti
on(
Young,
2002)
.

Comput
ati
onalchemi
str
yist
hebr
anchofsci
encei
nwhi
chweut
il
izedt
het
heor
eti
cal
pr
inci
plesofchemi
str
ybyt
heuseofcomput
ert
ocomput
e,cal
cul
ate,
repl
i
cat
eordet
ect
t
hephy
sicalandchemi
calpar
amet
ersbyr
unni
ngt
hesecal
cul
ati
onswi
tht
hehel
pof
someef
fi
cientcomput
erpr
ogr
amsi
ncompar
isont
oexper
iment
alcal
cul
ati
ons.I
tist
he
pr
act
icalappl
i
cat
ionofcomput
erski
l
lsi
ncombi
nat
ionwi
tht
heor
eti
calchemi
str
yand
mat
hemat
icst
o comput
ethechemi
calbehav
ior
.Impor
tantwor
kofcomput
ati
onal
chemi
str
yist
oanal
yzet
her
esul
tsofchemi
calcongr
uit
ybyt
heuseoft
heor
eti
cal
met
hodsandadv
ancedcomput
ati
onalpr
ogr
ams.I
not
herwor
dswecandef
inet
hat
comput
ati
onal
chemi
str
yist
hecomput
ati
onofcompoundsbycomput
er(
Jensen,
2007)
.

Comput
ati
onalchemi
str
yisan adv
anceaswel
lasan ol
dtechni
que.Theuseof
comput
ati
onalchemi
str
ywasst
art
edi
nthemi
dof20t
hcent
ury
.Itwasconsi
der
edas
mor
epr
omi
nentandol
dtechni
queduet
oit
susesi
npastf
ewdecadeswi
thaddi
ti
onof
adv
ancecomput
erpr
ogr
ams.I
twasconsi
der
edadv
ancet
echni
queasi
taddednew
comput
ati
onalt
ool
sdaybyday
.Theseday
scomput
ati
onalchemi
str
yhasbecomev
ery
essent
ial
par
tofchemi
cal
,phy
sical
andmedi
cal
resear
ch(
Cramer
,2010)
.

Theor
eti
calchemi
str
yisusedi
ndescr
ibi
ngt
hechar
act
eri
sti
csofdi
ff
erentt
hingsl
i
ke
phot
osensi
ti
zer
s,cer
ami
cs,
super
conduct
ors,
semi
conduct
ors,
plast
icset
c.wi
tht
heai
d
ofcomput
ati
onalsof
twar
e.I
tiscostef
fect
ive,t
imesav
ingandbel
ongst
ocat
egor
yof
gr
eenchemi
str
yduet
onopr
oduct
ionofhar
mfulsubst
ancest
hant
heexper
iment
al
chemi
str
y.I
t does not mean t
hat comput
ati
onalchemi
str
y has r
epl
aced t
he
exper
iment
alchemi
str
ybuti
sver
yusef
ulf
orcompar
ati
vest
udy
.Wi
thoutexper
iment
al
chemi
str
ynonew mat
eri
alcanbesy
nthesi
zedandr
esear
chi
sincompl
ete.Howev
er,
sci
ent
ist
s use comput
ati
ons f
orsome ext
ra knowl
edge aboutt
he f
easi
bil
i
tyofa
r
eact
ionbef
oregoi
ngt
owor
konsomeexper
iment
alpr
oject(
G.Lewar
s,2016)
.

Comput
ati
onalchemi
str
yisusedi
nnumer
ousway
s.Oneuseoft
hecomput
ati
onal
chemi
str
yismodel
i
ngamol
ecul
arsy
stem r
athert
hansy
nthesi
zi
ngi
nthel
abor
ator
ies.
Ev
en t
hough t
hese modelcompounds may notbe per
fect
,buti
tpr
ovi
des 90%
i
nfor
mat
ionabouti
tssui
tabi
l
ity
.Thi
sisgoodi
nfor
mat
ionbecauset
hesy
nthesi
zi
ng
pr
ocessi
scost
lyandt
imet
aki
ng.Comput
ati
onalchemi
str
ycanbeusedeasi
l
yin
f
indi
ngsomepr
oper
ti
esoft
hecompoundsascompar
etot
heexper
iment
almet
hods
andal
sof
indsomepr
oper
ti
esoft
hecompoundst
hatcan’
tbef
oundexper
iment
all
yli
ke
mol
ecul
arbondi
ngoft
hecompounds.Comput
ati
onalchemi
str
yisbei
ngusedbysome
exper
iment
alchemi
stsf
orgai
ningaddi
ti
onali
nfor
mat
ionoft
hecompoundsbef
ore
r
unni
ngi
nthel
abor
ator
ies(
Young,
2002)
.

Adv
ancementand mat
ure comput
ati
onalpr
ogr
ams ar
e hel
ping t
o comput
ethe
compl
i
cat
edcal
cul
ati
onsexact
lywi
tht
hehel
pofsomebasi
cset
sincomput
ati
on.But
t
he accur
acy ofr
esul
ts depends upon a l
otoff
act
ors.The r
easons ar
ethat
comput
ati
onalpr
ogr
amsar
eusedonl
ytogener
atet
her
esul
tsaf
tercomput
ingaser
ies
ofcal
cul
ati
onsbutt
hesecal
cul
ati
onsdonotpr
ovi
deanyi
nfor
mat
ionaboutt
hev
ali
dit
y
ofanycomput
ati
onalmet
hodwhi
chwasuseddur
ingcal
cul
ati
ons.Thesel
ect
ionofan
accur
atemet
hodi
nobt
aini
ngmor
eaccur
ater
esul
tsar
ecompar
edt
oexper
iment
al
r
esul
tswhi
chi
shi
ghl
yamat
terofexper
ience.Wecannev
erdenyt
hef
actt
hatsol
uti
ons
cr
eat
edbycomput
ersar
emor
eaccur
atet
hanbypeopl
e(Jensen,
1989)
.

Comput
ati
onalchemi
str
yhasmanyadv
ant
agesov
erexper
iment
alwor
kbecauset
hei
r
cal
cul
ati
onsar
eper
for
medv
eryeasi
l
y,i
tscosti
sfr
iendl
yandsaf
ely
.Comput
ati
onal
measur
ement
scanbeut
il
izedev
enf
orasy
stem whi
chcanhav
edesi
redchar
act
eri
sti
cs
bef
oret
hei
rexi
stence.Comput
ati
onalpr
obl
emsf
acedbychemi
stsi
sthesel
ect
ionof
comput
ati
onalmet
hod ofanysy
stem whi
ch i
s underconsi
der
ati
on and t
hen f
or
checki
ngi
tsr
eli
abi
l
ityi
nthesy
stem.Comput
ati
onalmet
hodshav
eal
argev
ari
etyof
dat
a so t
hese ar
e compar
ed wi
th exper
iment
alr
esul
tst
o check t
he v
ali
dit
y.
Comput
ati
onalchemi
str
y has no need f
or deep knowl
edge of quant
um and
exper
iment
aldat
ather
efor
eiti
sadv
ant
ageous( boutetal
Jal .
,2004)
.

The maj
or pr
obl
ems whi
ch f
ace t
he comput
ati
onalchemi
sts ar
e sel
ect
ion of
appr
opr
iat
etechni
quesf
orcomput
ati
onalanal
ysi
sandi
nter
pret
ati
ont
hei
rresul
ts.Onl
y
t
he comput
ati
onal dat
a i
s not enough t
o at
tai
n t
he concl
usi
ons about t
he
char
act
eri
sti
cs oft
he compounds butal
way
srequi
red exper
iment
aldat
afori
ts
compar
isont
oel
uci
dat
ethest
rengt
hofcomput
ati
onalmet
hodol
ogy
.Thebasi
cbenef
it
oft
hecomput
ati
onalchemi
str
yist
hatat
heor
eti
calchemi
staswel
lasanexper
iment
al
chemi
stcangett
headv
ant
agei
ftheyhav
eabasi
cknowl
edgeofchemi
str
ybecause
comput
ati
onal
chemi
str
ydoesn’
tnecessi
tat
edeepconsi
der
ati
ons(
Cramer
,2010)
.

Thecomput
ati
onalchemi
str
yoft
henewer
ahaspr
ovi
dedsur
pri
singr
esul
tsconcer
ning
pr
eci
si
onaboutmol
ecul
arst
ruct
ureandi
tsconf
igur
ati
ons.Comput
ati
onalchemi
str
yis
knownaspower
fult
echni
quebasedonasetofquant
um mechani
calandnon-
quant
um
mechani
cal
fori
nvest
igat
ingchemi
cal
probl
emsunderconsi
der
ati
onbyusi
ngcomput
er.
Themostwi
del
yexami
nedpar
amet
ersi
ncl
udemol
ecul
aropt
imi
zat
ionwi
thi
nfor
mat
ion
ofal
lgeomet
ri
cpar
amet
ers,
Inf
rar
edspect
rum,
NMRandUV-
visi
blespect
ra,
ener
giesof
t
hemol
ecul
es,
ther
mody
nami
cpar
amet
ers,
chemi
calr
eact
ivi
ty,
nat
uralbondi
ngor
bit
als
andt
ransi
ti
onst
ateoft
hecompounds( aetal
Padmaj .
,2008)
.

1.
2Comput
ati
onal
Cal
cul
ati
ons

1.
2.1Pot
ent
ial
ener
gysur
face

Comput
ati
onalmeasur
ement
s hel
pinf
indi
ng t
he st
abl
e st
ruct
ure ofmol
ecul
e by
opt
imi
zi
ngt
hest
ruct
ure.Opt
imi
zedst
ruct
uremeanst
hatst
ruct
urewhi
chhasl
owest
ener
gypoi
ntsoni
tspot
ent
ialener
gysur
facecal
l
edasgl
obalmi
nima.I
ncomput
ati
on
weconsi
der
edal
lpossi
blest
ruct
uresi
nst
eadofonest
ruct
ureandt
heor
eti
calr
esul
ts
ar
eobt
ainedf
rom i
t.Pot
ent
ialener
gysur
facei
schar
act
eri
zedf
orachemi
calf
ormul
a.I
t
i
sdef
inedasi
tisgr
oupofat
omswhi
char
etakenf
rom al
lpossi
blear
rangementof
at
oms.Buti
tisv
erydi
ff
icul
ttov
isual
i
ze compl
ete pot
ent
ialener
gysur
face f
or
pol
yat
omi
cmol
ecul
eswhi
chhav
ever
ylar
genumberofat
omsanddi
mensi
ons.But
pr
act
ical
l
yweconsi
der
edi
taspot
ent
ialener
gyasener
gycur
vewi
thr
espectt
oonl
ya
si
ngl
ecoor
dinat
eormaxi
mum t
wocoor
dinat
eandexpl
ainedt
hem wi
thr
espectt
oeach
ot
her(
Cramer
,2010)
.

Fi
gur
e1.
1:Pot
ent
ial
ener
gySur
faceDi
agr
am (
PEDDi
agr
am)

PEDSur
faces

Somei
mpor
tantf
eat
uresar
econsi
der
edaspot
ent
ial
ener
gysur
faces

Local
mini
ma

I
tist
hepoi
ntonpot
ent
ialener
gysur
faceshav
ingl
owestener
gyv
aluei
naspeci
fi
c
r
egi
onofpot
ent
ial
ener
gysur
facescal
l
edasl
ocal
mini
ma.

Gl
obal
mini
ma

Thatpoi
nti
spr
esentatl
owestener
gyv
aluei
nthewhol
epot
ent
ialener
gysur
facesi
s
cal
l
edasgl
obal
mini
ma.

Saddl
epoi
nt

Thatpoi
ntwhi
chhasmi
nimum v
alueonl
yinonedi
rect
ionofpot
ent
ialener
gysur
faces
cal
l
edassaddl
epoi
nt.

1.
2.2Si
ngl
ePoi
ntEner
gy(
SPT)

Wecancal
cul
atet
heSPTbyconsi
der
ingt
hecomput
ati
onalcal
cul
ati
ons.Si
ngl
epoi
nt
ener
gyi
sfi
xedpoi
ntener
gyonpot
ent
ialener
gysur
face.Mor
eappr
opr
iat
est
ruct
urei
s
ut
il
ized f
or f
urt
her cal
cul
ati
ons.St
ati
onar
y poi
nt i
s sear
ched dur
ing geomet
ri
c
opt
imi
zat
ionwhi
chi
spr
esentonSPTwher
enetf
orcesar
enegl
i
gibl
e.Att
hispoi
ntt
he
ener
gyf
oral
lthecoor
dinat
esbecomezer
oandcal
l
edassi
ngl
epoi
ntener
gy.The
pr
obl
emsf
orat
tai
ningsi
ngl
epoi
ntcal
cul
ati
onar
e;

 Tof
indt
hebasesf
oramol
ecul
etocomput
etheaccur
ateener
gy.

 To f
ind t
hechar
act
eri
sti
csofopt
imi
zed mol
ecul
arst
ruct
ure(
For
esmanand
Fr
isch,
2015)
.

1.
2.3Tr
ansi
ti
onSt
ate

I
tisdef
inedashi
ghener
gyst
atebutshor
tli
vest
ateofar
eact
ion.I
tisusedf
orpr
oduct
anal
ysi
s.Pot
ent
ialener
gysur
facehassaddl
epoi
ntwhi
chi
sact
ual
l
yast
ati
onar
ypoi
nt
wher
eener
gyi
smaxi
mum i
noneormor
ethanonedi
rect
ions.Saddl
epoi
nti
susedf
or
det
ermi
ning t
he t
ransi
ti
on st
ate.Butf
ornor
malr
eact
ions t
ransi
ti
on st
ruct
urei
s
det
ermi
nedexper
iment
all
ywhi
l
egeomet
ryoft
ransi
ti
ont
heor
eti
cal
l
y.Theset
heor
eti
cal
cal
cul
ati
onsar
eut
il
ized t
o descr
ibet
heener
gyand geomet
ri
cpar
amet
ers.These
t
ransi
ti
onst
ruct
uresar
ehi
ghl
ysensi
ti
vef
orcomput
ati
onal
wor
k.Fort
hispur
posehi
ghl
y
sensi
ti
ve comput
ati
onalmet
hodsar
e used f
orget
ti
ng mor
e accur
ate and r
eli
abl
e
r
esul
ts.

1.
2.4At
omi
cChar
ges

I
nter
act
ionsamongmol
ecul
esar
epol
arornon-
pol
ar.Theseel
ect
rost
ati
cint
eract
ions
amongmol
ecul
esar
eduet
oel
ect
ri
cchar
ges.Thr
oughcomput
ati
onalanal
ysi
swecan
cal
cul
atet
wot
ypesofMul
l
ikanchar
gesaswel
lasAPT(
Atomi
cPol
arTensor
)char
ges.
Thesechar
gesar
eusedt
odet
ermi
net
hephy
sio-
chemi
cal
proper
ti
esofcompoundsand
t
hei
rchemi
cal
react
ivi
ty( manetal
Sal .,
2018)
.
1.
2.5Di
pol
eMoment

I
tist
hemeasur
eofchar
gedi
str
ibut
ionanddi
stanceofchar
ges.I
tisal
sodef
inedas
pr
oduct
sofchar
gesonat
omspr
esenti
npol
arcov
alentbondanddi
stancepr
esent
bet
weent
hesechar
ges.I
tisav
ect
orquant
it
yandi
ncomput
ati
onalwor
kitdescr
ibes
t
hedi
rect
ionofchar
ges.

1.
2.6Mol
ecul
arDy
nami
c

Mol
ecul
ardy
nami
ccal
cul
ati
onsar
ever
ydi
ff
erentf
rom geomet
ri
copt
imi
zat
ion.Thr
ough
t
hesecal
cul
ati
onswecancal
cul
atet
het
her
mody
nami
cpr
oper
ti
es.

1.
3Comput
ati
onal
Met
hods

Weut
il
izedal
argenumberofmet
hodsf
oranal
ysi
s.Al
lthecomput
ati
onalmet
hodsar
e
expl
ainedasf
oll
ows;

1.
3.1Mol
ecul
arMechani
cs

Thi
smet
hodi
sdependentonconv
ent
ionalmechani
cs.I
nMM t
heener
gyi
scal
cul
ated
bysupposi
ngt
hat
,itdependsuponnucl
earcoor
dinat
epar
amet
ert
hat
’swhyi
tiscal
l
ed
f
orcef
iel
dmet
hod.At
omsasawhol
ear
econsi
der
edasbui
l
dinguni
tsl
i
kebal
l
sand
spr
ings.Thesebondsshowspeci
fi
cat
ionsaccor
dingt
othebondst
hatar
ehel
dtoget
her
.

I
n Mol
ecul
arMechani
cs,t
ype ofat
oms and f
orce f
iel
ds ar
ever
yimpor
tantand
pr
omi
nentconsi
der
ati
onswhi
char
eusedt
odet
ectt
heener
giesoft
hecompoundsi
n
speci
fi
edgeomet
ri
calst
ruct
ures.I
nMM met
hods,bal
l
sar
econsi
der
edasat
omswhi
l
e
spr
ingsasbonds.Thesebal
l
smayv
aryi
nsi
zewhi
l
espr
ingsmayv
aryi
nbondl
engt
h.
Mol
ecul
arMechani
csmet
hoddependuponani
deaaboutst
ruct
uralent
it
iest
hatar
e
r
elat
edt
odi
ver
semol
ecul
es,f
ori
nst
ancebonddi
stancebet
weent
heC―H l
i
nki
s
i
nvar
iantandt
ransf
erabl
e.St
ruct
uraluni
tshowsi
dent
icalbehav
iori
ndi
ver
sest
ruct
ures
butt
hecompl
etest
ruct
uralbehav
iorwasanal
yzedt
hroughsupposi
ngi
tast
hecompl
ex
uni
ts.Thephy
sicaluni
tsar
esupposedi
npar
ti
cl
ecat
egor
iesbutdependonl
yont
he
compl
exf
ragment
sofnei
ghbor
hood(
Jensen,
1989)
.InMM met
hodol
ogyt
hebasi
cidea
aboutener
gyev
aluat
ioni
stheconsi
der
ati
onofener
giesofmol
ecul
est
hatdependupon
i
tsbehav
iornearst
ret
chi
ng,bendi
ngandt
orsi
onwi
thgat
her
ingef
fect
sandst
ruct
ural
par
amet
ersar
eusedf
ort
hepar
a-mat
izat
ionofener
gy.Thi
sisgi
venbel
owi
nequat
ion,

E=∑ES +∑EB +∑ET +∑Enon-b (

eES=Ener
Wher gyofst
ret
chi EB=Ener
ng, gyofbendi ET=Ener
ng, gyoft
or onandEnon-b=
si
Ener
gyofnon-
bondi
ngor
bit
als. Her
eEnon-bondi
sthei
nter
act
ionamongt
hei
ndi
rect
ly
connect
edat
oms.Theset
ermsar
egi
venbel
ow,

ES=Ks(
Ι-Ι
eq) (
1.2)

EB =KB(
Ө-Өeq) (
1.3)

Wher
eӨ=bondangl
e,І
=bondl
engt
h,І
eqandӨeqar
eequi
l
ibr
ium v
alues(
Lewar
s,2003)
.

Ther
oleofmanysci
ent
ist
sisv
eryi
mpor
tanti
nadv
ancementoft
heMM met
hods.
TodaymanyMM met
hodsar
eint
roducedasMM+andAMBERet
c.,whi
char
edi
ff
erent
f
rom oneanot
herf
orex
plai
ningt
ypesofat
omsi
npar
amet
eri
zat
ion.Al
lthesemet
hods
ar
eusedi
nfi
ndi
ngt
hegeomet
ri
cpr
oper
ti
esandener
giesoft
hei
nter
estcompounds
(
KennyB.Li
pkowi
tzandBoy
d,2001)
.

MM met
hodshav
evar
iat
ionsas;

1.MM met
hod gi
ves pr
e-opt
imi
zed geomet
ryt
o anal
yze compounds wi
th ot
her
comput
ati
onal
met
hodsl
i
keDFT.

2.Byusi
ngMM met
hodwecancal
cul
atet
heener
giesandgeomet
ri
cpar
amet
ers.

3.Forconsi
der
abl
e accur
acy we can comput
ethe ener
gies and geomet
ri
es f
or
macr
omol
ecul
esaswel
lasbi
omol
ecul
es.

4.I
tiscal
l
edasHar
tree-
productwher
eeachel
ect
ronf
unct
ioni
scal
cul
atedt
hrought
his
met
hod.Thesemaybet
ime-
independentcal
cul
ati
ons.Hami
l
toni
anoper
atori
sused
wi
thnor
mal
i
zat
ionoft
hewav
efunct
iont
ocomput
etheener
gyf
orgl
obalmi
nima(
G.
Lewar
s,2010)
.

1.
3.2AbI
nit
ioAppr
oach
Ab-
Ini
ti
omeans“
tof
rom t
hef
ir
st”
.Abi
nit
iomet
hoddependsupont
hepar
amet
eri
zat
ion
t
hrough compl
etei
nfor
mat
ion.I
tis a comput
ati
onalmet
hod t
hatdepends upon
quant
um mechani
csandf
indsconcl
usi
onswi
thoutcompar
ingexper
iment
alv
alues.Ab-
I
nit
iomet
hodi
susedf
ort
hecal
cul
ati
onofcompoundpr
oper
ti
eswi
tht
hesol
uti
onof
equat
ions and r
elev
antat
omi
c number
s.Ab i
nit
io met
hod i
s concer
ned wi
tht
he
cal
cul
ati
onsbasedont
hebot
hti
medependentandt
imei
ndependent
.

Ab-
Ini
ti
omet
hodhasbeenusedf
ormeasur
ingt
hedi
ff
erentpar
amet
ersl
i
kespeedof
l
i
ghtat
omi
cchar
gesandPl
anksconst
antv
alues.Thi
smet
hodi
sal
sousedf
ort
he
measur
ementofwav
efunct
ionsand pot
ent
iall
evelcan’
tbemeasur
ed (
KennyB.
Li
pkowi
tzandBoy
d,2001)
.

1.
3.2.
1Impl
ement
ati
onofAbI
nit
ioMet
hods

AbI
nit
iomet
hodshav
eext
ensi
vev
ari
etyofi
mpl
ement
ati
onandot
hernamedas“
vir
tual
mat
terl
abor
ator
y”.Thesecal
cul
ati
onsar
edonewi
thl
i
ttl
eappr
oxi
mat
ionandbyt
heuse
ofbasi
cset
sbutwi
thoutanypar
amet
eri
zat
ion.Feat
uresl
i
keener
get
ics,st
ruct
ural
anal
ysi
sandpol
ari
zabi
l
ityar
ecomput
edt
hrought
hismet
hod.

Li
mit
ati
on

Al
thought
hismet
hodhaswi
der
angeofappl
i
cat
ionandadv
ant
agesi
thassome
l
i
mit
ati
ons.

 I
nthi
smet
hod,
Har
dwar
erequi
rement
sar
emor
ethanot
her
s.

 I
tist
imeconsumi
ngmet
hod.

 I
thashi
ghcostt
hanot
hercomput
ati
onal
met
hods(
Mar
xandHut
ter
,2009)
.

AbI
nit
iomet
hodsi
scomput
edv
ia,

 Har
tree-
Fockappr
oaches.

 Mol
l
erPl
essetPer
tur
bat
iont
heor
y.

 Mul
ti
-Ref
erencet
echni
ques.
1.
3.3Har
tee-
FockMet
hods

AHar
tree-
Fockmet
hodi
ssi
mpl
ety
peofAbI
nit
iomet
hod.Schr
odi
ngerwav
eequat
ion
canbesol
vedf
orpol
y-
elect
roni
cbyusi
ngt
hisappr
oach.Hami
l
toni
anoper
atori
sal
so
used f
orpr
otoni
c char
ges,Pl
ank’
s const
ant& per
mit
ti
vi
ty off
ree space as i
ts
component
s.

1.
3.3.
1Ty
pesofHar
tree-
Fockmet
hods

 Av
eraged-
fi
eld.

 LCAO.

 Bor
n-Oppenhei
mer
.

 Negl
ect
ingt
her
elat
ivi
sti
cef
fect
.

 At
omi
cuni
ts.

Har
tree-
Fockappr
oacheshel
pinpr
edi
cti
ngsomef
easi
bil
i
tywhi
chi
shel
pfulf
ort
he
geomet
ri
copt
imi
zat
ionandgeomet
ri
cpar
amet
ersofdi
ff
erentsy
stemsandsuper
ior
becausei
tdependupont
hepot
ent
ial
ener
gysur
facesandpol
ari
zabi
l
ityest
imat
ion.Thi
s
met
hodhassomedr
awbacksast
heexpensi
vet
echni
quet
hatr
equi
resgr
eat
erwei
ght
har
dwar
eappar
atusesandav
oidi
ngt
heel
ect
roni
c-cor
rel
ati
on(
Mar
xandHut
ter
,2009)
.

1.
3.4Semi
-empi
ri
cal
Met
hod

Thi
smet
hodi
sanadv
ancef
orm ofHat
ree-
Fockmet
hod.I
nthi
smet
hodweusedsome
exper
iment
al par
amet
ers f
or best per
for
mance. These met
hods hav
e many
appr
oxi
mat
ionsf
ort
hecal
cul
ati
onofpol
y-
mol
ecul
esbecauset
hecomput
ati
onofsuch
mol
ecul
esbyanyot
hermet
hodi
sexpensi
ve.Dur
ingt
hecomput
ati
onv
iat
hismet
hod
consi
stsofemi
ssi
onofcor
eel
ect
ronsf
rom cal
cul
ati
ons.Exper
iment
alpar
amet
ersar
e
mi
nimi
zedt
omakei
ter
rorf
reewhi
chmayoccurduet
oappr
oxi
mat
ion.Theadv
ant
age
oft
hismet
hodi
sthati
tmi
nimi
zedt
hebasi
cset
sforcal
cul
ati
on.Appr
oxi
mat
ionsf
or
Semi
-empi
ri
calmet
hodsar
eobt
ainedf
rom exper
iment
all
yrecor
deddat
aaswel
las
f
rom hi
gher l
evel
s of comput
ati
onal cal
cul
ati
ons t
hrough Ab-
Ini
ti
o and DFT
met
hodol
ogi
es.Semi
-empi
ri
calt
akesdi
ff
erentf
ormsbutal
lfor
msst
artwi
tht
hehel
pof
af
ock-
mat
ri
xfordet
ermi
nat
ionofener
giesofmol
ecul
aror
bit
alsandf
oraddi
ti
onal
pr
ocessi
ng.I
tisv
eryf
astmet
hodduet
other
educt
ioni
nthewor
kloadofcomput
ingso
manyi
ntegr
al.Thi
smet
hoddependsuponf
oll
owi
ngs.

1.Tr
eat
mentofv
alence-
elect
rons.

2.Theoper
ati
onofbasi
cfunct
ioni
sconcent
rat
ed.

3.Par
amet
eri
zat
ionoft
heel
ect
roni
c-cor
rel
ati
on.

4.I
dent
it
y-mat
ri
xasov
erl
ap-
mat
ri
x.

Thi
smet
hodi
susedf
ort
hedet
ermi
nat
ionofgeomet
ri
cpar
amet
ers,ener
get
icsof
di
ff
erentst
ruct
uresandI
P.Thecal
cul
ati
onsoft
hepol
yat
omi
cmol
ecul
esandr
elat
ed
f
ami
l
ymol
ecul
eshav
ebeencar
ri
edoutbyt
heseappr
oaches.Thesear
ever
ysi
mpl
e
t
echni
quest
hatr
equi
rev
erysmal
lamountoft
imeaswel
lasef
for
t.I
nshor
twecan
concl
ude t
hatbef
ore goi
ng t
o hi
gherl
evelcomput
ati
onalst
udy Semi
-empi
ri
cal
t
reat
mentcanbedone.Ther
ear
etwobasesf
ort
hedev
elopmentoft
hesemi
-empi
ri
cal
met
hodsasNDO andNDDO.Thesebasesar
ebasedont
hev
ari
anceconnect
ioni
s
equal
tozer
oandt
hesear
eusedf
orsol
vi
ngorabr
idgi
ngi
ntegr
als(
Jensen,
2007)
.

Forsameat
om orf
ort
hedi
ff
erentat
omsNDOappr
oachi
sut
il
izedasanest
imat
ewi
th
v
ari
anceconnect
ionf
oral
ltheor
bit
als.Thi
sbasei
susedf
orsev
eralsemi
-empi
ri
cal
met
hodsl
i
keCNDO,
MINDO,
INDO,
SINDO,
ZINDOandt
hei
rchangedf
ormsar
eZI
NDO/
S
andMI
NDO/
3.Forr
emov
ingt
heer
rorf
rom t
heconnect
ionofdi
ff
erentandsi
mil
ar
at
omi
cor
bit
alsNDDOappr
oacheshav
ebeenused.Thi
smet
hodwasdev
elopedt
hrough
appr
oachesasMNDO,
AM1,
PM3,
PM6andSAM1(
Leach,
2001)
.

ZDOappr
oxi
mat
ionsusedf
ort
hismet
hodar
egi
venbel
ow

 Ov
erl
ap-
mat
ri
xrepl
acementbyi
dent
it
y-mat
ri
x.

 Nul
l
ityoft
wo-
elect
roni
ntegr
als.

 Nul
l
ityofal
lthet
hreeandf
ourcent
eredi
ntegr
als.
  Decr
easeoft
hei
ntegr
alst
obesol
ved.

 Forbestr
esul
tsandaccur
acypar
amet
eri
zat
ionsi
sver
yrequi
rementnextt
he
ut
il
izat
ion ofZDO met
hodol
ogy and i
mpr
ovet
he ZDO appr
oach t
hrough
exper
iment
all
yrecor
deddat
aorbycomput
ati
onaldat
aofcancel
edi
ntegr
als
(
Jensen,
1989)
.

CNDO

I
tshowst
hatt
hecompl
eteabandonmentofv
ari
anceconnect
ion.I
tisbasedonNDO
appr
oach,whi
chi
spar
ent
alpr
ocedur
eofNDObasedmet
hod.I
tleadst
othet
heor
yof
omi
tt
ingf
oral
lthet
wo-
elect
roni
ntegr
alsandf
ort
hemul
ticent
re-
int
egr
als.I
tisut
il
ized
f
orv
alenceel
ect
ronsandal
sousedf
orcomput
ati
onoft
hepl
anarandnon-
planar
geomet
ri
es.

Ty
pesofCNDO

1.Ver
sionsCNDO/
1

2.Ver
sionsCNDO/
2

Thesemet
hodsar
eonl
yusedf
orscanni
ngmet
hod(
Lewar
s,2011)
.

I
NDO

I
tref
err
ed t
he i
nter
medi
ate negl
ectofdi
ff
erent
ialov
erl
ap.Thi
s met
hod i
sless
appr
oxi
mat
edmet
hodandi
tsr
esul
tsar
emuchbet
tert
hanCNDO.Forpr
iort
oquant
um
mechani
cal
cal
cul
ati
ont
hismet
hodi
sused..

ZI
NDO

I
tisZer
ner
’sI
NDO met
hod.I
tisbaseduponpar
amet
eri
zat
ionofI
NDO.I
tisusedi
n
spect
roscopi
cest
imat
ionsandal
sousedf
orel
ect
roni
cspect
rum.ZI
NDOcanbeused
f
orcomput
ati
onoft
ransi
ti
on-
met
als.Opt
imi
zedst
ruct
urear
eful
l
ydet
ermi
nedwi
th
ZI
NDO (
Chat
fi
eld,
2002)
.

NDDO
NDDOi
sther
epr
esent
ati
onoft
henegl
ectofdi
atomi
cdi
ff
erent
ial
over
lap.I
tisbasedf
or
MNDO,
AM1,
PM3andPM6(
Jensen,
1989)
.

MNDO

I
trepr
esent
sthe modi
fi
ed negl
ectofdi
atomi
c di
ff
erent
ialov
erl
ap.I
tis used f
or
i
nvest
igat
ionoft
hemul
ti
ple-
int
eract
ionsandqual
i
tat
iveanal
ysi
s.Buti
thasr
etai
ned
f
lawsast
heener
get
ics,
speci
fi
c-i
nter
act
ions,
chemi
cal
andgeomet
ri
cal
proper
ti
es.

AM1

AM1i
sabbr
evi
ati
onofAust
inModel1andi
sconsi
der
edasoneoft
hesemi
-empi
ri
cal
met
hods.Thi
smet
hodl
eadst
oNDDOcl
assandt
hei
rresul
tsar
ere-
par
amet
eri
zat
ionof
t
heMNDOt
echni
ques.Aust
inModel1i
smost
lyut
il
izedmet
hodamongal
lthesemi
-
empi
ri
calmet
hodsandcangi
veef
fi
cientr
esul
ts.AM1i
sbet
tert
hanMNDOasgi
veni
n
f
oll
owi
ng,

 Ef
fi
cienti
nener
get
icest
imat
ionascompar
edt
oMNDO.

 Excel
l
enti
nIPdet
ermi
nat
ion.

 Speci
fi
c-i
nter
act
ionsest
imat
ion.

Someassoci
atedf
lawsofAust
inModel
1ar
eas

 Poorgeomet
ri
cal
est
imat
ion.

 Compl
expr
ocessofpar
amet
eri
nduct
ion.

 Rot
ati
onal
anal
ysi
sisnotr
eli
abl
e.

 Leasti
nfor
mat
ionabouthy
drocar
bonscont
aini
ngni
tr
ogr
oups(
Leach,
2001)
.

PM3

PM3 i
sindi
cat
ion oft
he par
amet
ri
c met
hod 3.PM3 i
s pr
oduced as a r
esul
tof
modi
fi
cat
ioni
ntheAM1met
hod.Thi
smodi
fi
cat
iondependsupont
heer
ror
-f
unct
ion
di
ff
erent
iat
ion expr
essi
ons.Manyf
ree-
var
ying Gaussi
an-
funct
ionsar
eempl
oyed f
or
di
ff
erentmodi
fi
cat
ionsi
nor
dert
odev
elopot
hermet
hodsl
i
kePM5andPM6.PM3i
s
oneoft
hemostusef
ulsemi
-empi
ri
cal
met
hods.

Fol
l
owi
ngar
eshor
tcomi
ngoft
hismet
hod

 Uncer
tai
ntyi
nconf
ormat
ional
anal
ysi
s.

 Lessi
nfor
mat
ionaboutgeomet
ri
cal
proper
ti
esofni
tr
ogen.

 Hy
drogenbondi
ngdet
ermi
nat
ioni
snotsi
mil
art
oact
ual
figur
es.

 Pooranal
ysi
sofhal
ogensandsi
l
iconesr
egar
dingbondl
engt
h.

 Poorest
imat
ionofat
omi
cchar
gei
ncaseofni
tr
ogen.

 Poorsy
mmet
ryest
imat
ionf
orhy
drazi
ne.

1.
3.5Densi
tyFunct
ional
Theor
y(DFT)

I
tisat
ypeoft
heor
eti
calmet
hodwhi
chi
sbasedupont
heconceptofel
ect
ron-
densi
ty.I
t
al
so dependsupon t
he Hohenber
g-Kohn t
heor
ems.Act
ual
l
y,t
hese t
heor
emshav
e
compar
isonofener
giesandt
heel
ect
ron-
densi
t ñ)andspeci
y( fyt
hecal
cul
atedv
alues
t
hroughcomput
ati
onalmet
hodswhi
chwer
esl
i
ght
lygr
eat
ert
hanact
ualener
get
ics
v
alues.Wav
efunct
ionexpl
ainst
heel
ect
ron-
densi
tyñ(
x,y
,z)whi
chi
scombi
nedi
nthi
s
met
hod.Todescr
ibet
heel
ect
ron-
densi
tyanot
hert
ermi
susedknownaschar
ge-
densi
ty.
Appl
i
cat
ionofdensi
tyf
unct
ionalt
heor
ymet
hodi
smor
ecommont
hanAb-
Ini
ti
oand
Semi
-empi
ri
calmet
hods.Butwav
e-f
unct
ioncannotbemeasur
abl
efunct
iont
hrough
Semiempi
ri
calmet
hod.ButDFT met
hod measur
ed t
he el
ect
ron-
densi
tywhi
ch i
s
det
ermi
nedbyXRDanal
ysi
s.

Anot
herchar
act
eri
sti
cofDFTmet
hodi
stomeasur
ethewav
e-f
unct
ion,i
tsdependence
onposi
ti
oncoor
dinat
ewhi
char
ethr
eei
nnumber
sbutt
henumberofv
ari
abl
esconsi
sts
oft
hesemet
hodswhi
char
eaboutf
ourt
imesgr
eat
ert
hanel
ect
ronswhi
chhav
e100
v
ari
abl
esbutt
hesy
stem has25el
ect
rons.

I
thasf
oll
owi
ngaspect
s.
1.Measur
abl
e

2.Bet
termeasur
edbymat
hemat
ical
tool
s

3.Seemi
ngl
yconcei
vabl
e.

Ther
eisdi
ff
erencebet
weent
ermf
unct
ionali
ntheDFTandsi
mpl
efunct
ion.Thet
erm
f
unct
ioni
susedt
oexpl
aint
heexpr
essi
on,
rel
ati
onandequat
iont
hatpr
oduceanumber
.
Ont
heot
herhandf
unct
ional
isanoper
atort
hatoper
atesont
hef
unct
ionandconv
ert
sit
i
ntonumber
.Awav
efunct
ionaswel
lasel
ect
rondensi
tyi
stheexampl
eoff
unct
ion
whi
l
etheener
gyr
elat
ed t
o wav
efunct
ionand el
ect
rondensi
tyi
stheexampl
eof
f
unct
ional
.Char
act
eri
sti
cofmol
ecul
escanbedescr
ibedbyt
heuseofaf
unct
ionon
el
ect
ron-
densi
tyf
unct
ion.Basi
ctheor
emsoft
hesemet
hodsar
enotpr
ovi
dedbyexact
f
unct
ionbutal
sobyappr
oxi
mat
edf
unct
ion.Densi
tyf
unct
ionalt
heor
ymet
hodi
snot
v
ibr
ati
onal
met
hodduet
otheabsenceoft
hef
lawl
essf
unct
ion(
Lewar
s,2011)
.

Fol
l
owi
ngconcept
sar
eut
il
izedasbasi
cappr
oxi
mat
ionar
egi
venbel
ow

 Asum ofwav
efunct
ionsar
eusedt
oexpl
aint
heener
get
icsoft
hemol
ecul
es

 Ref
inement
sofpr
edi
ctedor
bit
ali
nSCFappr
oachar
emeasur
ed.

Appl
i
cat
ionsofDFTmet
hod

1.St
ruct
ure pr
oper
ti
es of v
ari
ous compounds ar
einv
est
igat
ed by usi
ng DFT
met
hodol
ogy
.

2.Ener
get
icf
airassessmentcanbedone.

3.Ther
mo-
chemi
cal
proper
ti
esofv
ari
ousmol
ecul
escanbei
nvest
igat
ed.

4.Vi
brat
ional
wav
enumber
sar
emeasur
edt
hanMP2.

5.El
ect
roni
ctr
ansi
ti
onbandsar
edet
ermi
ned.

6.Densi
tyf
unct
ionalt
heor
ymet
hodsar
eusedt
omeasur
eNMRbandsov
erHar
tree-
Fockappr
oach.
7.Di
pol
emoment
,at
omi
c-char
ge,EAs&I
Esar
emeasur
ed.Vi
sual
i
zat
ionofMol
ecul
ar
Or
bit
alcanbei
ncor
por
atedi
ngr
aphi
cal
int
erf
acef
aci
l
iti
es(
G.Lewar
s,2010)
.

Shor
tcomi
ngsofDFTmet
hodar
egi
venbel
ow;

 Conv
ersat
ionassoci
ati
onf
unct
ional
isnotdet
ermi
nedi
nit
sfaul
tl
essway
.

 Funct
ionar
emodi
fi
edbasedonhi
tandt
ri
albasedr
athert
hant
heor
eti
cal
l
y.

 Thi
smet
hodi
sanotav
ibr
ati
onal
met
hod.

 Weak-
int
eract
ionsar
enotcor
rect
lydet
ermi
ned.

 Exci
tedst
atesy
mmet
ryr
elat
ivel
ypoor
lyaccount
edf
ort
hismet
hod.

 Char
gedt
ransf
erpr
oper
ti
esf
orext
ensi
vet
ransl
ati
onar
enotwel
lexami
ned.

Exchange-
Cor
rel
ati
onFunct
ional

TheuseofExchange-
cor
rel
ati
onf
unct
ionmet
hodi
sver
ycommont
omeasur
ethe
el
ect
ron-
densi
tyf
unct
ion whi
ch i
s ut
il
ized f
orener
gycont
ri
but
ion f
orcoor
dinat
es
among compl
ement
ary el
ect
ron.I
tis al
so used f
orcont
ri
but
ion gener
ati
ng t
he
associ
ati
onoft
heel
ect
ronst
hatdev
iat
est
hedensi
tyofel
ect
ron.I
tcanbeexpr
essedby
t
headdi
ti
onofbot
hexchangeandcor
rel
ati
onf
unct
ions.Thebestut
il
izedf
unct
ioni
s
B3LYPt
hatgi
vebet
terr
esul
tsf
orgeomet
ri
copt
imi
zat
ionst
udi
es(
Dykst
ra,
2005)
.

Adv
ant
agesofMM met
hod

Mol
ecul
armechani
cmet
hodhasadv
ant
agesov
ermanycomput
ati
onalt
ool
s.Mol
ecul
ar
mechani
cmet
hodi
slesscompl
ext
hanot
hercomput
erbasedmet
hodswhi
char
e
dependentonquant
um mechani
cscal
cul
ati
on.I
tisusedi
sver
yeasybutr
elat
ivequi
ck
r
esul
tswi
thl
osecost
.Resul
tsar
emor
eaccur
ateandr
eli
abl
eandi
tsqui
cknessmakes
i
tauserf
ri
endl
ytool
.Foral
ltheel
ement
spar
amet
eri
zat
ioni
sdonet
hroughmol
ecul
ar
mechani
cmet
hod bycompar
ing t
heav
ail
abl
edat
a.Thebi
ggermol
ecul
escan be
comput
edt
hroughMM met
hodol
ogi
esbutconf
ormer
sar
eanal
yzedv
ia MM f
orce
f
iel
ds(
Hehr
e,1986)
.
Di
sadv
ant
agesofMM met
hod

Mol
ecul
armechani
chassomer
est
ri
cti
onst
ocal
cul
ateel
ect
roni
ctr
ansi
ti
ons,
mol
ecul
ar
or
bit
als,shape,spect
rum andener
gies.Par
amet
eri
zat
ionoft
ransi
ti
onsst
atescannot
becomput
edv
iaMM met
hodsandunst
udi
edspeci
esal
socannotbepar
amet
eri
zedby
i
t(Leach,
2001)
.

1.
4Basi
sSet
s

Abasi
sseti
sasetoff
unct
ionswhi
chcanbeut
il
izedt
orepr
esentt
heel
ect
roni
cwav
e
f
unct
ioni
nHFandDFTmet
hodsi
nor
dert
otur
nthepar
ti
aldi
ff
erent
ialequat
ionsoft
he
modeli
ntoal
gebr
aicequat
ionssui
tabl
eforef
fi
cienti
mpl
ement
ati
ononacomput
er.
Basi
cset
sar
eappl
i
edf
ort
hewav
e-f
unct
ionandel
ect
ron-
densi
tyt
echni
ques.Basi
cal
l
y
el
ect
rondi
str
ibut
ionar
oundnucl
eusi
sdet
ermi
nedbymanybasi
s-f
unct
ions.I
tcanbe
def
inedassum off
unct
ionswhi
chmat
hemat
ical
l
yfi
ndgeomet
ryofor
bit
als(
G.Lewar
s,
2016)
.Basi
ssetsel
ect
ioni
sreal
l
ysi
gni
fi
canti
ncomput
ati
onalchemi
str
yforqual
i
ty
r
esul
ts.Goodknowl
edgeofbasi
ssetsel
ect
ionf
ormol
ecul
arst
ruct
uralpr
oper
ti
esi
s
r
equi
redf
orcomput
ati
onal
chemi
st(
Hil
l
,2013)
.

Dev
elopmentofbasi
sset
sisnotcompul
sor
yforchemi
sthowev
er,knowl
edgehow
opt
imi
zat
ionofbasi
sset
stakespl
acei
simpor
tantf
orcomput
ati
onalchemi
st.I
tisof
hi
gh si
gni
fi
cancet
hatt
hepr
oper
tywear
eopt
imi
zi
ng t
hen usebasi
ssetf
ort
hat
pr
oper
ty,
thi
scangi
veaccur
ater
esul
ts(
Bar
anowskaandSadl
ej,
2010)
.

1.
4.1Cl
assi
fi
cat
ionsofBasi
sSet
s

Wor
kingwi
thi
ntheassumedf
ramewor
kofat
om-
cent
ered,ener
gy-
opt
imi
zedGaussi
an
t
ypeor
bit
als(
GTOs)
,basi
sset
scanbef
urt
hercl
assi
fi
edbasedont
henumberandt
ype
off
unct
ionsi
ncl
uded.Basi
ssetar
ecat
egor
izedi
nvar
iouscl
assesbasedont
henumber
ofwav
efunct
ions,
ast
hesi
mpl
ebasi
sset
sar
enamedmi
nimal
orSi
ngl
ezet
abasi
sset
s
duet
opossessi
onoft
hef
unct
ionsf
oronl
yel
ect
ronspr
esenti
nat
oms(
Schl
egeland
Fr
isch,1995)
.Fori
nst
ance,i
ncaseofneut
ralNeat
om,mi
nimalbasi
ssetwoul
d
possesst
wosf
unct
ionsaswel
last
hreecomponentpf
unct
ions.Mi
nimalbasi
sset
s
usei
srar
ebecauseoft
hei
rli
tt
leel
ect
roncor
rel
ati
on.Si
ngl
ezet
abasi
sset
scanbe
i
mpr
ovedbyi
ncr
easi
ngt
henumberoff
unct
ionsi
ndoubl
eort
ri
ple.Wecandoubl
e,t
ri
ple,
quadr
upl
e,andsof
ort
h,t
henumberoff
unct
ions,andar
enamedasdoubl
ezet
a(DZ)
,
t
ri
plezet
a(TZ)
,quadr
upl
ezet
a(QZ)
,respect
ivel
y(MaedaandMor
okuma,2010)
.In
commonpr
act
ice,basi
sset
sar
esl
i
ght
lychangedbyi
ncr
easi
ngt
hebasi
sfunct
ioni
n
zet
aconcer
nedt
oval
enceel
ect
ronofanel
ementandar
ecal
l
edspl
i
t-v
alencebasi
sset
s.
ForDZ,t
hesear
eabbr
evi
atedasv
alencedoubl
ezet
a(VDZ)anddoubl
ezet
aval
ence
(
DZV)andt
hesear
epr
efer
redduet
ohi
ghcl
ari
tyofr
esul
ts.Fur
ther
mor
e,t
hel
atest
comput
ati
onal
chemi
str
ycodessuppor
tbot
hsegment
edandgener
all
ycont
ract
edbasi
s
set
s,t
heal
gor
it
hmsar
ehi
ghl
yef
fi
cientf
oronecont
ract
ionschemet
hant
heot
her
(
Raf
fenet
ti
,1973)
.Fori
nvest
igat
ionofspeci
fi
cpr
oper
ty,ar
esear
chermustusesuch
knowl
edgef
orchoosi
ngbasi
sset
.

Gaussi
an t
ype basi
s set
s(GTO)ar
e bei
ng most
ly used t
o det
ermi
ne st
ruct
ural
pr
oper
ti
esofmol
ecul
est
hanpl
anewav
e(PW)basi
sset
s.PW basi
sset
sar
einl
i
mit
ed
useandar
euni
quel
ydef
inedbyt
heuni
tcel
ldi
mensi
onsandt
heener
gycut
off
.GTO
basi
sset
sconsi
stofl
argev
ari
eti
esofbasi
sfunct
ionsf
oral
lpr
oper
ti
esofmol
ecul
es.
Anybasi
sseti
srankedont
hebasi
soff
unct
ionsnumberf
oreachki
ndofpol
ari
zat
ion
f
unct
ions(
d,p)anddi
ff
usedf
unct
ions(
+,++)
,exponentv
aluesandt
hei
rcombi
nat
ion
pat
ter
n(Jensen,2013)
.Fort
hei
mpr
ovementofcomput
ati
onalef
fi
ciency
,iti
susef
ult
o
r
epr
esentcor
eor
bit
alsasaf
ixedl
i
nearcombi
nat
ionoff
unct
ions,apr
ocedur
edenot
ed
ascont
ract
ioncont
ract
edf
unct
ions.

1.
4.2Si
ngl
eZet
a/Mi
nimal
Basi
sSet

Ami
nimalorSZbasi
ssetexpl
ainst
heor
bit
alsi
nisol
atedat
omsbycar
ryi
ngt
heusef
ul
f
unct
ions.I
tcont
ainsbasi
sfunct
ionofSTO,
GTOandCGTOf
orat
omi
cor
bit
als(
AOs)i
n
t
heat
om.I
nst
artdesi
gni
ngofcomput
ati
onal
l
ymet
hods,
ali
mit
ednumberofbasi
sset
s
wer
e av
ail
abl
eforcomput
ati
onalcal
cul
ati
on butnow new v
ari
eti
es hav
e been
dev
eloped.Anear
lySZt
ypebasi
ssetwast nG,wher
heSTO- eni
spr
imi
ti
ve,GTOswer
e
f
it
tedt
oa(
STO)sl
atert
ypef
unct
ion,r
athert
hanopt
imi
zedexpl
i
cit
ly.Cal
cul
ati
ons
car
ri
edwi
tht
hisbasi
ssetshowedl
i
ttl
evar
iat
i ondn=3.STO-
onbey 3G basi
sseti
s
usual
l
yspeci
fi
edf
orel
ement
sint
heper
iodi
ctabl
efr
om Hy
drogent
oIodi
ne.Hav
ingl
ess
numberofbasi
sfunct
ions,t
her
esul
tsbySTO-
3Gbasi
ssetar
erar
elyaccur
ateandar
e
notofhi
ghqual
i
ty.Pr
obl
em wi
tht
heSTO-
3Gi
sthati
ttakesmucht
imet
ocomput
e
i
ntegr
alsusi
ng STOf
unct
ionswhi
chcanbe sol
vedby l
i
nearcombi
nat
ionofenough
GTO’
stomi
mict
heSTO( eetal
Hehr .,
1969)
.

1.
4.3Doubl
eZet
a(DZ)Basi
sSet

Adoubl
ezet
a(DZ)qual
i
tybasi
ssetconsi
stsoft
hedoubl
enumberofbasi
sfunct
ions
t
hanSZbasi
sset
s.Enhanci
ngt
henumberoff
unct
ionsmeanst
her
eisdi
ff
erentbondi
ng
i
ndi
ff
erentdi
rect
ionsi
nsy
stem underi
nvest
igat
ion(
Mul
l
iken,1962)
.The3-
21Gbasi
s
sethast
hesamenumberofpr
imi
ti
veasSTO-
3G,buti
scont
ract
edt
oadoubl
ezet
a
qual
i
typossessi
ngdoubl
enumberofbasi
sfunct
ions(
Bi eyetal
nkl .
,1980)
.3-
21Gbasi
s
seti
sspeci
fi
edf
oral
lel
ement
supt
oXenon(
Xe)
.Aser
iesofr
elat
edDZbasi
sset
swi
th
v
ary
ingnumberofpr
imi
ti
veGTOswasal
sot
est
ed,suchas4-
21G,4-
31G,and5-
31G,
bef
oreset
tl
ingont
hef
amous6-
31G combi
nat
ion(
Col
l
insetal
.
,1976)
.The6-
31G
cor
respondst
o6,3,and1pr
imi
ti
veGaussi
ant
ypef
unct
ionsGTOsi
nthecor
eandt
wo
v
alencef
unct
ions,r
espect
ivel
y.3-
21Gand6-
31car
rysamenumberofsandpt
ype
f
unct
ionsf
orr
esul
tsef
fi
ciency
.6-
31Gi
ssuppl
ement
edwi
thpol
ari
zat
ionf
unct
ions(
d,p)
t
o6-
31G(
d,p)
,whi
chi
sconsi
der
edmostef
fi
cientbasi
sset
sofDoubl
eZet
aqual
i
ty.6-
31
G(
d,p)i
sappl
i
edf
orel
ement
supt
oKr
,howev
ert
hisi
sal
soav
ail
abl
einmor
e2v
ersi
ons
or4thr
f owel
ement
s.Basi
sset6-
31G*or6-
31G(
d)i
sempl
oyedf
ornon-
hydr
ogenat
oms
whi
l
e6-
31G*
*or6-
31G(
d,p)f
orhy
drogenel
ement
s.

1.
4.4Tr
ipl
eZet
a(TZ)Basi
sSet

TZt
ypebasi
ssetar
econst
ruct
edbyt
ri
pli
ngt
henumberofv
alencebasi
sfunct
ionsand
i
ncl
udef
unct
ionswi
tht
wohi
gherangul
armoment
a.TheTZbasi
sset
sar
eempl
oyedf
or
t
hedet
ermi
nat
ionoft
heel
ement
spr
oper
ti
esf
rom Hy
drogent
oAr
gon,butcanshow
l
essaccur
ater
esul
tsf
orel
ement
sgoi
ngdownwar
dsi
nper
iodi
ctabl
e.

The6-
311G i
sofTZqual
i
tybasi
ssetandhasbeendev
elopedf
orcor
rel
atedMP2
comput
ati
ons(
J.Kr
ishnanetal
.,1980)
,ithassegment
edcont
ract
ionof6,3,1,and1
pr
imi
ti
veGTOs.6-
311G i
sspeci
fi
edf
ort
heel
ement oNe.For3rd and4t
supt hrow
el
ement
s,i
tis used by combi
ning wi
tht
he di
ff
used/
pol
ari
zat
ion f
unct
ions and
McLean–Chandl
erbasi
sset
s(Bi
nni
ngJrandCur
ti
ss,1990)
.McLean–Chandl
erbasi
s
set
shav
edi
ff
erentar
rangementofl
argernumberofcont
ract
edf
unct
ions,
ascompar
ed
t
othe6-
311Gbasi
sset
.The6-
311Gbasi
ssetar
eaugment
edwi
thdi
ff
usef
unct
ions(
s,p)
andf
urt
heraddi
ti
onofdi
ff
usedf
unct
ions(
+,++)canbedonef
ort
hir
dandf
our
thr
ow
el
ement
sbybui
l
dingbasi
ssetl
i
ke6-
311+G/
6-311++G.Pol
ari
zat
ionf
unct
ions(
d,p)
addi
ti
on(
Hil
l
,2013)t
o6-
311Gdev
elops6-
311++G(
d,p)basi
ssetwhi
chi
susef
ult
ofi
nd
t
heoccupi
edor
bit
alsf
orani
ons.Thedi
ff
usef
unct
ionsexponent
sar
ecal
cul
atedby
obt
aini
ngt
heHFmi
nimum ener
gyofani
ons.Numberoff
unct
ionsi
sdi
ff
erentf
oreach
basi
ssetused.Forbasi
sset
sli
ke6-
311G(
3df
,2pd)
,3set
sofdf
unct
ionsandonesetof
ff
unct
ionsi
sspeci
fi
edf
orheav
yat
omswhi
l
e2set
sofpf
unct
ionsandonesetofd
f
unct
ionsf
orhy
drogenat
oms(
Clement
iandPopki
e,1972)
.

1.
4.5Gener
alCont
ract
edBasi
sSet
s

Theconceptofener
get
icbal
ancef
orsel
ect
ingt
hebasi
ssetcomposi
ti
onhasr
esul
ted
i
naf
ami
l
yofcor
rel
ati
onconsi
stentbasi
sset
s,cc-
pVXZ,ai
medatf
indi
ngel
ect
ron
cor
rel
ati
onbywav
efunct
ionmet
hods.Theyar
eav
ail
abl
einDZP,
TZP,
andQZPqual
i
ties
f
orel
ement
supt
oKr
,andi
nconnect
ionwi
thpseudopot
ent
ial
sforel
ement
supt
oRn
( gendetal
Wei .,
2003)
.

1.
4.6Basi
sSetSi
ze

I
tisi
mpor
tantt
oknowhowl
argeabasi
sseti
srequi
redandnumberoff
unct
ionshoul
d
bef
oreachangul
armoment
um t
ype,
her
ear
esomeexampl
es,

 Hat
om,
mini
mal
basi
s:1s(
1funct
ion)

 Cat
om,
mini
mal
basi
s:2s1p(
5funct
ions)

 Cat
om,
doubl
e-zet
abasi
s:4s2p(
10f
unct
ions)

 Cat
om,
spl
i
t-v
alencedoubl
e-zet
abasi
s:3s2p(
9funct
ions)(
Clement
iandPopki
e,
1972)
.

Gener
alComment
s
  I
tisgener
all
yobser
vedt
hatt
hebi
ggert
hebasi
sset
,thebet
terwi
l
lber
esul
ts.
Mosti
mpor
tanti
srequi
redt
obal
ancewi
thcor
rel
ati
onmet
hod;e.
g.,cc-
pVQZi
s
gr
eatf
orCCSD(
T),
butov
erki
l
lforHF

 STO-
3Gshoul
dnotbeusedbecausei
tist
oosmal
l

 Har
dtoaf
for
dmor
ethanpol
ari
zeddoubl
e-zet
abasi
sset
sexceptf
orsmal
l
mol
ecul
es

 Ani
onsmusthav
edi
ff
usef
unct
ions

 cc-
pVDZi
snotnecessar
il
ybet
tert
han6-
31G(
d,p)
;howev
er,cc-
pVTZi
sbet
ter
t
han6-
311++/
6-311G(
d,p)orsi
mil
ar

 Conv
ergenceofabi
nit
ior
esul
tsi
sdi
sappoi
nti
ngl
ysl
owwi
thr
espectt
obasi
sset
f
ornon-
DFT met
hods.DFT i
slessdependenton basi
ssetsi
zet
han wav
e
f
unct
ionbasedmet
hods(
Sher
ri
ll
,2017)
.

Tabl
e1.
1:Basi
sSet

Basi
sSet Appl
i
est
o Pol
ari
zat
ionFunct
ions Di
ff
useFunct
ions

3-
21G H-
Xe +

6-
21G H-
Cl *or*
*

4-
31G H-
Ne *or*
*

6-
31G H-
Kr (
3df
,3pd) +,
++

6-
311G H-
Kr (
3df
,3pd) +,
++

LanL2MB H-
La,
Hf-
Bi

LanL2DZ H,
Li-
La,
Hf-
Bi

SDD,
SDDAl
l al
lbutFrandRa

cc-
pVDZ H-
Ar,
Ca-
Kr
cc-
pVTZ H-
Ar,
Ca-
Kr

cc-
pVQZ H-
Ar,
Ca-
Kr

cc-
pV5Z H-
Ar,
Ca-
Kr

cc-
pV6Z H,
B-Ne

SV H-
Kr

SVP H-
Kr

TZVandTZVP H-
Kr

QZVPandDef
2 H-
La,
Hf-
Rn

Mi
diX H,
C-F,
S-Cl
,I
,Br

EPR-
II
,EPR-
II
I H,
B,C,
N,O,
F

UGBS H-
Lr UGBS(
1,2,
3)P +,
++,
2+,
2++

DGDZVP H-
Xe

DGDZVP2 H-
F,Al
-Ar
,Sc-
Zn

DGTZVP H,
C-F,
Al-
Ar

CBSB7 H-
Kr +,
++

Theseal
lbasi
sset
sar
eav
ail
abl
einGaussi
anpr
ogr
am andi
nor
dert
ochooset
hebasi
s
setf
orspeci
fi
cel
ement
sincompounds,abov
etabl
e1.
1canhel
p,butf
oref
fi
cient
sel
ect
ionl
i
ter
atur
ewoul
dbeusef
ul.

1.
4.7I
deal
Basi
sSet

Pr
obl
em sol
vi
ngbasi
ssetwoul
drequi
resomei
mpor
tantpr
oper
ti
es.

1)Basi
sfunct
ionaddedt
obasi
ssetshoul
dhav
etheabi
l
ityt
osol
vet
hepr
obl
em f
or
whi
chwear
eusi
ngbasi
sset
. Basi
sfunct
ionssel
ect
ionf
ormaki
ngt
hei
deal
 basi
ssetshoul
dref
lectt
hesol
uti
onofpr
obl
em wi
thgoodr
esul
ts.

2)Basi
sset
sdev
elopedf
rom basi
sfunct
ionsmusthav
eext
rachar
act
eri
sti
cs,so
t
hatt
hebasi
ssetl
i
mitcanbeappr
oachedi
nasy
stemat
icf
ashi
on,andt
he
r
esi
dual
basi
sseti
ncompl
etenesscanbequant
if
iedateachqual
i
tyl
evel
.

3)Basi
s set
s shoul
d notal
l
ow onl
y cal
cul
ati
ons ofener
gy and i
tsr
elev
ant
pr
oper
ti
esbutbeabl
etocal
cul
ateot
herchemi
cal
proper
ti
es.

4)Ther
equi
redone-andt
wo-
elect
roni
ntegr
alsshoul
dbecomput
abl
eef
fi
cient
ly.

5)Forat
om-
dependentbasi
sfunct
ions,t
hebasi
sset
sshoul
dbeav
ail
abl
eforal
l
at
omsi
ntheper
iodi
ctabl
e,oratl
eastal
argef
ract
iont
her
eof
.

6)Theul
ti
mat
ecr
it
eri
oni
sthebal
ancebet
weenaccur
acyandcomput
ati
onalcost
,
t
hati
s,howt
hebestper
for
mancei
sachi
evedf
oragi
vencomput
ati
onalcost
.In
t
hepr
esentcont
ext
,weequat
egoodper
for
mancewi
thl
ow basi
sseter
ror
s
r
elat
ivet
othebasi
ssetl
i
mit(
NagyandJensen,
2017)
.

1.
4.8Si
gni
fi
canceofBasi
sSet
s

 Al
lcal
cul
ati
onsar
edonebyusi
ngbasi
sset
s.Wi
thoutcor
rectuseofbasi
sset
s,
i
nvest
igat
ionf
ordesi
redpr
oper
tyi
simpossi
ble.

 Basi
sset
sar
ebui
l
dingbl
ockst
hathav
eabi
l
ityt
osol
veanyspeci
fi
cpr
obl
em of
mol
ecul
esi
ncombi
nat
ionwi
thcomput
ati
onal
met
hodandf
unct
ional
.

 Ani
mpor
tantappl
i
cat
ionofbasi
sset
sissol
vi
ngt
heel
ect
roni
cSchr
odi
nger
equat
ion.Ri
ghtchooseofbasi
ssetwi
l
lpr
ovi
det
heov
eral
laccur
acyoft
he
r
esul
ts.

 Basi
sset
scont
ainanumberoff
unct
ionsf
orspeci
fi
ccal
cul
ati
ons.Foreach
pr
oper
tyofmol
ecul
es,
funct
ionsar
ecodedwi
thi
nthebasi
ssett
hatpr
oducev
ery
goodr
esul
ts.

 Basi
sset
sar
eappl
i
edi
ncomput
ati
onalchemi
str
yforget
ti
ngi
nfor
mat
ionf
rom
opt
imi
zat
iont
ovi
brat
ional
proper
ti
es.
  Ener
gyandener
gy-
rel
atedquant
it
iesar
emost
lycal
cul
atedwi
tht
hebasi
sset
s
l
i
ke631G/
6-311+Gandaddi
ng(
d,p)pol
ari
zat
ionf
unct
ions.

 Exceptal
kal
iandal
kal
i
neear
thmet
alsbasi
sset
shav
etendencyt
ocal
cul
ateal
l
pr
oper
ti
esofel
ement
s.Fort
hesemet
alsaugment
ati
onofbasi
sset
scanbe
done.

 Pat
hway
sofsi
mpl
easwel
lascompl
exr
eact
ionmechani
smsar
einv
est
igat
edby
usi
ng v
ari
etyofbasi
s set
s wi
th bet
termet
hods and f
unct
ional
.Formor
e
accur
acy
,li
ter
atur
esur
veywoul
dbeusef
uli
nor
dert
ochooset
hebasi
ssetand
r
elev
antmet
hodsf
ort
hepr
obl
em (
Dav
idsonandFel
l
er,
1986)
.

1.
5Model
sinComput
ati
onal
Chemi
str
y

Model
sinchemi
str
yar
ever
yimpor
tantf
ormol
ecul
arpr
oper
ti
escal
cul
ati
ons.Thesecan
bebui
l
twi
thdi
ff
erentmet
hodsandappl
yi
ngt
hesemet
hodwi
thspeci
fi
cfunct
ionaland
basi
sset
s.Forexampl
e,I
fDFT met
hod i
smi
xed wi
tht
he6-
31 G basi
ssetand
f
unct
ionalB3LYPt
henmodell
i
keDFT/
6-31G/
B3LYPwi
l
lbebui
l
t.Fur
therwecanadd
possi
ble(
1d)
,(2d)and (
3d)pol
ari
zat
ion f
unct
ions f
ort
he r
esul
tsi
mpr
ovement
.
Combi
ningdi
ff
erentbasi
sset
swi
thv
ari
etyofmet
hods(
especi
all
yDFTusi
ngdi
ff
erent
exchange-
cor
rel
ati
onf
unct
ional
s),
canpr
ovi
dehi
ghv
ari
etyofmodel
s.Foragi
vensetof
mol
ecul
esandpr
oper
ti
es,i
tisunav
oidabl
ethatcer
tai
nmodel
swi
thgoodagr
eement
wi
tht
her
efer
encedat
acanbef
oundf
rom l
i
ter
atur
eandbeusedout
sidet
hecal
i
brat
ion
r
ange.Asagener
alr
uleoft
humb,t
hemostadv
ancedandl
argemet
hodswoul
dneed
bi
gbasi
ssetsi
ze,whi
l
esmal
lsy
stem suchasHF,t
hebasi
sset
srequi
rementi
sless
andonl
yDZPqual
i
tybasi
sset6-
31Gwoul
dbeenough,unl
esst
heHFcal
cul
ati
onsar
e
empl
oyedf
ormor
eexpl
orat
ion(
Leszczy
ński
,1994)
.

DFTi
sofpar
amounti
mpor
tancei
nor
dert
oachi
evehi
ghper
for
manceandcanbe
appl
i
edwi
thDZP/
TZPbutt
hebesti
stochooseTZbasi
sset
stomi
nimi
zet
hebasi
sset
er
ror
s.Thi
sisal
soi
mpor
tantt
oest
imat
etheCBSl
i
mitbyi
ncl
udi
ngr
esul
tsf
rom atl
east
QZPqual
i
tybasi
sset
s.DFThasdi
ff
erentcombi
nat
ionswi
thSZ,DZandTZbasi
sset
s
byusi
ngdi
ff
erentf
unct
ionalandt
hesemodel
spr
ovi
deaccur
ater
esul
ts.Forst
ruct
ural
st
udyofor
gani
ccompoundsi
nsol
vent
s,Pol
ari
zat
ioncont
inuum model(
PCM)i
sused
dur
ingDFT.DFTst
udywi
thDZbasi
ssetl
i
keDGDZVPandt
hef
unct
ionalmPW1PW91i
s
known t
oimpr
ovet
he l
ong-
range def
ici
ency ofDensi
tyf
unct
ionalt
heor
y and i
s
si
gni
fi
canti
nthest
udyofnon-
cov
alenti
nter
mol
ecul
ari
nter
act
ionespeci
all
yfort
he
t
ransi
ti
onmet
alcompl
exes(
Adeni
yiandAj
i
bade,2017)
.DFTwi
thf
unct
ionalB3LYPas
wel
lasCAM-
B3LYP i
ncombi
nat
ionwi
th6-
31G (
d,p)basi
ssetf
ordy
eandor
gani
c
compoundsar
epopul
armodel
sforaccur
ater
esul
ts(
Si quaetal
ddi .
,2020)
.

Wi
thDFT/
CCSDmet
hods,
6-311Gi
sav
oidedt
ouse,
becausei
tlacksoff
unct
ions,
whi
ch
i
squi
tei
mpor
tantf
orobt
aini
ngr
easonabl
est
ruct
ureespeci
all
y,i
fthesy
stem cont
ains
het
eroat
oms(
e.g.sul
fur
,oxy
gen,ni
tr
ogen)
.Commonl
y,I
tisbet
tert
ouse6-
311G*or6-
311G++i
nst
ead.Whenhy
drogenpl
aysani
mpor
tantr
ole(
e.g.st
udy
ingH-
bond,
orbond
char
act
erst
hatr
elat
edt
ohy
drogen)
,6-
311G*
*issuggest
ed.6-
311G*canbeusedwi
th
DFT/
B3LYPbecausei
tischeapert
han6-
311G*
*.I
nourpr
esentst
udyweusedt
he6-
311++Gbasi
sset
,becausebasi
sset6-
311Gmusti
ncl
udet
hedi
ff
usef
unct
ions(
+,++)
f
ort
het
hir
dandf
our
thr
owel
ement(
Binni
ngJrandCur
ti
ss,
1990)
.Inourdy
esst
ruct
ure,
t
heel
ement
sar
eupt
othi
rdr
owso6-
311++car
ryi
ngdi
ff
usedf
unct
ionsgav
eef
fi
cient
r
esul
tswi
thDFTmet
hodandB3LYPf
unct
ional
wit
houter
ror
.

Opt
imi
zi
ng v
eryf
lexi
blesy
stems,whoseconf
ormat
ion/
conf
igur
ati
oni
ssensi
ti
vet
o
di
sper
sionef
fect
,weshoul
dadddi
sper
sioncor
rect
ion(
e.g.DFT-
D3)t
oB3LYP,
because
i
tiswel
l
-knownt
hatB3LYP compl
etel
yfai
l
stor
epr
esentdi
sper
sioni
nter
act
ion.I
f
sy
stem showswi
del
yconj
ugat
edchar
act
er,
B3LYPi
snotr
ecommended,
becausei
thas
st
rong t
endencyt
o opt
imi
zet
hesy
stem asaf
ull
ypl
anarst
ruct
ureand t
hebond
al
ter
nat
ionchar
act
eri
susual
l
yunder
est
imat
ed.Thef
ail
ureofB3LYP i
nopt
imi
zi
ng
annul
enesy
stemsi
sat
ypi
calexampl
e,WhenB3LYPdoesn'
twor
kwel
l
,usi
ngωB97XD
i
sthebestopt
ion,
whi
chdoesnothav
ethet
woaf
orement
ionedl
i
mit
ati
onsandi
tisabl
e
t
owel
lrepr
esentv
ari
ouski
ndsofor
gani
csy
stems.Ov
eral
l
,B3LYP i
sar
easonabl
e
choi
ceofper
for
mingopt
imi
zat
ion( eetal
Wanner .
,2004)
.

MP2i
sver
yaccur
atewav
efunct
ionmet
hodt
oincl
udet
heel
ect
roncor
rel
ati
onwhi
chi
s
appl
i
cabl
e wi
th DZP/
TZP basi
s set
s.MP2/
B3LYP/
6-31G,MP2/
B3LYP/
6-311G and
MP2/
B3PW91/
6-311Gar
edi
ff
erentmodel
susedt
hei
rresul
tsar
econsi
der
edv
erycl
ose
t
oexper
iment
al,
butf
orl
argerandcompl
exsy
stem MP2r
esul
tsar
enotr
eli
abl
e(Weav
er
etal
.,2001)
.Ont
heot
herway
,sophi
sti
cat
edmet
hodssuchasCCSD(
T)per
for
m wel
l
onusi
ngwi
tht
hebasi
sset
sofQZPqual
i
ty.CCSD(
T)-
F12i
smet
hodofhi
ghexpl
i
cit
ly
cor
rel
atedanddemandsf
orl
owqual
i
tybasi
sset
swi
thB3LYPorunr
est
ri
ctedUB3LYP
f
unct
ionalbuthav
ehi
ghi
ntegr
alr
equi
rement
.Hi
ghcosti
smaj
ori
ssuewi
tht
heuseof
sophi
sti
cat
edcor
rel
atedmet
hodscombi
nat
ionwi
thl
argebasi
sset
s;t
her
efor
e,i
tis
needt
odev
elopl
essex
pensi
vemodel
s.Pr
efer
encemet
hodi
sconsi
der
edi
mpor
tant
whi
ch gi
ves ef
fi
cientr
esul
ts wi
th smal
lbasi
s setsi
ze.CCSD(
T*)
(F12*
)/cc-
pVDZ-
F12/
B3LYPmodelof
fer
sapar
ti
cul
arl
yfav
orabl
ecompr
omi
sebet
weenaccur
acyand
comput
ati
onalcost(
Mar
ti
nandKeshar
wani
,2014)
.Forl
argesy
stems,model
sli
ke
DFT/
TZP/
B3LYPcangi
vepossi
bleout
putbyusi
ngmul
ti
lev
elappr
oach(
Gy ietal
őr .
,
2018)
.ADFT/TZP/
B3LYPmodeli
sofgr
eati
mpor
tancef
ort
hei
mpor
tantat
omsl
i
keO,
NandSf
orgeomet
ryopt
imi
zat
ionandf
requenci
escal
cul
ati
ons.Adoubl
ezet
aqual
i
ty
basi
ssetwi
th6-
31Gi
ssi
gni
fi
cantf
oral
ltheat
omsexceptFe,whi
chcanbedescr
ibed
wi
thanLACVPbasi
sset( ooretal
Ghaf .,
2019)
.