Importance of electron correlation effects and basis set superposition error in calculations of interaction energies and interaction-induced electric properties in hydrogen-bonded complexes: a model study

REGULAR ARTICLE
Impo ance o elec on co ela ion e ec s and basis se
supe posi ion e o in calcula ions o in e ac ion ene gies
and in e ac ion-induced elec ic p ope ies in hyd ogen-bonded
complexes: a model s udy
Angelika Ba anowska •Be a Fe na
´ndez •
And zej J. Sadlej
Recei ed: 17 June 2010 / Accep ed: 6 Sep embe 2010 / Published online: 24 Sep embe 2010
The Au ho (s) 2010. This a icle is published wi h open access a Sp inge link.com
Abs ac A de ailed s udy o he in e ac ion ene gies and
in e ac ion-induced elec ic dipole p ope ies in model
linea hyd ogen cyanide complexes (HCN)
m
(m=2–4) is
ca ied ou wi hin he ini e ield HF SCF, MP2, CCSD and
CCSD(T) app oxima ions using he ecen ly de eloped
LPol-n(n=ds, s, dl, l) basis se s. The impo ance o
high-o de co ela ion e ec s and he basis se supe posi-
ion e o is e alua ed. To co ec o he la e is c ucial o
ob aining accu a e in e ac ion ene gy alues, bu he e o
can sa ely be neglec ed in he es ima ion o induced elec-
ic p ope ies when he LPol-n(n=ds, s, dl, l) basis se s
a e used. Co ela ion e ec s a e impo an in he e alua ion
o bo h he in e ac ion ene gies and he induced elec ic
p ope ies o he sys ems.
Keywo ds Ab ini io calcula ions LPol-n(n=ds, s, dl,
l) basis se s Fini e ield app oxima ion In e ac ion-
induced elec ic p ope ies In e ac ion ene gy 
Hyd ogen cyanide complexes
1 In oduc ion
O e he decades, hyd ogen-bonded complexes ha e been
he subjec o de ailed heo e ical and expe imen al in es-
iga ions due o he ole hey play in chemical eac ions and
biological sys ems. Highly accu a e and hus ully eliable
heo e ical alues o in e ac ion ene gies and in e ac ion-
induced p ope ies can be ob ained wi hin he coupled
clus e singles and doubles including connec ed iples
co ec ions me hod (CCSD(T)) [1] combined wi h su i-
cien ly la ge and di use se s o basis unc ions. Howe e ,
he CCSD(T) me hod scales wi h he numbe o basis
unc ions Nas N
7
, and hus i s compu ing cos s ongly
delimi s he size o sys ems ha can be in es iga ed. The
high compu a ional cos o he CCSD(T) me hod s ill
emains an issue despi e o he as de elopmen o com-
pu ing esou ces and algo i hms. The p oblem can be
ackled ei he h ough a educ ion in he alue o N, i.e.,
using smalle basis se s o h ough a dec ease in he powe
o N, i.e., using a lowe cos me hod. Bo h solu ions a e
commonly used in heo e ical in es iga ions. The main
d awback o using smalle basis se s o lowe quali y
me hods lies in he ac ha hey may no be lexible
enough o desc ibe he sub le in e molecula in e ac ions.
Conside ing he basis se size p oblem, e icien educed-
size basis se s designed o calcula ions o pa icula ype
o p ope ies a e de eloped. Such p ope y-o ien ed basis
se s, al hough no able o desc ibe all he p ope ies o a
sys em as accu a ely as la ge all-pu pose basis se s,
Published as pa o he special issue celeb a ing heo e ical and
compu a ional chemis y in Spain.
P o . And zej J. Sadlej, 1941–2010.
Elec onic supplemen a y ma e ial The online e sion o his
a icle (doi:10.1007/s00214-010-0817-4) con ains supplemen a y
ma e ial, which is a ailable o au ho ized use s.
A. Ba anowska (&)
Ins i u e o Physics, Kazimie z Wielki Uni e si y,
Plac Weyssenho a 11, 85072 Bydgoszcz, Poland
e-mail: [email p o ec ed]
B. Fe na
´ndez
Depa men o Physical Chemis y and Cen e o
Resea ch in Biological Chemis y and Molecula Ma e ials,
Uni e si y o San iago de Compos ela,
15782 San iago de Compos ela, Spain
e-mail: [email p o ec ed]
A. J. Sadlej
Depa men o Quan um Chemis y, Facul y o Chemis y,
Nicolaus Cope nicus Uni e si y, Gaga ina 7,
87100 To un
´, Poland
123
Theo Chem Acc (2011) 128:555–561
DOI 10.1007/s00214-010-0817-4
compe e wi h hese in he e alua ion o he gi en class o
p ope ies o which hey a e designed.
The idea o basis se s ailo ed o calcula ions o
pa icula p ope ies da es back o 1937 and o he London-
ype o bi als (LAOs) [2]. Ano he example o p ope y-
o ien ed basis se s is he so-called pola ized basis se s
(Pol se s) de eloped o calcula ions o elec ic p ope ies
and o igina ing om a simple physical model o a ha -
monic oscilla o embedded in an ex e nal elec ic ield [3].
Pola ized se s ha e long adi ion and span om he
pionee Pol basis se s [4–6], h ough he compac ZPol se s
[7–9], o he ecen ly epo ed LPol basis se s [10]. The
ZPol basis se s a e ecommended o mode a ely accu a e
calcula ions o linea elec ic p ope ies in la ge molecula
sys ems [7–9]. The LPol se s ha e been shown o compe e
wi h he much la ge Dunning’s se s in he e alua ion o
elec ic p ope ies and o speci ic op ical o a ion in o ganic
molecules [10–12].
In e ac ion ene gies and induced p ope ies in la ge
hyd ogen-bonded complexes a e o en e alua ed using
second-o de Mølle –Plesse pe u ba ion heo y (MP2)
[13] ha scales as N
5
. Addi ionally, he basis se size is
kep as small as possible, conside ing he aimed accu acy.
Howe e , i should be s essed ha he neglec ion o
highe -o de elec on co ela ion con ibu ions, especially
in he e alua ion o non-linea induced elec ic p ope ies,
may cause a signi ican de e io a ion in he esul s. This
canno be igno ed when a highly accu a e es ima ion o he
e ec s is equi ed. I is hus o g ea impo ance o es ima e
he limi s o applicabili y o MP2 o o he lowe -o de
app oxima ions in he e alua ion o induced p ope ies in
hyd ogen-bonded sys ems.
An addi ional p oblem in he e alua ion o in e ac ion
ene gies and p ope ies is he basis se supe posi ion e o
(BSSE), p esen in all calcula ions ca ied ou wi hin he
supe molecula app oach. The co ec ion o i is manda o y
in he majo i y o he cases whe e high accu acy is equi ed.
This means a conside able inc ease in compu ing demands
ha ge s la ge wi h he numbe o monome s p esen in he
molecula complex. The minimiza ion o his e o is also a
challenge in he de elopmen o new basis se s.
In he p esen s udy, we employ he LPol-n(n=ds, s,
dl, l) se s and ou le els o heo y, namely HF SCF, MP2,
CCSD and CCSD(T), o he calcula ion o he non-ze o
componen s o he induced elec ic p ope ies (up o he
induced elec ic dipole second hype pola izabili y) in he
linea (HCN)
m
(m=2–4) complexes. Addi ionally, we
e alua e he in e ac ion ene gies. The linea (HCN)
m
clus e s ha e been he subjec o nume ous heo e ical and
expe imen al in es iga ions. He e, we gi e a b ie sum-
ma y o hose mos ele an o ou wo k. The heo e ical
s udies used mainly he HF SCF and he MP2 app oxi-
ma ions [14,15]. King e al. [14] e alua ed he
in e molecula ene gies o he linea (HCN)
m
(m=2–7)
clus e s. They used he RHF and he MP2 me hods wi h a
6-31?G* basis se . The dipole momen s o he complexes
we e also ob ained. The esul s we e only pa ially co -
ec ed o he BSSE; he au ho s claimed ha he coun-
e poise co ec ions a e physically ealis ic a he SCF
le el, bu un eliable a co ela ed le els.
In 1998, a po en ial unc ion o he (HCN)
2
clus e was
de eloped using he IMPT me hodology [16]. The p op-
e ies o he ene gy minima a e epo ed o he (HCN)
2
and he (HCN)
3
clus e s, oge he wi h HF and MP2
numbe s o he dime . The 6-311G** and a 5S4P2D/3S2P
basis se s we e used. The au ho s used he po en ial o
s udy la ge complexes.
The dime in e ac ion ene gy was ecen ly e alua ed by
Li e al. [17] a he MP2/aug-cc-pVTZ le el. The epo ed
alue was 4.696 kcal/mol. All he esul s we e coun e -
poise co ec ed.
Ri elino e al. [18] used a hie a chy o me hods (HF,
MP2, MP3, MP4, CCSD and CCSD(T)) and up o he aug-
cc-pVTZ basis se o e alua e he (HCN)
2
in e ac ion
ene gy. Fo he (HCN)
3
and he (HCN)
4
complexes, hey
employed a smalle basis se , i.e., he 6-311??G(d,p), bu
he (HCN)
2
esul s show ha he di e ences be ween he
aug-cc-pVTZ basis se esul s and hose ob ained wi h he
smalle basis se a e signi ican (a ound 0.5 kcal/mol).
Coope a i i y alues a e also epo ed. Wi h he MP2 and
he smalle basis se , hey e alua ed he coope a i i y
e ec s on he dipole momen s o he (HCN)
m
(m=2–7)
complexes.
Se e al densi y unc ional s udies a e also a ailable (see
o example Re . [19] and e e ences ci ed he ein). In Re .
[19], he (HCN)
m
complexes wi h mup o 10 a e s udied
and in e ac ion dipole momen s and pola izabili ies we e
e alua ed wi h a 6-311G??3d3p basis se and he BPW91
unc ional, bu he esul s a e a om accu a e. No a en-
ion has been paid o o he elec ic p ope ies.
The mos ele an expe imen al pape s o ou pu poses
a e he ollowing. The wo k by Bha acha ya and Go dy,
whe e he HCN dipole momen in he g ound ib a ional
s a e is calcula ed as 2.985 ±0.005 D [20]. The ib a ional
g ound-s a e o a ional spec oscopic cons an s and he
s uc u e o he HCN dime we e ob ained by Bux on e al.
[21], ha epo ed a non-linea ib a ionally a e aged
s uc u e and a well dep h o he po en ial o 4.4 kcal/mol.
The (HC15NÞ2dime elec ic dipole momen in he ib a-
ional g ound s a e has been measu ed by Campbell and
Kukolich as 6.552(35) D [22], which esul ed in an in e -
ac ion dipole momen o 0.77 D. The s uc u e o he linea
(HC15NÞ3 ime was de e mined om he mic owa e
spec a o 22 iso opic species [23]. The dipole momen was
ound as 10.6(1) D and he in e ac ion dipole as 1.8 D.
556 Theo Chem Acc (2011) 128:555–561
123
Wi h he use o he LPol-n(n=ds, s, dl, l) bases in he
s udy o he (HCN)
m
(m=2–4) complexes, we plan o
check he pe o mance o he new de eloped basis se s in
he e alua ion o in e ac ion ene gies and induced elec ic
p ope ies in hyd ogen-bonded complexes, h ough he
es ima ion o he coun e poise co ec ion and he e o
in oduced in he calcula ions wi h he use o MP2
app oxima ion.
The p esen pape is o ganized as ollows. Some ele-
an de ini ions and he compu a ional de ails a e gi en in
Sec . 2. Sec ion 3 epo s he esul s and discussion, and in
Sec . 4we summa ize and conclude.
2 De ini ions and compu a ional de ails
We conside he linea (HCN)
m
(m=2–4) complexes,
aligned along he z-axis o he Ca esian coo dina e sys em.
The HCN bond dis ances a e chosen equal o hose epo ed
by Ca e e al. [24] o an isola ed HCN molecule, i.e.,
R
HC
=1.06501(8) A
˚and R
CN
=1.15324(2) A
˚. The in e -
molecula hyd ogen bond dis ances a e adop ed om he
ecen wo k by Ad ian–Sco o and Vasilescu [19]. The
comple e se o molecula pa ame e s is epo ed in Table 1.
In e ac ion ene gies can be e alua ed using di e en
me hods. In he p esen in es iga ion, we employ he so-
called supe molecula app oach ha de ines he in e ac ion
ene gy o a dime , DEAB, as he di e ence be ween he
ene gy o he complex, E
AB
, and he ene gies o i s sub-
uni s, E
A
and E
B
:
DEAB ¼EAB EAEB:ð1Þ
We co ec all he esul s o he BSSE using he coun-
e poise co ec ion by Boys and Be na di [25], i.e., bo h he
ene gy o he complex and he ene gies o he monome s
a e calcula ed in he basis se o he dime . De ini ion (1)
can be gene alized o he case o he induced elec ic dipole
p ope ies by eplacing Ewi h P=l,a
ab
,b
abc
, e c.
(a,b,c,…=x,y,z).
In e ac ion ene gies and in e ac ion-induced p ope ies
in la ge ABNcomplexes a e calcula ed he e using he
si e–si e coun e poise me hod, as he espec i e di e ences
in he ene gy o elec ic p ope y o he complex and he
ene gies o elec ic p ope ies o all Nsubsys ems:
DPABN¼PABNX
N
i¼A
Pi:ð2Þ
The ene gies and he elec ic p ope ies o he monome s
a e calcula ed in he basis se o he complex.
We e alua e he in e ac ion ene gies, he induced dipole
momen and all non-ze o componen s o he induced dipole
pola izabili y and i s and second hype pola izabili ies in
he in es iga ed sys ems wi hin he HF SCF and he co -
ela ed (MP2, CCSD and CCSD(T)) app oxima ions. All
ou a ailable LPol-n(n=ds, s, dl, l) basis se s a e
employed in he s udy.
The LPol-nbases [10] belong o he amily o he
pola ized se s de i ed by Sadlej and co-wo ke s o e he
las decades [4–9]. The Pol se amily, including he ZPol
and he LPol se s, is designed o calcula ions o elec ic
p ope ies in molecula sys ems. The idea o hese pola -
ized se s exploi s a simple physical model o a ha monic
oscilla o pe u bed by an ex e nal s a ic elec ic ield [3].
The esemblance o he solu ions o he ha monic oscilla o
Sch o
¨dinge equa ion o he commonly used Gaussian- ype
o bi als in ab ini io and DFT calcula ions leads o he
model o gene a ion o he pola iza ion unc ions aug-
men ing a p ope ly chosen sou ce se o basis unc ions.
Recen ly, he model has been gene alized o he case o a
dynamic elec ic ield pe u ba ion [26], which esul ed in
he de elopmen o he LPol-nbasis se s [10].
Fo an isola ed sys em (F=0, wi h Fdeno ing he
Ca esian ec o o he homogeneous s a ic elec ic ield),
each p imi i e Gaussian- ype o bi al (GTO) {G
l,l
( ;R
l
(0), a
l
)} is a unc ion o he elec on coo dina e ec o and
is ully de ined by i s o igin R
l
(0), o bi al exponen a
l
and
he angula momen um quan um numbe l. In he p esence o
an elec ic ield, he GTOs become ield dependen ,
Gl;lð ;Rlð0Þ;alÞ!Gl;lð ;RlðFÞ;alÞ:ð3Þ
Thus, he eigen ec o u( ;0), being a linea combina ion o
GTOs, becomes a unc ion o he elec ic ield h ough he
basis se unc ions and he expansion coe icien s,
uð ;0Þ!uð ;FÞ¼X
l
clðFÞGl;lð ;RlðFÞ;alÞ:ð4Þ
The i s -o de pe u bed unc ion u
(1)
( ;0), e e ed o as
he i s -o de pola iza ion unc ion, can be w i en as [7,26]:
uð1Þð ;0ÞX
1
n¼1
bnð ð1Þ
nþ ð1Þ
nþÞ;ð5Þ
wi h
ð1Þ
n¼X
l
clð0Þanþ11=2
lGl;l1ð ;Rlð0Þ;alÞ;ð6Þ
and is added o he sou ce basis se {G
l,l
( ;R
l
(0), a
l
)}. The
pola iza ion unc ion con ac ion coe icien s a e ob ained
Table 1 In e molecula hyd ogen bond dis ances in he (HCN)
m
(m=2–4) complexes
nR
H_N
R
H_N
R
H_N
2 2.269
3 2.204 2.193
4 2.185 2.127 2.171
All alues epo ed in A
˚. Monome bond dis ances a e R
HC
=1.06501
A
˚and R
CN
=1.15324 A
˚
Theo Chem Acc (2011) 128:555–561 557
123
om he ield–independen GTO con ac ion coe icien s
h ough he simple scaling gi en by Eq. 6. The o al size o
he esul ing pola ized se is educed h ough (1)an
app op ia e con ac ion o he inne mos o bi als, (2)
gene a ion o he pola iza ion unc ions only o he
alence o bi als and o he ou e mos p imi i e GTOs, i.e.,
hose a o ed by he scaling de ined by Eqs. 6and 3
assuming ha he majo i y o he unc ions co esponding
o he
n-
componen s o (5) a e al eady p esen in he
ini ial se o GTOs.
In gene al, pola ized se s can be gene a ed om any se
o GTOs. Howe e , he quali y o he sou ce se o unc-
ions de e mines o a la ge ex en he quali y o he
esul ing pola ized basis se , and hus he sou ce se should
be ca e ully chosen. In he case o he LPol-nbases, he
sou ce se was chosen o be he an Duijne eld
13s8p(10s o hyd ogen) basis se [27], addi ionally aug-
men ed wi h one di use s- and one di use p- ype unc ions
o a 14s9pse (one di use s- ype unc ion o a 11sse o
hyd ogen) o inc ease he lexibili y o he sou ce se . The
esul ing ini ial se was con ac ed a e ca e ul a omic es s
and augmen ed wi h he i s - (ds and dl bases), o he i s -
and second-o de ( s and l bases) pola iza ion unc ions.
Due o he size o he in es iga ed sys ems and o he
employed basis se s, he ini e ield app oxima ion is used
in he e alua ion o he induced elec ic p ope ies. Elec ic
ields a e loca ed in he zand he xdi ec ions. In wide
in oduc o y es s pe o med in ou ea lie s udy [10],
elec ic ield s eng hs o 0.005 and 0.010 au we e ound o
be op imal o he calcula ion o linea and non-linea
elec ic p ope ies o an isola ed HCN molecule. He e, we
use he same ield s eng h alues. Pe pendicula ly aligned
elec ic ields a e used in he calcula ion o he mixed
enso ial componen s o he elec ic hype pola izabili ies.
The coupled clus e LPol- l calcula ions o o he han he
axial componen s o he induced p ope ies a e ound o be
oo demanding o he (HCN)
4
complex.
All calcula ions ha e been ca ied ou using he
MOLCAS 6.5 and 7.4 package [28,29]. In he ollowing,
only a limi ed numbe o he esul s is p esen ed, hose
c ucial o a comp ehensi e analysis and discussion o he
esul s. The comple e se o esul s is a ailable in he
Suppo ing In o ma ion.
3 Resul s and discussion
We s a he discussion wi h he s udy o he esul s o he
basis se dependence o he induced elec ic p ope ies and
he in e ac ion ene gies in he in es iga ed complexes. The
esul s o he coun e poise-co ec ed CCSD(T) ini e ield
calcula ions a e p esen ed in Table 2. I can be seen ha he
in e ac ion-induced elec ic dipole momen alues a e s a-
ble in all ou LPol-n(n=ds, s, dl, l) se s wi h di e -
ences smalle han 0.5%. The MP2/6-311??G(d,p) esul s
o Ri elino e al. [18] o he n=2, 3, 4 clus e s a e well
bellow ou MP2 alues, maybe due o he basis se hey
use. And ou alues conside ably imp o e hose calcula ed
by Ad ian-Sco o and Vasilescu [19], bo h wi h espec o
me hod and basis se s. Fo he HCN dime , all ou heo-
e ical esul s ag ee well wi h he expe imen ally de e -
mined alue (0.303 au [22]). Al hough one has o conside
ha he ab ini io esul s e e o he s udied linea con igu-
a ion, and he expe imen al alues bea he e ec s o he
ze o-poin ib a ions. Fo he ime , ou alue is 0.022 au
bellow he expe imen al alue in Re . [23].
Any o he LPol-n(n=ds, s, dl, l) se s can also be
used in eliable e alua ions o he induced pola izabili y
componen s and he zzz-componen o he induced i s
hype pola izabili y. Changes in Daaa and Dbzzz alues
calcula ed wi h he di e en LPol-nse s a e well below 1%
o all in es iga ed sys ems. Also he alues o Dczzzz in he
dime and in he ime a e s able in all basis se s. In he
e ame , Dczzzz changes up o almos 5% wi h he inc ease
in he basis se size. O he componen s o he induced i s
and second hype pola izabili ies a e sub le , and hei
eliable es ima ions a e a mo e challenging. A basis se o
a leas LPol- s quali y is manda o y in eliable calcula ions
o Dbzxx. The es ima ion o he Dcxxxx and Dcxxzz alues is
mo e demanding.
In he case o he in e ac ion ene gies, he ds and he dl
bases gi e esul s ha di e abou 3% om he s and l
basis se esul s. Fo he HCN dime , he ds and he dl
in e ac ion ene gies a e close o he expe imen al alue
(po en ial well dep h o -4.40 kcal/mol, Re . [21]) han he
s and l. This conclusion has o be aken wi h cau ion,
conside ing he abo e-men ioned di e ences be ween he
expe imen al and he heo e ical geome ies. The bes
p e iously a ailable heo e ical esul [18], ob ained wi h
he CCSD(T) me hod and he aug-cc-pVTZ basis se , is
close o he s and l esul s han o he ds and dl. F om
Re . [18], we can es ima e CCSD(T) aug-cc-pVTZ in e -
ac ion ene gies o he n=3 and n=4 complexes as
-10.11 and -15.97 kcal/mol, espec i ely. We do his
by co ec ing he MP2/6-311??G(d,p) esul s wi h he
6-311??G(d,p) CCSD(T) – MP2 and he CCSD(T) aug-
cc-pVTZ – 6-311??G(d,p) di e ences ob ained o he
dime , by adding hem, and scaling he esul by a ac o o
2 in he case o he ime , and o 3 o he e ame .
We now u n ou a en ion o he analysis o he o de o
magni ude o he in e ac ion-induced e ec s. In his ana-
lysis, we e e o he LPol- l esul s, and whe e e hose a e
no a ailable, o he LPol- s alues. The induced dipole
momen in he dime is equal o 0.293 au. Addi ion o he
558 Theo Chem Acc (2011) 128:555–561
123
nex hyd ogen cyanide molecule inc eases his alue by
0.393 au, i.e. o e 130%. This ag ees well wi h he
expe imen ally de e mined enhancemen (0.405 au [22,
23]), bu as poin ed ou abo e, a quan i a i e compa ison o
expe imen is no s aigh o wa d. The induced dipole
momen in he e ame is equal o 1.121 au, abou
3.8 imes la ge han ha in he dime . An analogous
enhancemen is obse ed o he zz-componen o he
induced elec ic dipole pola izabili y, he induced e ec
changes om 4.5 au in he dime , h ough 10.5 au in he
ime , o 17.2 au in he e ame . In he case o he xx-
componen o he induced pola izabili y, he addi ion o he
hi d HCN molecule o he dime causes an inc ease o he
induced e ec in he o de o 120%. The xx-componen o
he induced pola izabili y in he e ame is almos
3.5 imes la ge han ha in he dime .
The obse ed enhancemen o he induced e ec s in he
ime and in he e ame is e en mo e p onounced in he
case o Dbzzz and Dczzzz. Addi ion o he hi d HCN
molecule o he dime inc eases he in e ac ion-induced
e ec s abou 2.5 imes. The induced e ec s in he e ame
a e abou 4.3 and 4.5 imes la ge han in he dime o
Dbzzz and Dczzzz, espec i ely. Dbzxx in he ime ( e ame )
is app oxima ely 1.8 (2.6) imes la ge han in he dime .
The in e ac ion ene gy g ows wi h an inc easing numbe
o HCN molecules simila ly o Daxx, namely he in e ac ion
ene gy in he ime is app oxima ely 2.2 imes la ge han
in he dime , and in he e ame app oxima ely 3.5 imes
la ge han in (HCN)
2
.
Table 3 epo s he coun e poise-co ec ed MP2/LPol- l
and CCSD(T)/LPol- l induced elec ic p ope ies and
in e ac ion ene gies in he in es iga ed complexes. The
MP2 app oxima ion sys ema ically unde es ima es he
induced elec ic p ope ies and o e es ima es he in e ac-
ion ene gy in he s udied sys ems. The di e ences be ween
he CCSD(T) and he MP2 esul s a e in he o de o 2.5%
o Dl, 4% o Dazz and DE, 3% o Dbzzz and o e 5% o
Dczzzz. Conside ing his, we can conclude ha he CCSD(T)
me hod is necessa y in o de o ge accu a e in e ac ion
p ope ies and ene gies. The ag eemen be ween he MP2
and he CCSD(T) esul s is much be e in he case o Daxx.
In Table 4, we epo he coun e poise-co ec ed and
non-co ec ed CCSD(T)/LPol- l esul s. The coun e poise
co ec ion o he esul s p o es o be manda o y in he case
o he in e ac ion ene gies, whe e he non-co ec ed alues
a e o e es ima ed by o e 20%. Such a la ge e o is
obse ed o all in es iga ed basis se s and a all co ela ed
le els o heo y (see Table IX in he Suppo ing In o ma-
ion). Fo he CCSD(T)/LPol- l in e ac ion-induced elec ic
p ope ies, he BSSE p o es o be well below 1%, and hus
i can be sa ely neglec ed. A simila end in he size o he
BSSE is obse ed o he o he LPol-n(n=ds, s, dl) se s
and all employed le els o heo y (see he Suppo ing
In o ma ion).
4 Summa y
We in es iga e he in e ac ion ene gies and induced (linea
and non-linea ) elec ic dipole p ope ies in he linea
(HCN)
m
(m=2–4) complexes. Calcula ions a e pe o med
wi hin he HF SCF, MP2, CCSD and CCSD(T) le els o
Table 2 Coun e poise-co ec ed CCSD(T) ini e ield in e ac ion-induced s a ic elec ic dipole p ope ies and in e ac ion ene gies o he (HCN)
m
(m=2–4) complexes
nLPol-ds LPol- s LPol-dl LPol- l LPol-ds LPol- s LPol-dl LPol- l LPol-ds LPol- s LPol-dl LPol- l
DlDazz Daxx
2 0.292 0.293 0.292 0.293 4.47 4.50 4.47 4.50 -0.96 -0.96 -0.95 -0.96
3 0.683 0.686 0.684 0.686 10.45 10.51 10.46 10.52 -2.11 -2.13 -2.10 -2.12
4 1.116 1.120 1.117 1.121 17.09 17.20 17.12 17.21 -3.33 -3.35 -3.31 –
Dbzzz Dbzxx Dczzzz
2 37.3 37.2 37.3 37.3 0.9 1.2 1.1 1.2 1.54 1.70 1.54 1.55
3 94.1 94.0 94.1 93.9 1.9 2.1 2.0 2.2 3.90 3.87 3.90 3.90
4 160.5 160.2 160.7 160.2 2.5 3.1 3.0 – 6.68 6.98 6.62 6.91
Dcxxxx Dcxxzz DE
2-0.33 -0.43 -0.32 -0.33 0.01 0.10 -0.01 0.04 -4.39 -4.49 -4.41 -4.51
3-0.73 -0.60 -0.72 -0.93 -0.03 0.08 -0.03 -0.11 -9.77 -10.02 -9.83 -10.07
4-1.11 -1.26 -1.15 – -0.03 -0.03 -0.09 – -15.49 -15.90 -15.59 -15.98
The induced elec ic dipole momen , pola izabili y and i s hype pola izabili y in au, he induced elec ic dipole second hype pola izabili y in
10
3
au and he in e ac ion ene gies in kcal mol
-1
Theo Chem Acc (2011) 128:555–561 559
123

app oxima ion using he LPol-n(n=ds, s, dl, l) se s. The
elec ic p ope ies a e e alua ed using he ini e ield
me hod. The MP2 me hod is shown o sys ema ically
unde es ima e he induced elec ic p ope ies and o e es-
ima e he in e ac ion ene gies. The MP2 esul s di e om
he CCSD(T) alues by as much as 2.5% o he induced
dipole momen , 4% o Dazz and DE, 3% o Dbzzz and o e
5% o Dczzzz. Thus, in o de o ob ain accu a e in e ac ion
ene gies and/o elec ic p ope ies one needs o eso o he
CCSD(T) le el o app oxima ion. The coun e poise co -
ec ion p o es o be manda o y in he e alua ion o he
in e ac ion ene gies o he in es iga ed sys ems, whe e he
BSSE is in he o de o 20%. The induced elec ic p o-
pe ies a e a less sensi i e o he BSSE, wi h he e o s
well below 1%. This will imply a conside able sa ing in
compu ing ime when e alua ing in e ac ion p ope ies in
la ge complexes. A eliable es ima ion o he induced
dipole momen s, pola izabili ies and i s hype pola iz-
abili ies in linea hyd ogen cyanide complexes can be done
using he smalles among he LPol-nse s, he LPol-ds basis
se , p ac ically wi h no de e io a ion o he esul s. The
in e ac ion-induced second hype pola izabili ies a e mo e
demanding, and basis se s o LPol- s o LPol- l quali y a e
necessa y o an accu a e e alua ion.
Acknowledgmen s This wo k was suppo ed by he Spanish
Minis e io de Ciencia e Inno acio
´n (CTQ2008-01861/BQU p ojec ),
he Xun a de Galicia and FEDER (Axuda pa a Consolidacio
´ne
Es uc u acio
´n de Unidades de In es igacio
´n Compe i i as do Sis ema
Uni e si a io de Galicia 2007/050, and 2007-2013 and INCITE09 314
252 PR p ojec s), and by he Founda ion o Polish Science wi hin he
Homing Plus p og amme (Homing Plus/2010-1/2), co inanced om
Eu opean Regional De elopmen Fund wi hin Inno a i e Economy
Ope a ional P og amme. The In o ma ion&Communica ion Technol-
ogy Cen e o he NCU To un
´and he Cen o de Supe compu acio
´nde
Galicia (CESGA) a e acknowledged o compu a ional esou ces.
Open Access This a icle is dis ibu ed unde he e ms o he
C ea i e Commons A ibu ion Noncomme cial License which pe -
mi s any noncomme cial use, dis ibu ion, and ep oduc ion in any
medium, p o ided he o iginal au ho (s) and sou ce a e c edi ed.
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