Ab initio prediction of the rovibrational levels of the He-CO+ ionic complex

HAL Id: hal-00823746

https://hal.archives-ouvertes.fr/hal-00823746

Submitted on 17 May 2013

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Ab initio prediction of the rovibrational levels of the He-CO+ ionic complex

M. Mladenovic, Marius Lewerenz

To cite this version:

M. Mladenovic, Marius Lewerenz. Ab initio prediction of the rovibrational levels of the He-CO+

ionic complex. Molecular Physics, Taylor & Francis, 2013, pp.1. �10.1080/00268976.2013.783722�.

�hal-00823746�

Vol.00,No.00,Month2013,128

RESEARCH ARTICLE

Ab initio predition of the rovibrational levels of the He-CO

+

ioni omplex

MirjanaMladenovi¢

a∗

andMariusLewerenz

a a

UniversitéParis-Est,LaboratoireModélisation etSimulation MultiEhelle, MSME

UMR8208 CNRS,5bdDesartes, 77454Marne la Vallée, Frane

(January2013)

Theintermoleularpotentialforthe vanderWaalsomplexofthearbon monoxideation

with heliumisstudied bymeansof the partiallyspinadapted oupled lusterRCCSD(T)

method and the aug--pVXZ family of basis sets. In the ground eletroni state, or-

related with the lowest eletroni asymptote X²Σ^{+ of the monomer CO+, the omplex}

He(

1S^)-CO+(2Σ^{+)hasa nonlinear}equilibrium struturewithaJaobi angleofabout46

◦

andabindingenergyofabout275m

−1

.FortheomplexHe(

1S^)-CO+(A²Π^)wendequi-

libriumJaobianglesof78

◦

and90

◦

andeletronibindingenergiesofabout160m

−1

and

303m

−1

fortheA^′′andA^{′omponents,}respetively,oalesingintotheΠ^{stateatlinearity.}

Two-dimensionalintermoleularpotentialenergysurfaesareonstrutedforthegroundele-

tronistateandusedtoomputerotation-vibrationstatesuptoJ= 10^{withthenumerially}

exat disrete variable representation (DVR)tehnique.TheHe-CO

+

omplexisfound to

have19boundeven-parityJ= 0^{statesand16boundodd-parity}J= 1^{statesandtoexhibit}

strongangular-radialouplingandquasilinearbehaviour.

Keywords:moleularions;vanderWaalsomplex;arbonmonoxideation;helium;

rovibrationalstruture;abinitioalulation;eletriproperties;quadrupolemoment

1. Introdution

Carbon monoxide isa relatively abundant moleule ininterstellar spae, where its

positive ion CO

+

has also been identied [1, 2℄. Even before its laboratory ob-

servation the

A

²

Π − X

²

Σ

^{+ system in CO+ was observed in the tail of a omet}

[3 , 4℄ and is still known as 'omet-tail bands'. CO

+

was the rst moleular ion

for whih a mirowave spetrum was reorded [5℄. Low energy ollisions of CO

+

with its seond most abundant ollision partner in spae, helium atoms, are gov-

ernedbytheweakintermoleularinterationleading tothevanderWaalsomplex

He-CO

+

. Evidenefor the formation ofthis omplex has been observed inseveral

ion drift tube experiments: onventional measurements at room temperature [6℄,

laser-indued uoresene measurements from various initial rotational states at

305K [7 ℄, and ion drift tube measurements at very low temperatures [8℄. No high

resolution spetraldatahave everbeen reported forthis omplex.

The relatively strong binding between CO

+

and heliumatoms should allowthe

reation ofmixedlustersof theompositionHen^-CO+

indrifttubesormixedgas

expansionsoupledtoeletridisharges.Thelattertehniquehasbeensuessfully

applied in a series of elegant spetrosopi experiments on the energetially very

∗

Correspondingauthor.Email:mladenovuniv-mlv.fr

ISSN:0026–8976print/ISSN1362–3028online

^{2013Taylor&Franis}

DOI:10.1080/0026897YYxxxxxxxx

2 Mladenovi¢andLewerenz

similar Hen^-N+

2 ^{omplexes[912℄,where size seletedhighresolution spetraould}

be reorded. High resolution infrared spetrosopy of Ar-N

+2 ^{reated in a plasma}

slit jet experiment has been reently reported [13℄ indiating the possibility of an

infrared experiment on He-CO

+

.

Hen^-CO+

lusters appearto be an ideal target for luster size spei high res-

olution depletion spetrosopy. Both mirowave and infrared experiments would

prot from the large permanenent dipole moment and large vibrational transition

moments ofthis system.Experiments onthis type oflusterwouldhelpus to bet-

ter understand mirosopi superuidity [14 ℄ byexpliit ontrol ofthe systemsize

and measurement ofthelustersizedependent evolution oftheeetiverotational

onstant of the CO

+

dopant. Neutral CO moleules embedded into large helium

lusters have been studied theoretially [15 18℄ and experimentally by high reso-

lution spetrosopy [17,19 23℄. Reent ionization experimentson CO doped large

heliumlustersdidnotyieldanyindiationfortheformationofHen^-CO+

fragments

whereas speiesof the type Hen^-(CO)+

m ^{werereadily observed [24℄. TheCO/CO}+

pair inside heliumis ofpartiular interestfor high resolution experimentsbeause

the rotationalonstantsofbothspeiesareverysimilarwhiletheirinterationwith

helium atoms isofvery dierent strength.Theoretial and experimental studiesof

Hen^-CO+

an make amajor ontribution to this eld.

The He-CO

+

omplexhasbeen onlypartiallyharaterized inearliertheoretial

studies[24 28℄.Hamiltonetal.[25 ℄employedunrestritedHartree-FokandMøller-

Plesset perturbation theory to fourth order (MP4) to study linear and T-shaped

arrangements for the groundand rst exited eletroni states. For linearand T-

shaped He-CO

+

in the ground eletroni state, Lotrih and van der Avoird [27℄

tested a newmethodfor thedeterminationof interationenergies ofationi om-

plexesfrominterationenergiesandvertialionizationpotentialsofneutralspeies.

Salazar etal.[28℄usedspinunrestritedopen-shell oupledlustertheoriesinom-

binationwiththe-pVTZbasissetplusbondfuntionsandidentiedbentequilib-

rium geometries witha Jaobiangle of

θ

_e

= 45

^{◦,a Jaobidistane of}

R

_e

= 2.85

^A

and a binding energy of

D

_e

= 275

^{m−1 for the ground eletroni state, whereas}

theyfound

θ

_e

= 90

^◦,

R

_e

= 2.70

^{A and}

D

_e

= 218

^{m−1 fortherstexitedeletroni}

state. A MP4potential energy surfae developed byMalagan et al. [26 ℄ wasused

in lassial trajetory alulations for thetransport ross setions of CO

+

ions in

helium gas.

The main purpose of the present study of He-CO

+

is the onstrution of an

aurate potential energy surfae and the predition and interpretation of au-

rate vibration-rotation levels whihould be heked against futuredetailed spe-

trosopi experiments. This potential surfae will serve as a building blok in

many-bodymodels for CO

+

ionsinside larger heliumlusters [29 ℄.

Ab initio alulations have been arried out with supermoleule oupled luster

tehniques inombination withthe aug--pVXZfamily ofbasis funtionsfor the

ground andrstexited eletronistates.The ounterpoise proedureofBoys and

Bernardi and extrapolations to innite basis size have been used to orret for

nite basissizeeetsonthe shapeofthesurfaeandinpartiular onthedissoia-

tionenergy andtheequilibriumgeometry (Setion2).Inadditiontothestrutural

parameters, we have also studied the spetrosopi and eletri properties of the

monomers (Setion3) and the omplex (Setion4) inthe ground and rst exited

eletronistates.TheomplexHe-CO

+

isboundbyindutionanddispersionfores,

responsiblefor long-rangeattration between thetwo monomers.Two-dimensional

(2D)intermoleularpotentialenergysurfaeshavebeenonstrutedforHe-CO

+

in

the ground eletronistate (Setion5) and are usedto alulate the rovibrational

energy spetra bya numerially exat method based on a disrete variablerepre-

R

r

µµµµ

O z

He

C

θθθθ

x

Figure1. Jaobioordinatesr, R, θ^{and theaxissystemusedforthe vander WaalsomplexHe-CO+.}

Thedipolemomentvetorµorrespondingtotheequilibriumstrutureoftheomplexisalsoshown.

sentation (Setion6). The omplex is found to belong to the lass of quasi-linear

moleules. Indiations for lowenergy resonanes arealso observed.

2. Eletroni struturealulations

The ab initio omputations have been arried out by means of the partially spin

adapted oupled-luster RCCSD(T) methodwith fulliterative treatment of single

and double exitations and perturbative orretion for triple substitutions [30?

, 31℄, as implemented in the MOLPRO quantum hemistry program pakage [32 ℄.

Thesinglyaugmentedorrelationonsistentpolarizedvalenebasissets,ommonly

labelledaug--pVXZ,havebeenused[33,34 ℄.Fullyrelaxedgeometryoptimizations

and harmoni frequeny determinations were performed by means of numerial

derivatives.

The three Jaobi oordinates

r

^,

R

^{, and}

θ

^{, shown in Figure 1, are employed to}

desribe the internal geometry of the omplex. Here,

r

^{is the bond length of the}

diatomi fragmentCO

+

,

R

isavetoroflength

R

^{runningfromthe}enter-of-mass of the diatom to the He atom, and

θ

^{is the angle enlosed by}

R

and the CO

+

axis. The Jaobi angle

θ

^{is measured from the C side of CO+, suh that}

θ = 0

^◦

orrespondsto alinearomplex withHe loserto arbon.

The interation energies of the omplex were alulated in the supermoleular

approah as

E

_int

= E

_ab

(AB) − E

_a

(A) − E

_b

(B),

⁽¹⁾

where AB, A, and B stand respetively for He-CO

+

, He, and CO

+

. The lower

index

p

ⁱⁿ

E

_p

(Q)

^{referstothebasissetofthespeies}

P

^{usedtoomputetheenergy}

E(Q)

^forthespeies

Q

^{.Theinterationenergies}

E

_int^{wereorretedforthebasisset}

superpositionerror (BSSE) bymeans of the ounterpoise orretion (CP) method

of Boys andBernardi [35℄,givingthe CPorretedinteration energy

E

_int^{CP as}

E

_int^CP

= E

_ab

(AB) − E

_ab

(A) − E

_ab

(B ),

⁽²⁾

where themonomerandomplexwavefuntionsareallomputedinthebasissetof

the omplex.The geometry optimizations were arriedout at theCP unorreted

level.

Theinteration energiesattheompletebasisset(CBS)limitwereestimatedby

4 Mladenovi¢andLewerenz

extrapolationfor the Hartree-Fok Self-Consistent Field(SCF) ontribution

E

^SCF

(X) = E

_∞^SCF

+ ae

^{−bX (3)}

and a

1/X

³ extrapolation for the orrelationpart

E

^corr

(X) = E

_∞^corr

+ c/X

³

,

⁽⁴⁾

where

X

^{denotesthebasissetardinalnumber.Inthisfashion,theestimatedtotal}

CBS energy for speiesQbeomes

E

_∞

(Q) = E

_∞^SCF

(Q) + E

_∞^corr

(Q)

⁽⁵⁾

and theinteration energy isomputed from thebest total energy estimatesas

E

_int

= E

_∞

(He − CO

⁺

) − E

_∞

(He) − E

_∞

(CO

⁺

).

⁽⁶⁾

The eletridipolemoments

µ

q ^{andeletriquadrupolemoments}

Θ

ij ^with

i, j = x, y, z

^{were obtained numerially at the RCCSD(T) level of theory by means of}

nite-eld alulations, using eld strengths of 0.001-0.00005 a.u. It is noted that

Θ

_xx

+ Θ

_yy

= −Θ

_zz ^{holdsforthequadrupolemoment}

Θ

^{,whihisatraelessseond}

momenttensor.Theeletripropertiesreportedinthepresentworkwereevaluated

withrespetto theaxissystem

x, y, z

^{shown inFigure1,where the}

z

^{-axis isalong}

the diatombond vetor

r

,the

z ∧ x

^{planeoinides withthemoleular plane, and}

the originofthe frame isat the enterof massofthe

12

C

16

O

+

unit.

The quality of our RCCSD(T) alulations was investigated by means of sev-

eralothereletroni-struture approahes,inludingtheompleteative spaeself-

onsistent eld method (CASSCF), multi-referene Rayleigh-Shrödinger seond-

order perturbationtheory(RS2)inonnetionwiththemulti-statemulti-referene

omplete ative spae perturbation theory(CASPT2), and themulti-referene in-

ternally ontrated onguration interation (MRCI) method [3739 ℄. The latter

approahes were partiularly useful for the alulation of geometri and eletri

properties of the eletronistate

2

²

A

^{′ ofthe omplex He-CO+.}

3. Monomerproperties

3.1. Carbon monoxide ation

ThegroundstateeletroniongurationofCOis

(1σ)

²

(2σ)

²

(3σ)

²

(4σ)

²

(1π)

⁴

(5σ)

^2.

Removal of an eletron from the highest energy

σ

^{orbital leads to the ground}

eletroni state

(1σ)

²

(2σ)

²

(3σ)

²

(4σ)

²

(1π)

⁴

(5σ)

^{1 ofCO+ whih is}

X

²

Σ

^+.Removal

of an eletron from the

1π

^{orbital leads to}

A

²

Π

_i ^{as the rst exited state,}

(1σ)

²

(2σ)

²

(3σ)

²

(4σ)

²

(1π)

³

(5σ)

^{2, whih is split by a spin-orbit interation on-}

stant

A

SO ^{of -117.5 m}−1

(Ref. [40℄). The singly oupied

5σ

^{moleular orbital}

of CO

+

(

X

²

Σ

^{+) isprimarily omposed ofthe}

2s, 2p

_z ^{atomi orbitals ofC, whereas}

the singly oupied

1π

^{moleular orbital of CO+(}

A

²

Π

^{) is primarily omposed of}

the out-of-bond-line

2p

_x,y ^{atomiorbital ofoxygen.}

Atomi oxygen has a

3

P

_g ^{ground state whih is split by spin-orbit interation}

into

3

P

₂ ^at

E = 0

^,3

P

₁ ^at

E = 158.265

^m−1,3

P

₀ ^at

E = 226.977

^{m−1,and has}

an ionizationlimit of150305.6m

−1

leading toO

+

(

⁴

S

_u

)

^{.Thearbonatomground}

state

3

P

_g ^{asymptote is split into 3}

P

₀ ^at

E = 0

^{, 3}

P

₁ ^at

E = 16.40

^{m−1, 3}

P

₂ ^at

E = 43.40

^{m−1. The arbon atom ionization limit is 90820.42 m−1 leading to}

0 5000 10000 15000 20000 25000 30000 35000 40000

1 1.2 1.4 1.6 1.8

E / cm-1

r(CO) / angs X ²

Σ

⁺

A ²

Π

MRCI MRCI CASPT2 RCCSD(T) RCCSD(T)

Figure2. PotentialenergyurvesfortheX²Σ^+andA²Π^{statesofCO+fromtheRCCSD(T),}three-state CASPT2,andMRCIalulationswiththeaug--pVQZbasisset.

C

+

(

²

P

_1/2

)

^{and to C+}

(

²

P

_3/2

)

^{at90883.84 m−1.Thelowest} dissoiationasymptote for CO

+

isthereforeC

+

(

²

P

_u

)

^+O

(

³

P

_g

)

^{whihorrelateswiththemoleular states}

(2,4)

(Σ

⁺

, Σ

⁻

, Σ

⁻

, Π, Π, ∆)

^.

The

2

Σ

^{+ and 2}

Π

^{urves of CO+ rossat about}

r = 1.5

^{A at an energy approx-}

imately 30000m

−1

above the potential energy minimum ofthe ground eletroni

state, as found in our CASPT2 and MRCI alulations with the basis set aug-

-pVQZ (see Figure 2). This nding is in agreement with Rydberg-Klein-Rees

urves derived by Coxon and Foster [41℄ in their deperturbation analysis of the

A

²

Π ↔ X

²

Σ

^{+ spetrosopidata.The}

Ω = 1/2

^{omponentsofthesetwostatesare}

mixed by spin-orbitoupling whihaets aidentally near-degenerate zero-order

vibration-rotation levelsin thetwo eletroni statesat energiesfar belowtheele-

troni intersetionenergy. Thisis theorigin of theperturbations observed [4143 ℄

inthe

A

²

Π(v = 0)

^{statebyrotational levelsof the}

X

²

Σ

⁺

(v = 10)

^{state,bothlying}

about 22000m

−1

abovethe minimum(Figure 1 ofRef.[41 ℄).

In the present work, we onsider the eletroni states

X

²

Σ

^{+ and}

A

²

Π

^{of CO+}

within the Born-Oppenheimer approximation, aiming only at a good zero-order

(adiabati)desription.Spin-orbitinterationanditseetonrovibrationalspetra

of CO

+

willbean important partof afuture study.

3.1.1. Results for CO

+

Strutural, spetrosopi, and eletri propertiesof the arbon monoxide ation

alulated bymeans oftheRCCSD(T) methodare reportedinTable 1alongwith

availableexperimentaldataprovided byRef.[40℄.All strutural andeletri prop-

ertieslearly exhibitsmooth andverysatisfatoryonvergene uponinreasingthe

size of thebasisset.

The theoretial values for

r

_e ^{obtained using the aug--pV5Z and aug--pV6Z}

basis sets agree within 0.0003

A for both CO

+

(

X

²

Σ

^{+) and CO+(}

A

²

Π

^{). The ex-}

ponential extrapolation for

r

_e ^{from the}

X = 3 − 6

^{data gives}

r

^∞_e ^{of 1.1166A and}

1.2459

Afor

X

²

Σ

^+and

A

²

Π

^,respetively.Theseresultsareoverestimatedbyabout

y17,201318:21MoleularPhysisartile-provera

6Mladenovi¢andLewerenz

Table1. Geometri,spetrosopi,andeletripropertiesofCO

+

(X²Σ⁺)^andCO+(A²Π)^{obtainedbytheRCCSD(T)method.The}experimentaldataintheolumndenotedbyExparetaken fromRefs.[40℄and[42℄.ThetheoretialBv ^{valuesareomputedasexpetationvalues}hBiv ^{oftherotationalonstant}B^inthevibrationalstatev^.TheabbreviationaVXZstandsforthebasis setsaug--pVXZ.Foradditionalinformation,seethemaintext.

CO

+

(

X

²

Σ

^{+) CO+(}

A

²

Π

⁾

Property aVTZ aVQZ aV5Z aV6Z Exp aVTZ aVQZ aV5Z aV6Z Exp

re^{/A 1.1225 1.1181 1.1170 1.1167 1.11514 1.2523 1.2473 1.2462 1.2459 1.24377}

T

_e^{/m−1 19801 20254 20374 20417 20733.3}

˜

ν

_1←0^{/m−1 2164.7 2183.0 2186.2 2187.7 1531.0 1539.3 1540.6 1541.4}

˜

ν

2←0^/m−1

4300.2 4336.5 4342.8 4345.8 3036.7 3053.1 3055.9 3057.5

B

0^/m−1

1.941 1.958 1.962 1.963 1.967465 1.560 1.572 1.574 1.575 1.5786

B

₁^{/m−1 1.923 1.939 1.943 1.944 1.541 1.554 1.555 1.556}

hri

₀^{/A 1.127 1.122 1.121 1.121 1.257 1.252 1.252 1.251}

hri

₁^{/A 1.135 1.130 1.130 1.129 1.269 1.264 1.263 1.263}

ω

_e^{/m−1 2192.9 2211.5 2214.7 2216.2 2214.2 1556.7 1565.0 1566.2 1566.9 1562.1}

ω

_e

x

_e^{/m−1 13.800 13.887 13.935 13.938 15.164 12.874 12.922 12.862 12.835 13.532}

ω

_e

y

_e^{/m−1 -0.177 -0.202 -0.196 -0.197 0.039 0.043 0.045 0.043}

B

_e^{/m−1 1.951 1.968 1.971 1.972 1.9772 1.569 1.582 1.583 1.584 1.5894}

α

_e

× 10

^{2 /m−1 1.875 1.890 1.891 1.891 1.896 1.847 1.865 1.862 1.861 1.942}

µ

e^/

ea

0 ^{1.030 1.033 1.034 1.035 0.315 0.310 0.309 0.309}

Θ

_zz^/

ea

²₀ ^{1.904 1.894 1.890 1.890 0.076 0.063 0.056 0.055}

Θ

xx^/

ea

²₀ ^{-0.952 -0.947 -0.945 -0.945 -0.631 -0.619 -0.614 -0.613}

Θ

_yy^/

ea

²₀ ^{-0.952 -0.947 -0.945 -0.945 0.555 0.556 0.558 0.558}