Energy levels of HCN + and DCN + in the vibronically coupled X 2 and A 2 + statesRiccardo Tarroni, Alexander Mitrushenkov, Paolo Palmieri, and Stuart Carter Citation: The Journal of Chemical Physics 115, 11200 (2001); doi: 10.1063/1.1414347 View online: http://dx.doi.org/10.1063/1.1414347 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/24?ver=pdfcov Published by the AIP Publishing

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JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 24 22 DECEMBER 2001

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Energy levels of HCN ¿ and DCN¿ in the vibronically coupledX 2P and A 2S¿ states

Riccardo Tarroni, Alexander Mitrushenkov, and Paolo PalmieriDipartimento di Chimica Fisica ed Inorganica, Universita` di Bologna, Viale Risorgimento 4,40136 Bologna, Italy

Stuart CarterDepartment of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom

~Received 30 May 2001; accepted 10 September 2001!

The X 2P andA 2S1 electronic states of HCN1 have been studied using a previously developedmethod @Carter et al., Mol. Phys. 98, 1967 ~2000!# suitable for triatomic molecules showingthree-state~Renner-Teller1vibronic! interactions.Ab initio three-dimensional diabatic potentialenergy surfaces for the2P(1 2A8,12A9) and 2S1(2 2A8) states have been computed at themultireference configuration interaction level of theory, using extended Gaussian basis sets.Additional computations were done to determine the barrier to isomerization over the three surfacesand the spin–orbit constant for the2P state. Energies, spin–orbit splittings, and rotational constantshave then been calculated for all rovibronic levels ofS and P symmetry up to 5800 cm21 forHCN1 and 4800 cm21 for DCN1. Assignments based on plots of vibrational wave functions arealso provided. These computations have been finally used to revise previous interpretations ofphotoelectron spectra. ©2001 American Institute of Physics.@DOI: 10.1063/1.1414347#

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I. INTRODUCTION

Recently we have extended the treatment of RennTeller ~RT! triatomic molecules to include the vibronic efects due to a third electronic state of appropriate symmeinteracting at bent geometries with one of the componentthe RT pair.1 Methods and programs have been checkagainst gas-phase spectroscopic data of the ethynyl radC2H, proving that it is possible to obtain, even in casesstrong interactions, agreement between theory and expment to within '20 cm21 for energies up to 5500 cm21

above the ground state.Here we shall apply the same theory and methods to

isoelectronic radical cation HCN1, which is known topresent very similar problems.2,3 Compared to C2H, theamount of experimental information is quite limited, proably due to its metastability to isomerization to HNC1. Thelargest part of these data come from photoelectspectra,4–9 of which only the most recent8,9 possess a resolution sufficient to make the comparison with theory reainformative.

The latter two of these represent very important pieof information. By using high resolution threshold photelectron spectroscopy, Wideman and White8 were able torecord 11 rotationally resolved bands for HCN1, obtaininginformation about the vibronic symmetry, the spin–orsplitting, and the rotational constants. In a more recent paElandet al.9 recorded the photoelectron spectra of HCN aDCN with a resolution better than 4.5 meV~36 cm21), al-most doubling the number of known bands.

To our knowledge, the only infrared observation avaable to date is in a Ne matrix,10 which yielded bands attributed to then1 fundamental of HCN1 and DCN1.

The first well resolved photoelectron spectra were

11200021-9606/2001/115(24)/11200/13/$18.00

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corded by Fridh and A˚ sbrink,7 which pointed out all the dif-ficulties in the interpretation of the experiment, tracing batheir origin as due to a strong vibronic interaction betwethe groundX 2P state and the first electronically exciteA 2S1 state. In this respect, the problem is very similarthat arising in C2H, where an inverted order of the statespresent.

Cederbaum and co-workers2,3 performed a theoreticaanalysis of the spectra, using a model Hamiltonian whproved to be very effective in describing the main featuresFridh and Asbrink’s HCN1 photoelectron spectrum up t4000 cm21. Hitherto it represents the only attempt to analythe complex pattern of energy levels originating from tinteraction of vibrational and electronic states in this radiion. However the assumptions of the model are quite sevsince intrastate RT coupling, CH stretching modes, andharmonicity have been neglected. The only physical featuretained in this representation are the vibronic couplingtween oneX 2P component and theA 2S1 state, and thecoupling between CN stretching and bending motion.spite of the simplicity of the Hamiltonian, they were ablereproduce very well the lowest photoelectron bandsHCN1. Their assignments have been recently confirmedWidemann and White,8 who, from the analysis of rotationacontours, were also able to infer the vibronic symmetrythe most intense photoelectron bands.

Ab initio computations are also quite scarce. Peteret al.11 calculated the pure-stretching potential energy sface ~PES! of HCN1 in the X 2P state, using single reference configuration interactions~CI! techniques. Spectroscopic constants were subsequently derived usperturbation theory. The bending potential was evalua

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TABLE I. Stationary points of the 1A8, 2A8, 1A9 surfaces of the HCN1 –HNC1 system.

RCN /bohr RCH /bohr /HCN/deg

CASSCF/cc-pVQZCASSCF/cc-pVQZ

//ICMRCI~1Q!/cc-pVQz

Energy/hartree DE/eV Energy/hartree DE/eV

1A8 surfaceHNC1(X 2S1) 2.162 63 4.097 43 0.000 292.653 379 0.00 292.897 483 0.000HCN1(X 2P) 2.312 15 2.079 71 180.000 292.604 853 1.320 292.860 825 0.998HCN1 –HNC1 saddle 2.284 16 2.285 65 79.012 292.560 261 2.534 292.817 073 2.188

2A8 surfaceHNC1(A 2P) 2.384 27 4.347 13 0.000 292.572 661 2.196 292.830 814 1.814HCN1(A 2S1) 2.171 81 2.070 35 180.000 292.604 515 1.330 292.854 315 1.175HCN1 –HNC1 saddle 2.234 44 2.529 88 61.746 292.428 890 6.109 292.688 396 5.690

1A9 surfaceHNC1(A 2P) 2.384 27 4.347 13 0.000 292.572 661 2.196 292.830 814 1.814HCN1(X 2P) 2.312 15 2.079 71 180.000 292.604 853 1.320 292.860 825 0.998HCN1 –HNC1 saddle 2.423 52 2.448 14 67.261 292.504 319 4.056 292.764 650 4.250

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only within the harmonic approximation at the computequlibrium geometry.

More recently, Botschwinaet al.12 extended the study tothe first excitedA 2S1 state by means of coupled clusttechniques, evaluating its electronic originTe , the crossingseam with the ground state and some spectroscopic paeters. However, they still restrict their computations to linegeometries, being aware of the difficulties associated wthe treatment of the bending coordinate.

This paper is organized as follows. In Sec. II we descrthe procedure adopted to calculate accurate nearly equrium diabatic energy surfaces for theX 2P andA2S states ofHCN1. We also calculate the spin–orbit matrix elements athe transition state energies for the HCN1→HNC1 isomer-ization. In Sec. III we perform the variational calculationthe rovibrational levels of HCN1 and DCN1. Finally in Sec.IV we revise previous assignments of photoelectron spec

II. DIABATIC POTENTIAL ENERGY SURFACES

A. HCN¿\HNC¿ isomerization

This preliminary computation was performed in orderestablish a valid range of coordinates for the thrdimensional mapping of the HCN1 PES’s. Previous computations put the transitions state for the HCN1 – HNC1

isomerization on the lowest 1A8 surface at 1.15~Ref. 13!and 0.75 eV~Ref. 14! above the HCN1 minimum. Sincethese estimates are quite different, we decided to repeacomputation using the highest level of theory. We alsotend our computations to explore not only the lowest 1A8surface, but also the 1A9 and the 2A8 surfaces.

Three stationary points~two minima, corresponding toHCN1 and HNC1 structures, and a saddle point connectithem! were determined for all three surfaces (1A8, 2A8,1A9) at the CASSCF level,15,16using a full valence completeactive space~CAS! and a cc-pVQZ basis.17 Transition statestructures were validated by calculation of second dertives, obtaining in all cases a single imaginary frequenOrbitals were optimized independently for each surface,cept for those geometries implying some degeneracy~linear

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geometries,P states!. In this case the degenerate states wconsidered together with equal weight in a state averacomputation.

The 1A8 surface correlates at linear geometries with ocomponent of theX 2P state of HCN1 and theX 2S1 stateof HNC1. The second surface ofA8 symmetry connects theA 2S1 state of HCN1 to theA2P state of HNC1. Finally the1A9 surface connects theX 2P andA 2P A9 components ofHCN1 and HNC1, respectively. Whilst the ground 1A8 sur-face has been characterized previously,11,13,18no informationis available for the remaining two.

Relative stabilities and transition state energies weretermined by means of single point calculations at the statiary points optimized at the CASSCF level. We used theternally contracted multireference configuration interact~ICMRCI! method of Werner and Knowles,19,20 correlatingall 9 valence electrons, with a full valence reference spand the same cc-pVQZ basis, followed by Davidson sconsistency correction.21,22 The MOLPRO code23 was usedthroughout.

The results of these computations are summarizedTable I. At the chosen level of theory, the adiabatic electrotransition energyTe of A 2S1 of HCN1 is found to be only0.177 eV~1430 cm21). This value is 0.134 eV lower thanour best estimate ofTe ~see Sec. II B!, hence it seems reasonable to attribute an error of60.15 eV to all ICMRCIenergy differences reported in Table I.

Taking theX 2S1 state of HNC1 as reference, we foundthat theX 2P of HCN1 is 0.998 eV higher in energy. Bysubtracting the differences of the zero point energies~ZPE!between HNC1 @0.420 eV~Ref. 18!# and HCN1 ~0.384 eV,from variational calculations of Sec. III! we obtain a differ-ence of 0.962 eV, in quantitative agreement and withinexperimental error of a recent and very precise thermochecal determination of 0.98060.022 eV.24 However suchagreement seems to be rather fortuitous, on the basis oerror estimates of our computations, and our value shoalso be compared to previousab initio results of 0.90,25

0.84,11 0.87,18 and 1.32 eV.14

The saddle point energy on the 1A8 surface is found at

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2.188 eV above theX2S1 of HNC1, corresponding to only1.190 eV ('9600 cm21) above theX 2P of HCN1. Consid-ering the high~although fortuitous! accuracy achieved fothe isomerization energetics, we believe that this vashould be considered much more reliable than previousabinitio determinations of the same quantity.13,14

For the isomerizations on the 1A9 and 2A8 surfaces, noprevious computations are available. We found that the trsitions states lies 3.252 eV ('26 000 cm21) above theX 2Pof HCN1 for the 1A9 surface and 4.515 eV ('36 000 cm21)aboveA 2S1 of HCN1 for the 2A8 surface. Since the saddlpoints for these excited state surfaces lies much higheenergy than for the ground 1A8 surface, the range of bendinangles to be chosen for the three-dimensional mapping othree surfaces is essentially limited by the ground 1A8 stateenergetics.

B. Calculation of adiabatic ab initio energies

The procedure adopted for theab initio calculation ofthe HCN1 adiabatic energies is essentially the same aspreviously used1 for C2H. The energies of theX 2P(1 2A8,12A9) and A2S1(2 2A8) electronic states oHCN1 were calculated using the ICMRCI method, with thfull valence CAS as reference. Molecular orbitals were otained from full-valence state-averaged CASSCF comptions, followed by orbital diabatization.26

As for C2H, we adopted two different levels of theorfor linear and bent geometries. For 76 linear geometries, cering the range 1.9<RCN<2.9 bohr and 1.6<RCH<2.9 bohr,all 13 electrons were correlated in the ICMRCI treatmeusing the cc-pcVQZ basis of Woon and Dunning27 and ex-ploiting C2v symmetry properties. These linear geometrare shown in Fig. 1, together with the contour plots of tX 2P andA 2S1 surfaces.

FIG. 1. Contour plots of the PES at linear geometries for theX 2P andA 2S1 states of HCN1. Energy increments of 1000 cm21 starting from theminimum of theX 2P state. The crossing seam is shown as a bold liwhile full symbols indicate the geometries selected for the ICMRCIab initiocomputations.

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For a second set of points, including both linear and bgeometries ofCs symmetry, only the 9 valence electronwere correlated, using the cc-pVQZ basis.17 424 points, cov-ering the range 1.9<RCN<2.9 bohr, 1.6<RCH<2.9 bohr,and 180°>u>100° were computed in this way. A step o10° was used, excluding the region of the crossing sewhere angles of 179° and 175° were added. In this waythree-dimensional PES of all three states were mapped,equal accuracy, for energies up to'9000 cm21 above theminimum of theX 2P state, avoiding the region of the lowesaddle point. This choice in turn results, after the elaboraoutlined in the next subsection, in single minimum analyticexpressions for the PES’s, i.e., no tunneling to the HNC1 isallowed. The Davidson correction21,22 was finally applied toall adiabatic energies.

C. Diabatization and fitting of ab initio energies

For each bent geometry, the diabatic energiesV11, V33

and the couplingsV13 were obtained from theA8 symmetryadiabatic energies~the state ofA9 symmetry, hereafter referred asV22, obviously does not need any diabatizatio!using the block diagonalization of the electronic Hamiltonimethod of Pacher, Cederbaum, and Ko¨ppel.28,29

The method is based on the construction of a 232 trans-formation matrix from the two leading CI coefficients giveby the ICMRCI treatment. The method implicitly assumthat, for any particular value ofRCN andRCH, the molecularorbitals maintain the same physical character at all bentometries. Hence the CASSCF state-averaged moleculabitals need to be diabatized prior to the MRCI, by maximing their overlap with the molecular orbitals obtainedlinear geometries. This is possible because of the invariaof the CASSCF wave function with respect to any orbirotation within the active space.26

As for C2H, theV11 andV33 diabatic energies recovereby the method were fitted quite well with a low order polnomial expansion~see below!, independently on whether thDavidson correction to the adiabatic energies has beenplied or not. However theV13 obtained from Davidson corrected energies showed a numerical noise and for this rewe had to evaluate theV13 values from noncorrected enegies.

The V11, V22, and V33 energies were fitted with theSURFIT program30 using a symmetry restricted polynomiaexpansion in the bond stretchingRCN, RCH and angle bend-ing u coordinates,

Vaa~RCN,RCH,u!5(i , j ,k

Ci jk~RCN2RCNref,a! i

3~RCH2RCHref,a! j ~u2u ref,a!k,

k even, a51,2,3 ~1!

where RCNref,a ,RCH

ref,a ,u ref,a are the corresponding theoreticequilibrium geometries.

The V13 values were in turn fitted using the modifiepolynomial form,

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11203J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Energy levels of HCN1

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FIG. 2. One dimensional cuts of the adiabatic~fulllines! and diabatic ~dotted lines! PES of the1 2A8,1 2A9,2 2A8 states along the CN stretching coodinate, for different values ofu. RCH fixed to 2.0 bohr.The component ofA9 symmetry of the2P state isshown as a dashed line.

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V13~RCN,RCH,u!5sin~u2u ref!@12tanh~RCN2RCNref !#

3@12tanh~RCH2RCHref !#

3(i , j ,k

Ci jk~RCN2RCNref ! i

3~RCH2RCHref ! j ~u2u ref!k, ~2!

whereRCNref 52.1a0 , RCH

ref 52.1a0, andu ref5180°.The two sets of points at linear and bent geometries w

first fitted independently and then the coefficients mergusing the procedure outlined in Ref. 1. The resulting expsion coefficients of the four surfaces are available frEPAPS.31

The contour plots of the 1A8,2A8(1A9) surfaces at lin-ear geometries are shown in Fig. 1, together with the croing seam between the two states.

In addition, we plot in Fig. 2 four one-dimensional cuof the adiabatic and diabatic PES’s along theRCN stretchingcoordinate, for a fixed value ofRCH and different bendingangles, showing the strong avoided crossing occurringbent geometries

In order to obtain a better agreement between calculaand experimental frequencies, two small additional empiradjustments were applied. First theC000 coefficient of theV33 surfaces was increased by 0.000 249 hartree~54.6cm21), so fixing the electronic transition energyTe to0.011 450 hartree~2513.0 cm21). Second, theC000 coeffi-cient of theV13 surface was lowered by20.000 646 hartree(2141.8 cm21). This second adjustment compensates bthe increasing of theTe and the errors made by taking noDavidson-corrected energies for the evaluation of theV13

coupling coefficients.Our equilibrium geometry for theX 2P state (RCN

51.2142 Å,RCH51.0891 Å! compares well with the resultof Botschwinaet al.12 (RCN51.2139 Å,RCH51.0902 Å! andof Petersonet al.11 (RCN51.2160 Å,RCH51.0902 Å!, whilethe results of Kraemeret al.18 (RCN51.204 Å, RCH51.079Å! appear to be shorter by about 0.01 Å. All these resagree within experimental uncertainty with the experimenvalues of Hollas and Sutherley5 (RCN51.21 Å, RCH51.09Å!, obtained from Franck–Condon analysis of photoelectspectra.

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For theA 2S1 the only data available for comparison athe theoretical computations of Botschwinaet al.12 Our equi-librium geometry (RCN51.1432 Å, RCH51.0866 Å! agreevery well with that of Ref. 12 (RCN51.1420 Å, RCH

51.0876 Å!, while ourTe ~2458 cm21 purelyab initio, 2513cm21 empirically corrected! is about 200 cm21 lower.

D. Spin–orbit matrix elements

One final piece of information which might be usefbefore proceeding to the calculation of energy levels isspin–orbit constantASO for the X 2P of HCN1. To ourknowledge, such quantity has never been evaluated theocally and, for the only experimental value8 put forward intothe literature at present~249.8 cm21), a negative value hadto be assumed by analogy with the isoelectronic speCO1 and N2

1 . In addition such value is expected to be lowered by the vibronic mixing with theA 2S1 state.8

Ab initio calculations are then needed to firmly establboth sign and magnitude of such parameter. The latestsion of theMOLPRO ~Ref. 23! program allows quite a straighevaluation of spin–orbit matrix elements between electrostates. The calculations were performed at the theoreequilibrium geometries of theX 2P andA 2S1 states and weused both the cc-pVQZ and the cc-pcVQZ, in order to estlish the effect of core correlation on the value of the matelements. The results are summarized in Table II.

TABLE II. Nonzero spin orbit matrix elements between thX 2P(1 2A8,1 2A8) and theA 2S1(2 2A8) states of HCN1, computed to theCASSCF and ICMRCI levels with the cc-pVQZ and cc-pcVQZ bases. Wthe cc-pcVQZ basis all 13 electrons were correlated. Upper line:X 2P equi-librium geometry (RCN52.294 39 bohr,RCH52.058 31 bohr,u5180°!;lower line: A 2S1 equilibrium geometry (RCN52.160 38 bohr, RCH

52.053 45 bohr,u5180°!. All values in cm21.

CASSCF/cc-pVQZ

ICMRCI/cc-pVQZ

ICMRCI/cc-pcVQZ

2^1 2A8uHLSu1 2A9& 251.90 252.51 253.48252.75 253.46 254.39

2^2 2A8uHLSu1 2A9& 36.18 35.46 36.1837.93 37.16 37.92

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We can confirm that the sign of the1 2A8uHLSu1 2A9&matrix element is negative and its geometry dependencquite limited, as well as the effects of core correlation. Tcomputed values are somewhat in between the obsesplitting of 249.8 cm21 for the X(000)1 vibronic state ofHCN1 and the value of257 cm21 for the ASO effectiveparameter used in our variational computations necessareproduce the observed splitting.

III. THE ROVIBRONIC ENERGY LEVELSOF HCN¿ AND DCN¿

The spin-rovibronic energy levels of HCN1 and DCN1

have been computed by applying the variational methodscribed in Ref. 1. We shall refer to that paper for the theand all technical details concerning the computer progra

As anticipated in Sec. II, ourab initio surfaces wereslightly adjusted in order to improve the agreement withperiment. The recent measurements of WiedmannWhite8 are sufficiently accurate to justify such a proceduIn a preliminary series of variational computations theC000

coefficients of theV33 andV13 were then slightly modified inorder to best match the energies of 10 out of the 11 ba@the band corresponding to theX(000)1 state was obviouslyexcluded# reported in Ref. 8. With the corrections reportedSec. II, the 10 bands corresponding to vibrationally exciHCN1, covering an energy range up to'4200 cm21, werereproduced with a maximum deviation of 13 cm21. Thisrepresents a great improvement on the computations of Cerbaum and co-workers2,3 which, for the same bands, shodeviations as large as 55 cm21, making us confident to tryalso a complete assignment of all bands observed in rephotoelectron spectra of HCN1 and DCN1 ~Ref. 9! ~see Sec.IV !.

The basis set for the variational calculations has bbuilt from the products of 25 one-dimensional harmoniccillators for CN and CH~CD! stretching coordinates and 2associated legendre functions for the bending~NBF15NBF25NBF3525!, from which 38 two-dimensional contractestretching functions were selected~NVP5NVM538!. Nocontraction was applied to bending functions~NV3525!.This basis ensures a convergence of all levels up to 6cm21 to within 0.5 cm21, and levels up to 12 000 cm21 towithin 2 cm21.

For a total angular momentumJ, the rovibronic statesare classified according toP (P<J) andK5P2S, wherePandS are the projections of total angular momentum andelectron spin along the intermolecular axis. For the prescase, we performed computations forJ<9/2 and S51/2,henceK50,1,2,3,4, corresponding to vibronic wave funtions of S,P,D,F,G symmetry.

Frequenciesn and rotational constantsBn have beenevaluated by setting to zero the spin–orbit constantASO @seeEq. ~2! in Ref. 1# and averaging the energies ofe/ f levels.Spin–orbit splittingDnSO has been determined in a secoseries of computations by settingASO5257 cm21, and tak-ing the differences betweenJ andJ11 levels. The value ofASO was chosen since it reproduces the observed8 splitting ofthe lowestX(000)1P state of HCN1 to within 0.1 cm21 andis in nice agreement with the computed value.

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In Tables III and IV we report frequencies, rotationconstants and spin orbit splittings for all states ofS andPsymmetry up to 5800 cm21 for HCN1 and 4800 cm21 forDCN1. Comparison with available experimental data is aprovided. The remaining states with higher values ofK areshown in a graphical way in Figs. 3 and 4.

Tables III and IV also report tentative assignments ofcomputed levels. Due to the vibronic interaction, the vibtional and electronic angular momenta quantum numbelandL are no longer good quantum numbers, but their sK5 l 1L is a conserved quantity. In addition, since all levewith the sameK can in principle mix, also the vibrationaquantum numbersv1 ,v2 ,v3 may lose their significance, either partially or totally. In case of strong vibronic couplinthe word assignment should then take the loose meaninfinding the parentage between the observed level andlevels of some unperturbed model system.

In our experience, based on the previously studied C2Hand the present case, the simple inspection of the coefficientering into the wave function is generally not sufficientmake assignments, except for the lowest levels and sparticular cases. Nevertheless we found that the inspectiothe plots of the vibrational wave functions for each separelectronic component is much more informative, thoughsome cases not conclusive. For this reason we supporassignments proposed in Tables III and IV with the corsponding plots of the wave functions. These plots are avable from EPAPS.31

The plots of the vibrational wave functions have begenerated by first scaling to 1, for each separate electrblock, the absolute value of the purely vibrational wafunctions obtained from the diagonalization of theK,P diag-onal representation of the rovibronic Hamiltonian@Eqs. ~1!and ~2! of Ref. 1#, that is, from the diagonalization of throvibronic Hamiltonian where all terms coupling basis funtions with different values ofK andP have been neglectedThese scaled electronic components of the total wave fution have been further scaled by a factor resulting fromsum of the squared coefficients of the expansion functibelonging to each electronic component. These factwhich sum to one, are then a measure of the fraction of eelectronic component (12A8,12A9,22A8) entering into thetotal wave functions, and are very useful in characterizand possibly attributing to a particular electronic state evibronic level. Scaling the partial wave functions by thefactors has the advantage of giving an immediate visualtion of the electronic composition of each vibronic state.

In order to better exploit benefits and weakness of suctool in assignments we show in Fig. 5 the wave functiplots for all levels ofP symmetry of HCN1 in the 4500–4800 cm21 energy range. For most states the total wafunction is dominated by a single electronic state and shoa well developed pattern of nodes. In these cases their cacterization in terms of vibrational quantum number israther trivial task. However, for some states the situationsimilar to that depicted on top of Fig. 5. Neither the nodstructure nor the composition in terms of pure BornOppenherimer states is simple enough to allow an unamb

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TABLE III. Calculated energies, spin–orbit splittings, and rotational constants of HCN1 for all levels of S1,S2, and P symmetry up to 5800 cm21.Assignment based on the inspection of expansion coefficients and plots of the wave functions~see text!. Levels left unassigned are marked as (•••). All valuesin cm21.

n DnSO Bn Symm. Assignment

Experiment

n ASO* B

0.0 249.9 1.3533 P X(000)1 0.0 249.8a 1.36a

294.1 1.3772 S1 X(010)0m 292,a 290,b 298c 1.38a

821.5 1.3398 S2 X(010)0k824.6 24.4 1.3844 P X(020)1m 831,b 839c

1312.7 1.3926 S1 X(030)0m 1331b

1493.3 6.9 1.3521 P X(020)1k1788.7 241.6 1.3532 P X(001)1 1785,a 1782,b 1799c 242.9a 1.35a

1874.6 29.4 1.3917 P X(040)1m1939.1 1.3887 S1 X(011)0m 1944,a 1944,b 1968c 1.38a

2215.2 1.3508 S2 X(030)0k2382.2 1.4064 S1 X(050)0m 2395b

2522.2 25.2 1.3802 P X(021)1m 2523,a 2525,b 2549c 25.5a 1.36a

2639.2 1.3354 S2 X(011)0k2869.6 22.7 1.3748 P X(040)1k2936.9 1.4161 S1 X(031)0m,A(0000) 2950,a 2960,b 2984c 1.38a

2970.5 221.3 1.3909 P X(060)1m3071.9 249.1 1.3445 P X(100)1 3049.8d

3233.1 1.3974 S1 X(011)0m,A(0000) 3231,a 3242,b 3258c 1.37a

3269.0 24.6 1.3562 P X(021)1k3352.0 1.3710 S1 X(110)0m3468.2 1.4185 S1 X(070)0m3490.3 213.8 1.3686 P X(002)1,A(0110) 3488,a 3492,b 3508c 216.5a 1.34a

3599.6 1.3556 S2 X(050)0k3624.5 218.9 1.3710 P X(041)1m,X(002)1 3615,a 3621,b 3638c 217.5a 1.35a

3854.8 23.7 1.3739 P X(120)1m 3880b

3881.0 1.3366 S2 X(110)0k3946.3 1.4118 S1 X(051)0m,X(012)0m,A(0200) 3992,b 4000c

4011.9 7.7 1.4253 P X(080)1m4023.4 1.3402 S2 X(031)0k4095.7 214.0 1.3733 P X(022)1m,A(0110) 4094,a 4097a 216.5a 1.35a

4192.4 1.3878 S1 X(051)0m 4187,a 4202b 1.36a

4291.1 25.4 1.3601 P X(060)1k4327.6 1.3841 S1 X(130)0m4435.2 1.3252 S2 X(012)0k4524.5 20.9 1.3957 P (•••) 4541b

4534.5 8.1 1.3615 P X(120)1k4543.8 1.4344 S1 X(090)0m4734.4 21.6 1.3515 P X(041)1k4743.8 1.3835 S1 X(032)0m 4751b,c

4797.3 213.0 1.3790 P X(061)1m 4815c

4860.7 220.2 1.3745 P X(140)1m,X(101)1

4882.4 224.2 1.3645 P X(101)1,X(140)1m4938.8 1.4032 S1 A(0001)4973.2 1.3613 S2 X(070)0k5036.6 1.4028 S1 X(111)0m,A(0001) 5065b, 5073c

5083.6 0.1 1.4382 P X(0100)1m5144.2 14.6 1.3379 P X(022)1k5167.5 1.4241 S1 X(071)0m,A(0600) 5186b

5237.2 1.3421 S2 X(130)0k5327.5 227.2 1.3562 P X(003)1 5323b, 5355c

5353.8 1.3996 S1 X(150)0m5398.5 1.3445 S2 X(051)0k5408.8 210.0 1.3856 P X(042)1m 5412b

5501.2 1.4230 S1 (•••) 5541b

5562.7 -6.1 1.3756 P X(121)1m5603.8 1.4432 S1 X(0110)m5656.1 20.5 1.3656 P X(080)1k5686.5 1.3271 S2 X(111)0k5725.7 22.3 1.4052 P X(081)1m,A(0710) 5727b

aReference 8.bReference 9.cReference 7.dReference 10.

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and

11206 J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Tarroni et al.

This article is copyrighted a

TABLE IV. Calculated energies, spin–orbit splittings, and rotational constants of DCN1 for all levels ofS1,S2, andP symmetry up to 4800 cm21. Assignment based on the inspection of expansion coefficientsplots of the wave functions~see text!. Levels left unassigned are marked as (•••). All values in cm21.

n DnSO Bn Symm. Assignment

Experiment

n

0.0 250.4 1.1107 P X(000)1 0.0235.1 1.1288 S1 X(010)0m 242,a 234b

648.6 23.6 1.1351 P X(020)1m 645,a 661b

662.0 1.1067 S2 X(010)0k1028.7 1.1441 S1 X(030)0m1196.5 8.7 1.1127 P X(020)1k1461.7 28.3 1.1485 P X(040)1m1681.2 246.2 1.1080 P X(001)1 1678,a 1686b

1771.9 1.1132 S2 X(030)0k1817.1 1.1369 S1 X(011)0m 1815,a 1823b

1870.2 1.1545 S1 X(050)0m2244.5 20.4 1.1401 P X(021)1m 2258,a 2266b

2285.3 14.8 1.1370 P X(020)1k2347.2 227.7 1.1338 P X(040)1k2367.3 1.0997 S2 X(011)0k2397.9 244.1 1.1050 P X(100)1 2387,a 2412,b 2374.1c

2562.3 1.1256 S1 X(110)0m 2565a

2622.3 1.1501 S1 X(031)0m 2629,a 2629b

2723.0 1.1697 S1 X(070)0m2873.3 1.1199 S2 X(050)0k2881.2 6.1 1.1123 P X(021)1k 2896,a 2887b

2981.5 24.0 1.1269 P X(120)1m3051.2 1.0970 S2 X(110)1k3078.0 1.1522 S1 X(011)0m,A(0000) 3105,a 3113b

3082.9 29.5 1.1508 P X(041)1m3161.8 1.3 1.1713 P X(080)1m3316.7 231.6 1.1136 P X(002)1 3307,a 3315b

3352.3 1.1358 S1 X(130)0m3421.4 23.2 1.1245 P X(060)1k3466.0 1.1598 S1 X(051)0m 3476a

3478.4 1.1059 S2 X(031)0k3560.4 8.1 1.1058 P X(120)1k3579.8 1.1835 S1 X(090)0m 3573a

3737.1 213.5 1.1269 P X(140)1m3740.2 1.1514 S1 X(012)0m 3750,a 3758b

3797.0 211.2 1.1334 P X(140)1m3890.8 8.3 1.1589 P X(061)1m3965.9 1.1301 S2 X(070)0k4003.7 23.3 1.1795 P X(0100)1m4045.6 211.5 1.1147 P X(041)1k4057.5 1.0927 S2 X(012)0k4068.2 228.7 1.1245 P X(101)1 4049,a 4057b

4106.9 1.1376 S1 X(111)0m4132.2 1.1042 S2 X(130)0k4178.9 1.1448 S1 X(150)0m4316.9 1.1538 S1 X(071)1m4320.8 213.3 1.1469 P (•••) 4331,a 4355b

4408.3 1.1773 S1 (•••) 4420a

4463.2 1.1781 S1 X(0110)0m 4420a

4508.3 20.5 1.1452 P X(080)1k4533.0 0.8 1.1338 P (•••)4578.1 14.0 1.1317 P (•••)4580.1 1.1128 S2 X(051)0k4648.7 0.4 1.1110 P X(022)1k4679.3 215.8 1.1162 P X(140)1k4694.6 1.1593 S1 A(0001) 4702,a 4686b

4730.2 1.0893 S2 X(111)0k4738.3 235.5 1.1023 P X(200)1

4758.5 24.1 1.1755 P X(081)1m

aReference 9.bReference 7.cReference 10.

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11207J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Energy levels of HCN1

This a

ous labeling. These puzzling cases have been left unassiand marked with (•••) in Tables III and IV.

Before discussing the assignments in more detail, iinteresting to compare our results with those quotedKoppelet al.3 In Ref. 3 they reported the most intense leveof S (K50! andP (K51! symmetry for energies up to 400cm21 above theX(000)1 origin, together with the leadingcoefficients of the wave functions. These levels differs froours by at most 63 cm21. In addition the composition of thewave functions is essentially the same determined byconsidering all the simplifications of their model~that is theneglect of Renner–Teller coupling and of CH stretchimodes!. Hence all the assignments of Widemann and Whi8

based on the analysis of Ko¨ppel et al.3 are fully confirmed,except for the band ofS1 symmetry at 14.1265 eV~4187cm 21 in Table III!, which we predict at 4192.4 cm21 andassign as theX(051)0m state. Unfortunately Ko¨ppel et al.did not present their result in numerical format for DCN1,thus a more complete comparison is not possible.

Our computations reproduce the high resolution resof Wideman and White with a root mean square deviationonly 5.3 cm21. The experimental effective spin–orbit constantsASO* are also well reproduced, together with the rotional constants, which unfortunately are not very accura8

FIG. 3. Calculated rovibronic levels ofS,P,D,P,G symmetry ~with J5P) of HCN1 for energies up to 7000 cm21.

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Having ascertained the accuracy of our computations,assignment of the remaining bands observed in photoelecspectra only at medium resolution is quite straight forwaat least for energies below'6000 cm21 for HCN1 and'5000 cm21 for DCN1. The reasonings behind these asignments will be explained in Sec. IV. Here we merely poout that many levels are still unobserved, even in low eneregions. In particular the missing levels, both in the HCN1

and DCN1 spectra, are allk states arising from the RennerTeller interaction in theX 2P state~with possibly one excep-tion for DCN1, see next section!, and those withK>2.

The location of then1 band has been a matter of debafor a while,2,6,7 but most recentab initio computations11,12

agree to place it around 3080–3100 cm21 for HCN1. Theassignment asn1 of the only bands detected by infrareobserved at 3049.8 for HCN1 and 2374.1 for DCN1 in neonmatrix10 is confirmed by our computations, but our preditions are higher by about 20 and 10 cm21, respectively. Thismay be either due to a small deficiency of theab initio sur-faces, or to the fact that only one component of the doub@probably theX(100)1P3/2] is observed. For DCN1 only, thecorresponding band is observed also in medium resoluphotoelectron spectra.7,9 In HCN1 then1 band might be hid-den by the tails of the intense peaks at 2950 and 3242 cm21.

FIG. 4. Calculated rovibronic levels ofS,P,D,P,G symmetry ~with J5P) of DCN1 for energies up to 6000 cm21.

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11208 J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Tarroni et al.

This a

IV. ASSIGNMENT OF PHOTOELECTRON SPECTRA

In this section we shall try a complete assignment ofphotoelectron spectra of HCN1 and DCN1. In the discussionwe shall refer to the most recent photoelectron spectra,corded by Elandet al.9 The spectra of Fridh and A˚ sbrink7 arereported in Tables V and VI for comparison.

As shown in the previous section, our variational calclations reproduce the high resolution photoelectron spectrWideman and White to within 15 cm21 so providing a verypowerful tool for the assignment of the photoelectron speat medium resolution of Elandet al.9 These spectra showmany features which were not evident in previoexperiments,7 nevertheless many levels are still unobserv

In addition the HCN1 and DCN1 spectra are similaronly as far as the most intense transitions are concernemany weak features suggest totally different assignment

In Tables V and VI we report the bands observedEland et al.9 and by Fridh and A˚ sbrink,7 together with thelevels ofS andP symmetry predicted in the neighborhoo~usually within650 cm21) of the band peak. We also repothe corresponding wave function composition in termspure ~Born–Oppenheimer! electronic states, and, whenevpossible, their assignment in terms of ‘‘unperturbed’’ pare

FIG. 5. Contour plots of the vibrational parts of vibronic wave functionssome selected levels ofP symmetry (K51) of HCN1. The three electroniccomponents@152A8(S1);251A8(P1);351A9(P2)# are plotted in adja-cent panels, with the sum of squared coefficients shown in the uppercorner. Thex-axis is the bending coordinate while they-axis is the CNstretching coordinate. Positive and negative lobes of the wave functionplotted with continuous and dashed lines, respectively. See text for mdetails.

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levels, inferred from the plot of the wave function. Thshould provide support for our assignments. In doubtcases we also extend our search to states withD multiplicity,but we never need to invoke any of these states. ‘‘k ’’ levels,that is levels with a dominance of the 12A9 electronic state,were considered as potential candidates only when otherels were too far apart in energy. This bias come fromobservation that, for energies below 4000 cm21, ‘‘ m ’’ or‘‘unique’’ levels are undoubtedly the most intense ones.

A. HCN¿

1. Band at 3880 cm À1

It is tentatively assigned asX(120)1m, even if it has arather high intensity and lower terms inn1 and n2 are notobserved, since no other better candidates are found w6100 cm21.

2. Band at 4541 cm À1

We attribute this band to aP level calculated at 4525cm21, characterized by an equal mixture o1 2A8,12A9,22A8 electronic states, which could not be asigned to any particular state. It is unlikely to be the alterntive X(090)0 state since then2 progression ceases to be oserved atn255.

3. Band at 5541 cm À1

This band is attributed to an unidentifiedS1 level cal-culated at 5501 cm21 with nearly an equal contribution o12A8 and 2 2A8 electronic states. This seems to us moplausible than the closestX(121)1m state.

4. Band at 5848 cm À1

Two unidentifiedP levels, calculated at 5833 and 586cm21 and both characterized by an equal mixture1 2A8,12A9,22A8 electronic states, can be attributed to thband. It is not possible to choose between them.

5. Bands above 10 000 cm À1

These three bands lies above the calculated transstate for the HCN1→HNC1 isomerization. In such an energy range any level involving bending excitation, besidbeing intrinsically wrong in our model, would lead tisomerization. Hence we attribute the band at 10 098 cm21

to the A(1002) level and the remaining two, at 10 759 an12 348 cm21, to theX(006)1 and (007)1 levels.

2. DCN¿

1. Band at 2896 cm À1

This band is particularly puzzling. In Table VI three aternatives are presented. Two of them are direct transitifrom the (0000) state of DCN, while the third is a hot bandNone of them is completely satisfactory since the two dirtransitions have a ‘‘k ’’ state as final state, while the hot baninvolve a final state for which the corresponding direct trasition has a low intensity. Our temptative choice is to assit as theX(021)1k state.

ht

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21 1

11209J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Energy levels of HCN1

This a

TABLE V. Assignment of the HCN photoelectron spectra of Elandet al. ~Ref. 9!. All energies in cm , relative to theX(000) vibronic state.

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TABLE V. ~Continued.!

11210 J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Tarroni et al.

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2. Band at 3573 cm À1

It is assigned asX(090) since no other reasonable leveare available within650 cm21. Previous terms of the bending progression are not observed as probably obscuredmore intense transitions.

3. Band at 4420 cm À1

The only two calculated energy levels within650 cm21

of this peak are ofS1 symmetry. Both involve a strongmixture of a highly excited bending state and some otunidentified state. Since the peak is of medium intensity,previous bending states are not observed, the nature offeature is very dubious.

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V. CONCLUSIONS

The energy levels of the HCN1 and DCN1 radical cat-ions in the vibronically coupledX 2P andA 2S1 electronicstates have been studied using a previously develomethod1 taking into account both Renner–Teller anHerzberg–Teller interactions.

Accurate diabatic three-dimensional PES for t2P(1 2A8,12A9) and 2S1(2 2A8) states have been buifrom ICMRCI computations using a large basis set. Sepacomputations have been performed to determine also therier to isomerization over the three surfaces and the sporbit matrix elements.

Vibronic energy levels, spin–orbit splittings and rottional constants have been obtained from variational calctions up toJ59/2, achieving a very good agreement wiexperimental data from rotationally resolved photoelectspectra.8

The high accuracy of the theoretical predictions was

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11211J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Energy levels of HCN1

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TABLE VI. Assignment of the DCN photoelectron spectra of Elandet al. ~Ref. 9!. All energies in cm , relative to theX(000) vibronic state.

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TABLE VI. ~Continued.!

11212 J. Chem. Phys., Vol. 115, No. 24, 22 December 2001 Tarroni et al.

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nally exploited to revise the assignments of the recent hresolution photoelectron spectra of HCN1 and DCN1.

ACKNOWLEDGMENTS

This work has been supported by the MURST of Itaand the EEC under the RTN Program 7~Contract No.HPRN-CT-1999-00005!. One of the authors~S.C.! wouldlike to acknowledge financial support from the MINUproject, administered by the EEC at CINECA, the CompuCentre of the University of Bologna, Italy. S.C. would allike to acknowledge financial support from the U.S. OfficeNaval Research, Grant No. N00014-95-1-0493. All authare grateful to P. J. Knowles and H. -J. Werner for providthem with access to theMOLPRO code.

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~1983!.23MOLPRO is a package ofab initio programs written by H. J. Werner and P

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~1993!.30J. Senekowitsch, Ph.D. thesis, Frankfurt, 1988.31See EPAPS Document No. E-JCPSA6-115-301145 for five Posts

files: the expansion coefficients of the four PES’s used in this workthe wave function plots for all levels ofS and P symmetry reported inTables III-VI. This document may be retrieved via the EPAPS homep~http://www.aip.org/pubservs/epaps.html! or from ftp.aip.org in the direc-tory /epaps/. See the EPAPS homepage for more information.

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