Theory Success and Failure on Silver Monohalides

8/3/2019 Theory Success and Failure on Silver Monohalides

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Theor Chem Acc (2006) 116: 641654DOI 10.1007/s00214-006-0110-8

R E G U L A R A R T I C L E

A. Ramrez-Sols

The spectroscopy of copper and silver monohalides: what modern

quantum chemistry can and cannot do

Received: 7 December 2004 / Accepted: 2 March 2005 / Published online: 2 March 2006 Springer-Verlag 2006

Abstract A comprehensive analysis on the successes andfailures of the theoretical spectroscopy of copper and sil-ver monohalides is presented in light of the recent theo-

retical versus experimental information for these systems.It is shown that although for copper monohalides the stan-dard quantum chemical multireference SCF, perturbationalor CI approaches work well to describe their spectroscopy,for their silver counterparts this is not the case always. Whiledensity functional theory is intrinsically unable to deal withthe most intense transition (B1+X1+) observed in thewhole CuX and AgX series, the CASSCF+CASPT2 methodfails for the AgX family is describing this excitation, evenwith the largest physically meaningful valence orbital ac-tive space. The complexity of silver halides arises from theconcatenation of three independent problems: first, the iso-lated atom spectroscopy is much more complex for Ag than

for Cu, since for silver the Rydberg 2P(4d105p1) state liesclose but below the valence 2D(4d95s2) one; secondly, thespin-orbit coupling for silver is much largerand thus the fine-structure components of these doublets are intertwined, lead-ing to very large S mixing effects in the molecular case.Finally,ratherstronginteractions exist betweenthenumerousAg(4d95s2)X(np 5) and Ag(4d105p1)X(np5) neutral con-figurations with the Ag+(4d95s1)X(np 6) ionic structures,making the accurate description of these mixtures an ex-tremely difficult task, especially for the second 1+ state,where even large CASSCF calculations fail at providing con-tinuous state-specific potential energy curves. This remainsa true theoretical impasse related to the still unsolved and

complex convergence for the coupled CI-orbital multivariateminimization problem. Therefore, it is only possible to prop-erly describe the electronic structure of the excited states ofsilver monohalides using the full valence active space, to per-form variational treatments of the non-dynamic and dynamic

A. Ramrez-SolsLaboratoire de Physique Quantique, IRSAMC, UMR 5626 du CNRS,Universit Paul Sabatier, 31062 Toulouse Cedex, France.Depto. de Fsica, Facultad de Ciencias,Universidad Autnoma del Estado de Morelos. Av. Universidad 1001Cuernavaca, Morelos, 62210 MxicoE-mail: [email protected]

electronic correlation treatments with especially optimizedand extended RECP-basis sets; then the spin-orbit effectsmust imperatively be taken into account to qualitatively

explain the nature of the observed AgX spectra. However,non-negligible errors are found for some of the basicspectroscopic quantities suchas transition energiesand vibra-tional frequencies for the most spectroscopically activeexcited states.

1 Introduction

The spectroscopy of noble metal monohalides has been stud-ied experimentally for several decades but theoretical studiesof systems containing atoms of the third and higher periods

call for themostaccurate methods of ab initioquantumchem-istry. These calculations require new techniques that have tobe tested on small systems like diatomics, in order to provetheir reliability for properly treating larger systems. This hasbeen achieved since the early 1990s for copper halides while,for the silver monohalide family, this has been possible onlyin the last few years. The quality of the spectroscopic resultsstrongly depends on the theoretical approach used. In partic-ular, for silver halides, this means that, even qualitatively, theresults concerning the nature of the observed excited states isuncertain unless the most sophisticated algorithms for elec-tronic structure are applied. Also, such basic spectroscopicproperties as the theoretical vibrational frequencies for thefirst excited states are completely wrong by factors of 2 or3 from the experimental values for some of these diatomics.This explains why, by as late as 1995, no theoretical workat all had been devoted to the AgX diatomics. Such a sit-uation is unimaginable for most of the other types of mol-ecules, even for large organic complexes, fullerenes, dopedpolymers, catalytic sites of enzymes or whole families ofchromophores, since these can be extremely well described(from the structural as well as from the spectroscopic point ofview) using standard ab initio or density functional theory(DFT)-derived methods. This complexity is found, of course,for many other transition metal diatomics.


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The situation for noble metal dihalides (MX2) is evenmore precarious, since even from the experimental point ofview there is little or no information at all concerning CuI2and the whole silver dihalide family. From the theoreticalpoint of view, the accurate description of these systems issubstantially harder to achieve than for the monohalides forreasons that will be discussed further on.

Moleculesofthiskindhavebeendetectedalready80yearsago.Theyweredifficulttostudyinthegasphasebutnewtech-niques were developed for their production such as high tem-perature cells, electric discharges or laser ablation of atomsfrom solid metal in the presence of the dihalogen, makingeven fine structure investigations at low temperatures feasi-ble.Theexperimentalstudiesforthemonohalidesrangefromthe vibrational structure of the lowest electronic states, accu-rate radiative lifetimes, rotational and hyperfine structure ofthe observed bands, microwave spectroscopy for the groundand excited states; for some of the dihalides (CuF2, CuCl2and CuBr2) laser-induced fluorescence to study rovibration-al spectra as well as accurate transition energies from rare-

gas matrices for the lowest excited states exist. However,since the aim of this article is to point out some of the out-standing difficulties encountered and failures of the modernquantum chemical methods concerning the spectroscopy ofthe monohalides, the interested reader is directed to find allthe relevant experimental information for the monohalideswithin the extensive bibliography provided by Guichemerreet al. [1] comprising nearly 60 experimental citations con-cerningthesemolecules,exceptthecopperandsilveriodides,for which we shall provide the appropriate references.

2 What quantum chemistry has done

2.1 CuX

Copper monohalides have received the most attention fromtheoreticians since they represent a paradigm of chemicalbonding and present the least amount of problems from thecomputational point of view. A brief panoramic view of theknowledge on this family is due.

The first emission spectrum on CuF was observed since1925 by Mulliken; then three bands named A,B,C, at 5700,5060 and4920 wereanalyzed inthe absorptionspectrumbyRitschl, and in emission spectra by Woods, improved later bySteele and Broida. A photoelectron spectrum was recorded

by Lee andPotts. Ahmed et al. obtained absorption andemis-sion spectra of the five lowest excited electronic states whichwere assigned to 3+, A(0+, 1), B1+C1 and D( = 1).

Fine and hyperfine structures of these states were alsostudied and radiative lifetimes were measured. Many theo-retical investigations of the ground state were performed abinitio by SCF calculations[26], by density functional theory(DFT) [710], and by CI, second-order Mller-Plesset per-turbational and coupled-cluster (CC) methods [1114]. Thepotentialenergycurvesandthespectroscopicconstantsofthefirst 1,3+,1,3 ,and 1,3 excitedstates have beenevaluated

using various types of methods to deal with the electroniccorrelation effects [1517]. Calculations of the radiative life-times of these six excited states were reported [18,19].

The first spectroscopic experiments on CuCl and CuBrwere done by Ritschl in 1927, then by Bloomenthal in 1938.In CuCl, six bands (A, B, C, D, E and F systems) were de-tected. The vibrational structure of these lowest electronic

states was analyzed and radiative lifetimes were measured.The rotational and hyperfine structure of these bands wasanalyzed for CuCl and CuBr. A recent spectroscopic studylead to a reassignment of the excited states of CuCl. Accu-rate data were obtained by microwave spectroscopy for theground state of both CuCl and CuBr.

From the theoretical part, the ground state of CuCl wasstudied by HartreeFock (HF) [4,6,13,20] and DFT or CCmethods [9,10,2123]. The excited states were studied byNguyen et al. [16], Ramrez-Sols et al. [24] and Sousa et al.[25,26]. Radiative lifetimes were theoretically determinedby Ramrez-Sols, Daudey, Schamps and Delaval [2729].WinterandHuestis[30]performedSCFcalculationsonCuCl

andincludedspinorbit interactionsemi-empiricallyusing anatoms-in-moleculestechnique. The ground state of CuBrwasstudied by DFT calculations [5], and the lowest excitedstatesthrough MRCI and CC methods [1]; the radiative lifetimesof some excited states were investigated experimentally andtheoretically [25,26, 31].

For CuI, there are a number of experimental studies (thefirst one by Mulliken in 1925) concerning the visible spec-trum that lead to a tentative identificationof thefour observedbands arising from the A, C, D and E systems. The E and Csystems were confirmed as arising from 1+X1+ transi-tions, while the D system arises from 1X1+ transition.The experimental assignment of the A system was

considerably more complicated and took several years tobe elucidated; it changed as arising from another 1X1+

transition, to a 1+X1+, and back again to a 1X1+

transition (see the experimental bibliography cited in [32]).However, only two theoretical studies have been done

concerning the excited states of CuI. Ramrez-Sols et al.[32] were the first to perform a coupling of highly correlatedelectronic wavefunctions and include the spinorbit (SO)effects through the use of an effective Hamiltonian using theoptimized MCSCF+CIPSI energies to produce the 18 low-est fine structure states of CuI. Several years later, Sousaet al. [25,26] studied the spectroscopy of CuCl, CuBr andCuI using explicit four-component relativistic calculations

where, in a natural way, fine-structure states arise that canbe directly compared with the experimental data. Howeverthe use of double-group representation imposes some seri-ous constraints from the orbital optimization and CI pointsof view; thus some drastic measures had to be taken in or-der to approximately introduce the interaction of ionic andneutral configurations. For the ionic and for the neutral ex-cited states the spinors were optimized without the Cu(4s).Including the 4s orbital introduces two open shells of thesame symmetry. This exclusion is really a major inconve-nience since this precludes the crucial 3d 4s hybridization


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The spectroscopy of copper and silver monohalides. what modern quantum chemistry can and cannot do 643

andtheCu(4s)X(p) mixing whichare important for allthe1,3+ states, but no solution was found since this cannot behandled in the MOLFDIR program package. Nevertheless,in their calculations, the Cu 4s virtual is rather localized andthe authors expected the spinors to give a reasonable descrip-tion of the relative energies of the ionic and neutral excitedstates. Innon-relativistic calculationsthe molecular states can

be assigned using S coupling. In these relativistic calcu-lations, the intermediate coupling was used, so only the and quantum numbers applied. To connect to the previousdiscussion [32] on the assignment of fine structure states,Sousa et al. [25,26] have analyzed the calculated states interms of components ofS parent states. The ionic trip-let and singlet excited states arise from the Cu+(3d94s1)X

(ns 2np6) configuration. For these states the halogen is closedshell andthe spinorbit coupling will arise basically from theatomicCu+(3d94s1) splitting(into 3D3,3 D2 and 3D1)whichis about 2,000cm1; this effect was expected to be the samefor all species. However, besides the splitting of the d-orbi-tals there is also a spinorbit interaction between states of the

same symmetry which allows them to mix. Note that foriodine the 2P SO effects are quite large (around 7,600cm1)but these are expected to quench in the molecular states,since the weight of the neutral Cu(3d104s1)X(ns 2np 5) com-ponent in the active FranckCondon region is rather small.Both spinorbit effects have been properly included in [25,26] and [32].

Guichemerre et al. [1] have recently carried out a system-atic MRCI+SO and CC+SO study of the family of monoha-lides of metals from group I-B, comprising atoms from thesecond to the sixth row of the periodic table. However, theydid not include in their study the CuI and AgI molecules.The importance of relativistic effects and spin-orbit interac-

tions have also been analyzed and compared for this seriesof molecules in [1]. Their orbital optimization procedure forthe excited states was based on the state-averaged version ofthe CASSCF method and shall be carefully discussed in thefollowing section.

2.2 AgX

Most of the basic research on silver halides is related to thephotophysics of the latent image formation, since these mol-ecules are of great practical importance due to their wide usein photographic materials. These molecules are also impor-

tant from the theoretical point of view since they represent,along with copper and gold halides, a paradigm of chemicalbonding in transition metal-containing molecules.

Itwasin1927thatMullikenobservedforthefirsttimeUVemissionoftheAgFmoleculearound280nmandpointedoutthat interactions between the 0+ states arising from neutralatoms and from Ag+ andF ions were likely to be important.The B0+X0+ system was found in the 311343nm regionand was analyzed vibrationally. Much later its dissociationenergy was measured. The rotational structure of the twoAX and BX systems was studied by Clements and Barrow

in the late 1960s, who showed that all these states were ofthe = 0+ type. One of the most outstanding features oftheir article was the fact that they suggested that, at variancewith the isovalent CuFmolecule, these A andB excited statesmight be predissociated, since their T00 transition energy at29,251 cm1 for the A state is rather close to the dissocia-tion limit of 29, 660 cm1. Some rough sketches of the forms

of the potential energy curves of these states were later pro-posed, but the important new fact they found was that theA state may be a highly anharmonic state, possibly with apotential maximum. However, until 1995, it was not possi-ble to say whether these A and B states arise from electronicstates of + or symmetry, since the theoretical workshad until then considered only the ground state [4,9]. By1993, the last andthe most accurateexperimental studyof thespectrosocpy of AgF was published by Wang and Gole [33]where they reportedthe discovery, at thefringes of the visibleregion, of two close and low-lying new excited states (calledA and a) that are located about 4,300cm1 below A0+, thestate previously known as the lowest excited state. They per-

formedarotationalanalysisoftheA

state and concluded thatit was an = 1 state, from which they suggested its label-ing as A 1. At the same time, they tentatively assigned the = 1 value for the a state and called it a 1. The radiativelifetimes of the four lowest-lying electronic states were mea-sured to be 7.1 s (A), 9.1 s (a), 240ns (A0+), and 21ns(B0+). These lifetimes strongly suggest that the two lowest-lying states are likely to be of triplet character while the two = 0+ states are of singlet character. So, up to date, onlyfive states are known. The energy difference between the Aand B states is only around 2,300cm1, a fact that makes itvery difficult for theoreticians to elucidate the nature of thecorresponding parent states, given the uncertainties already

associated with the atomic and ionic fine-structure asymp-totes (the errors associated with the IP of Ag and the EA ofCl will be presented later) that might be involved in the dia-batic composition of the several states that can be generatedfor each spin-space symmetry.

From the theoretical point of view, the first study [34]regarding the spectrocopy of AgF appeared. In that article,we reported two-configuration SCF+CIPSI calculations anda semiempirical treatment of the spinorbit interactions; wealso showed that the labeling proposed by Wang and Goleforthea 1 state was inadequate and gave strong theoreticalarguments to prove this erroneous assignment. It was con-cluded that the newly found a and A states were actually

the = 0

and = 1 components of the3

+

parent andrelabeled them as a 0 and A1.The question of the nature of the electronic parent of the

observed B0+ state, responsible for the most intense tran-sition and which is the shortest lived excited state of AgF,was also addressed and we suggested that this state could becorrelated with the Rydberg Ag+(4d95p1)F(2s22p6) ionicstructure. Five years later, in a much more refined study [35],using a large ANO basis set for F, a small-core RECP anda large polarizedoptimized valence basis for Ag, we per-formed extensive CASSCF+CASPT2 calculations for the


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644 A. Ramrez-Sols

seven lowest lying electronic states.These new resultsclearlyshowed that the B0+ state is not correlated with the Rydbergionic structure, as previously proposed; since the 21+ statehad been shown to be the S electronic parent state of thefine-structure A0+ state, and given the difference betweenthe calculated Te 1513cm1 (exp. 2,300cm1) of the21+ and 3 states, these resultspointedto this latter state as

the S parent of the experimental B0+ state. At the CAS-PT2 level of calculation, the next higher lying state that couldcontribute (31+) through spinorbit couplings to this B0+

stateliesmorethan8,000cm1 away. This 3 assignment forthe B state, however, was not consistent with the accuratelymeasured radiative lifetimes of 240ns (A0+), 21ns (B0+)for the highest-lying excited states, which suggest that thetwo = 0+ excited states are of singlet character. There-fore, the first important contradiction between experimen-tal and highly sophisticated ab initio calculations arose forAgF.Later,severalotherstudiesappearedbutthesewerecon-cernedonlywiththegroundstateofAgF[10,12,14];theB0+

puzzle still remainssince the recent CASSCF+MRCISD+SO

and CC+SO calculations of Guichemerre et al. [1] confirmedour previous assignment of the triplet state as the parentof this extremely short-lived state.

For the AgCl and AgBr molecules, several rotationalanalysesweremade.AgBrwasdetectedinabsorptionin1927by FrankandKuhn, and was analyzed vibrationally by Brice.Photoelectron spectra have also been observed [36], and theB state (again the most intense transition) was carefully ana-lyzed [37]. More recently, the B state of both molecules hasbeen studied by fluorescence excitation and mass spectrome-try [38]. These studies stressed the lack of knowledge on thenature of the observed transitions for AgCl and AgBr.

From the theoretical part, until very recently, all the stud-

ieswereonlyconcernedwiththegroundstates:HartreeFock[4]and DFT [5,7,9,10,21,22,39,40] calculations were madefor AgCl while CASSCF-MRPT2 [41] and DFT [42] calcu-lations were done for AgBr (the molecule and its clusters). Itwas ony in 2002 that the first ab initio study concerning theexcitedstates of AgCl and AgBr appeared [1] through the useof small-core RECP and spinorbit optimized potentials forAg, and small state-appeared averaged CASSCF referencewavefunctions for MRCI calculations of the seven lowestelectronic states. A few weeks before that work was submit-ted, another larger CASSCF+ACPF study, only focused ontheaccuratespectroscopyofAgCl,waspublished[43]before[1], but in a different journal. Although this study did not

include the SO effects (though they were carefully discussedandpredictedontheresultingelectronicstates,seeSect.III.Cof[43]).Theessentialdifferencewiththeapproachpresentedin [1] is that a more physically coherent (but much larger)complete active orbital space (CAS) was used and that fullstate-specific CASSCF wavefunctions instead of state-aver-aged ones were used as references for the highly correlatedACPF algorithm. This is actually a key difference when try-ing to reproduce results that are aimed at comparison withexperimental data for the AgX series; this will be explainedin the next section.

For AgI thesituation is quite meager, both from theexper-imental as well as from the theoretical points of view. Thedissociationenergy is 2.20eV from atomic fluorescence[44],or with the 2.10 eV value from Mulliken [45]; Gaydon gives2.20.3eV, according to [46]. Five excited states have beenso far observed, the A state around 23,900 cm1, the B statearound 31,190cm1, the C state around 44,700cm1, the D

statearound46,000cm1 andtheEstatearound47,500cm1.It should be stressed that none of these states has beenassigned any fine-structure quantum number nor any Selectronic parent, except for the B state, for which a 30+assignment has been proposed [46]. We should also say that,contrary to the situation found for AgF where accurate radi-ative lifetimes are known for all the excited states, no equiv-alent data regarding AgI are available. This could certainlyprovide important insight as to the multiplicity of the domi-nant electronic parents of the experimentally observed states.

Besides their harmonicvibrational frequencies(206, 151,123, 156, 165 and 130cm1, respectively, for the X, A, B,C, D and E states) [4753] nothing more is known about the

higher-lying excited states, neither from newer experimentsnorfromthetheoreticalpointofview.Thislackofexperimen-tal information makes the theoretical comparison incompleteand difficult; newer and reliable observations are nowneededto fill in the large blank entries in the spectroscopic tables ofAgI.

However, a very important work on the B X transi-tions by Stueber et al. [38] reported fluorescence excitationand mass-resolved excitation spectroscopy (MRES) of jet-cooled AgCl, AgBr andAgImolecules; two hypotheses wereput forward to explain the observed AgI, B X transitionsbetweenvibrational levelsof these twostates,one involvingalevel crossing between two excited states (B/B) and another

with a single complicated excited (B) potential surface. Thesingle B surface was obtained through the RydbergKleinRees (RKR) fitting method and shows a rather strange shape,like the one seen for the shelf states of the alkali dimers, witha minimum around 5.4a.u. and a large plateau that extendsfrom 6 to 8 a.u. (see Fig. 8 in that reference). It must be saidthat a better agreement with the experimental intensities wasachievedusingaslightlymodifiedBcurveintheshelfregion,with a local minimum well depth of about 30cm1 around7.2a.u. Nonetheless, neither of these hypotheses gives a fullysatisfactory model for what is known as vibrational isotopicsplitting.

Fromthetheoreticalpointofview,until2003,notasingle

study had been reported for molecular AgI (although manyworks exist for the solid); therefore, in [54] we presentedequivalent CASSCF(16,12)+ACPF results for the seven low-est states providing benchmark-like potential energy curvesthat could explain the observed BX spectra, as had been re-cently done for AgCl. Since we aimed at comparing our cal-culated potential energy curves with those provided in [38]through the RKR fitting, it was absolutely essential to obtaincurvescoveringamuchlargerinternuclearrangethanstudiedin [34,35,43], so the studied range goes from 4.0 to 20a.u.Given the previous experience with the CASSCF description


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for the excited states of AgCl, for the 21+ state we decidedto obtain quasi-state-specific CASSCF(16,12) calculationsthat could be coherently extended to such long internucleardistances. The best relative weights beyond 5.3a.u. werefound to be 1:7 (0.12, 0.88), which provide an excellentapproximation to the true state-specific CASSCF referencesforthesecondrootofthe 1+ manifold.Thiswasascertained

by comparing thesecurves for the region (3.85.2a.u.) wheretrue state-specific solutions could be obtained.

One important fact that is relevant for spectroscopic pur-poses is that for all states, the weights of the CASSCF ref-erence in the overall ACPF wavefunctions are very similar,around 0.95; this also means that since the size of the sin-gly and doubly excited external spaces are huge compared tothe CASSCF wavefunctions, the latter are actually excellentreferences in all cases.

These results provided a preliminary confirmation of thesingle-surface hypothesis put forward by Stueber et al. toexplain the mass-resolved excitation spectroscopy experi-ments on the B X transitions, where the RKR fitted

excited state potential energy shows a shelf-like curve, withone deep main well and a shallower one at a longer internu-clear distance.

The inclusion of the spinorbit effects in a second stepusing these highly correlated ACPF energies through the useof an effective spinorbit Hamiltonian to obtain the fine-structure states that arise from these S parents was laterachieved [55], finally providing solid support for the singleB excited surface hypothesis of Stueber et al.

3 Quantum theoretical considerations

3.1 Asymptotic atomic states

It is clearthat for molecular calculations to be reliable, beforeanything else is done, a proper account of the asymptoticatomic states is essential. In particular, a rather accurate posi-tioning is necessary for the 2S2D and 2S2P transitions ofthe metal atoms, for the first ionization potential, for the1S3D and 1S1D transitions of the M+ ions as well as forthe electroaffinity of the halogen in question.

One particular important aspect concerns the inclusionor lack of the scalar relativistic effects (the Darwin and themassvelocity corrections) which alreadyare crucialfor cop-per. It should be recalled that these scalar effects are large

enough to invert, at the DiracFock level, the 3d10

4s1

and3d94s2 configurations of Cu, placing the latter 900 cm1 be-low the former. Then, the inclusion of correlation effectsupon these relativistic states corrects this wrong ordering.For molecular problems, a more practical approach has beengenerally adopted through the use of small-core relativis-tic effective core potentials, that already include the Darwinand massvelocity scalar relativistic corrections, and largebasis sets in conjunction with sophisticated non-dynamicand dynamic electronic correlation treatments; this has beenrecently achieved using the MRCI, CASSCF+CASPT2,

CASSCF+ACPF and CCSD(T) methods for both metals.The complete failure of the large-core 11-active electron AgRECP [56], both at theCCSD(T) andACPF levels,has shownexplicitly[57]thatonlysmall-coreRECPwith19-activeelec-trons can accurately reproduce the complex fine-structurespectra for Ag and Ag+.

Table 1 contains a comparison of the best theoretical and

experimental values for the ionization potentials (IP) andexcitation energies (Te) of the metal atoms, as well as of theelectron affinity (EA) of the halogen atoms, obtained withdifferent methods (MRCISD, CCSD(T), ACPF) and largead-hoc optimized valence Gaussian basis sets. The authorsof [1] also considered inclusion of the Davidson correction(+Q) in the MRCISD case to take into account the effect ofhigher-than-double excitations, and determination of excita-tion energies by means of the equation-of-motion coupledcluster (EOMCCSD) method [58] for some of the singletexcitations. The theoretical results are compared to the spinorbit J-averaged (using Lands rule for the isolated multi-plets) experimental values.

Some interesting remarks arise from an analysis of thistable. It is clear that the CCSD(T) and CASSCF+ACPF cal-culations perform better than the multireference methodslike the MRCISD+Q, both with absolute errors of less than800cm1 for IP values of about 62,000cm1. For the tran-sition energies between the ground and excited states Te ofthe copper atom and cation, both the CCSD(T) andthe ACPFapproaches yield excellent results, with errors smaller than200cm1 (and 600 for Te of about 85,000cm1 for the cat-ion). For the Cu(3d104s1)Cu(3d94s2) transition, the MR-CISD method, even with Davidsons correction, is off by2,000cm1 (+Q:1,400cm1)fora Te of 12,000cm1,whichrepresentsalargeerrorof16%;thiscouldbeexplainedbythe

fact that more accurate methods are needed to properly takeinto account the contribution of higher than double excita-tions on the differential correlation energy, due to the changeof occupation in the 3d shell from 10 to 9 electrons. It wouldappear that the intrinsic size-consistent formulation of theCCSD(T) and ACPF approaches insures a better descriptionof these transitions where a varying number of electrons inthe d shell is involved.

For silver, the situation is more complex and the behav-ior of the CCSD(T) and ACPF differs depending on thetransition under consideration. Also, it turns to be a bit sur-prising that the MRCISD+Q method produces the best esti-mation for the Ag(4d105p1)Ag(4d95s2) difference around

1,800cm1

, while the CCSD(T) approach underestimatesthis difference as 700 cm1 and the ACPF methodoverestimates it as being 3,000cm1. Here the argument ofthe size-consistency of the CCSD(T) and ACPF versus theapproximate inclusion of it by the MRCISD+Q is thus inval-idated. The calculated IPs are within 1,000cm1 from theexperimental value for all methods. These purely electronicenergies and wavefunctions usually represent the startingpoint for the consideration of the spinorbit effects.

A word concerning the brand new multiconfigurationDiracHartreeFock pseudopotentials for Cu and Ag [61]


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Table 1 Best theoretical transition energies and ionization potentials for Cu and Ag in wavenumbers, experimental J-averaged values, halogenelectroaffinities in electron volts

Atomic state MRCISD/+Qa CCSD(T)a CASSCF+ACPFb Exp.

Cu+(1D : 3d94s1) 81133/85408 84924c 88020 88634Cu+ (3D : 3d94s1) 77585/80972 84763 (83626)d 84360 84958Cu+ (1S : 3d10) 58551/60164 62019 61510 (IP) 62310(Cu2P0 : 3d104p1) 29679/30647 31211 30816 30618

(Cu2D : 3d94s2) 9919/10645 11855 (10715)d 11836 12019(Cu2S : 3d104s1) 0 0Ag+(1D : 4d95s1) 100893/102909 103554c 102789 107129Ag+(3D : 4d95s1) 96538/98634 100328 (99901)d 98740 101701Ag+(1S : 4d10) 57261/59197 60487 60103 (IP) 61084Ag(2D : 4d95s2) 32179/31453 30888 (30006)d 31384 32030Ag(2P0 : 4d105p1) 28630/29679 30163 28332 30165Ag(2S : 4d105s1) 0 0F (EA:2p52p6) 2.99/3.21 3.35 3.34e 3.41Cl (EA:3p53p6) 3.38/3.52 3.59 3.44f 3.62Br (EA:4p54p6) 3.29/3.41 3.46 3.52I (EA:5p55p6) 2.87f 2.90g 2.91g 3.06

* Experimental values from [59]a 19-active electron RECP/contracted basis [7s6p4d3 f2g] values from [1]; MRCISD with Davidsons correction noted as +Q

b 19-active electron RECP/contracted basis [7s9p6d2 f2g] values from [60] for Cu and 19-active electron RECP/contracted basis [6s5p4d2 f]from [43] for Ag. CASSCF(11,9) used as references for both atomsc Same as (a) but the EOM-CCSD(T) was used to describe the 1 S:(n 1)d101 D:(n 1)d9ns 1 transitionsd 19-active electron with new MCDHF-PP/[6s6p4d3 f2g] contracted basis values from [61]e ANO-large [5s4p3d2 f] contracted basis from [35]. CASSCF(8,4)+ACPF value reported heref 7-active electron RECP/optimized [5s5p2d1 f] contracted basis, CASSCF(8,4)+ACPF from [43]g 7-active electron RECP/optimized [6s7p2d1 f] contracted basis; CASSCF(8,4)+ACPF from [54]

is due here since, for the d10s1d9s2 and the d10d9s1

transitions where a change in occupation of the d orbitalsoccurs, they provide less accurate CCSD(T) atomic resultsusing equivalent correlation treatment and basis sets as withtheoldMWBones;theauthorsstressthattheirnewCCSD(T)energies lead to errors that are rather large, up to 2,180cm1

(seeTable5 of[61]),and explicitlyshow that only a fullyhugeuncontracted valence 14s13p10d6 f4g4h4i basis set can re-ducetheseerrorsto1,100cm1.However,itisclearthatsuchbasis sets cannot be used for highly correlated molecular cal-culations. The connection of this with the spectroscopy ofMX molecules is that all the excited states of these halidesare diabatically correlated to the M+(d9s1)X(p6) atomicasymptotes and that, for the silver ones, these are some-timesmixedwiththeM(d9s2)X(p5) neutralones.Theconse-quencesoftheseatomicerrorsonthespectroscopyoftheMXfamilieshave to be met when trying to obtain accurateenoughzerothorderwavefunctions(CASSCF),sinceitisatthatpointwhen the approximate positioning of all the neutral and ionic

asymptotes proves to be essential for the adequate mixingof configurations in the delicate balance between competing(IPEA) with the excitation energies for the metals (atom orion). Thus, various types of mixings are possible betweenionic M+X and covalent MX states that are later described.

3.2 Spinorbit effects on the isolated atoms

Itisclearthatifthemolecularstatesthathavetobeelucidatedlie within an energy range that is as small as the SO splittings

for Cu or Ag (and their ions), the SO effects will have tobe extremely well accounted for in the isolated atoms firstbefore these effects can be safely transferred to the molecu-lar environment.

To place the reader in the appropriate perspective of thissection, the fine-structure experimental spectra for Cu, Cu+,Ag,Ag+ andthehalogenseriesareshowninTable2.Itcanbereadily seen that the SO splittings for silver are about twiceas large as those found for equivalent multiplet of copper,both for the neutral species and for the ions.

For silver, we have already mentioned that the 2 P Ryd-berg state lies below the 2D one. In this respect, silver istruly a unique case in the whole periodic table. A furthercomplication arises when spinorbit (SO) effects are con-sidered, since the SO coupling constant for the 4d orbitalsis rather large (4d(Ag+) = 1, 830cm1) and, as a conse-quence, the lowest component (J=5/2)ofthe 2Ddoubletliesjust below the highest component (J=3/2) of the 2P0 dou-blet, their difference being barely 230cm1. These two facts

together induce great complexity in the theoretical approachif one aims at spectroscopic accuracy, even for the isolatedatom. But extreme care must be taken here to properly definethis accuracy. Given our experience with the rather complexmolecular spectra for these metal halides, we have chosen tousethepragmaticdefinition,i.e.,bythisspectroscopicaccu-racy term we mean that the final computed fine-structurestates can unambiguously be associated (through their hier-archical energetic order) to the correct experimental quan-tum numbers, these being the J value of each component ofa given atomic multiplet (recall the above-mentioned 2D2P


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Table 2 Best theoretical spinorbit splittings versus experimental data

State Theoretical Experimental*Cu(a) 2S 0 02D5/2 11610 112022D3/2 13655 (2045) 13245 (2043)2P1/2 30730 305352P3/2 30981(251) 30784 (249)

Cu+(a) 1S 0 03D3 21802 219283D2 22890(1088) 22847 (919)3D1 23767(1965) 23998 (2070)1D2 25987 26264Ag(b) 2S 0 02P1/2 29574 295522P3/2 30416(842) 30472 (920)2D5/2 28547 302422D3/2 32849(4302) 34714 (4472)Ag+(b) 1S 0 03D3 36,867 391643D2 38466(1599) 40741 (1577)3D1 41477(3011) 43739 (2998)1

D2 44885 46045F (2P3/22P1/2) - 404Cl (2P3/22P1/2)c 912 881Br (2P3/22P1/2)c 3739 3685I (2P3/22P1/2) 7738c, 7610d, 7580e 7603

* Experimental values from [59]a From [60]. ESOP-Diagonal effective Hamiltonian elements, CASSCF+ACPF energiesb From [56]. ESOP-Diagonal effective Hamiltonian elements, CASSCF+ACPF energiesc Optimized-level DiracCoulombFock from [61]d Averaged-level DiracCoulomb CISD from private communication with E. Fromager, L. Vischer, L. Maron and C. Teichteil. 4s4p4d5s5pshells as active spacee ESOP diagonal effective hamiltonian elements from CASSCF+ACPF energies, [54]All energies in wavenumbers. For an easier assessment of the theoretical SO effects, differences within multiplets are given in parentheses

fine-structure mixing in Ag), or the value for the molecularcases.

For the treatment of the SO term in the electronic Hamil-tonian, there are several different approaches, ranging fromthe treatment of an all-electron four-component Dirac equa-tion[63], or an approximate two-component reduction of thisequation [64] to more approximate but more versatile scalardescriptions followed by additional calculations for the SOsplittings [65,66].

In a conventional two-step method, the SO coupling istakenintoaccountafterthecorrelationtreatment.Thishasthemain advantage to allow a CI process in non-relativistic sym-metries, and then to use the most sophisticated and extendedCI calculations. Moreover, the use of both RECP techniques

and effective Hamiltonianmethods, considerablyreduces thesize of the total Hamiltonian, generally expressed on the ba-sis of correlated LS (or S for linear molecules) states.However, the main drawback here is to use only contractedmulticonfigurational wavefunctions, or in other words, toexclude the effects of the SO interaction on the correlatedwavefunctions. One can, in principle, overcome this diffi-culty by introducing in the matrix representation of the totalHamiltonian buffers of highly excited states which have tobe computed (at a much higher cost) even if they are notsearched for.

Another way to accurately take into account a strong SOeffect on a correlated wavefunction is to treat in a one-stepmethod correlation and spinorbit coupling simultaneouslyat the same level [64]. However, such a treatment is foundto be very demanding computationally and does not allowthe best possible CI treatment due to the loss of nonrelativ-istic symmetries; this method must be avoided for complexproblems like the spectroscopy of copper and silver halides.

The EPCISO algorithm[67] keepsthe advantages of bothtypes of the previously mentioned methods. It uses aneffective Hamiltonian method in a two-step way, and in thismanner allows extended as well as sophisticated electroniccorrelation treatments. This point is crucial for the spectros-copy of silver, as pointed out previously. The effects of the

SO coupling on the correlated wavefunctions is taken intoaccount by introducing in the total Hamiltonian, expressedinadeterminantalbasis,allthesingleexcitationsfromagivenreference space which are important for the SO coupling (viaan energy threshold). The reference CSF space is chosen insuch a way that only the states of interest are represented;this can be done in a somewhat poor representation since thecorrelation effects have already been accurately introducedthrough the effective Hamiltonian technique. In this way, thepolarization effects of the SO interaction due to higher-lyingconfigurations on the lower correlated states are taken into


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648 A. Ramrez-Sols

account. In the complex case of Ag, where the fine-structurecomponents of the silver 2D and 2P states are intertwined,this procedure presents a great advantage since it leads toaccurate fine-structure calculations, even though only the LSstates of interest have been really computed at theACPF level[57].

FortheCu,Ag,aswellasforthehalogenatomstheeffec-

tive spinorbit potentials (ESOP) of Stuttgart [68,69] havebeen successfully used (see the comparison with the latestfour-component DiracCoulumb correlated calculation foriodine in Table 2). It is worth noting that the SO splittingsfor the metal ions are also reproduced quite well, in spite ofthe fact that these ESOPs have been basically derived for theneutral atoms.

The most important thing that can be concluded from theapplication of the effective Hamiltonian SO calculations isthat, even though in [57] we were able to correctly repro-duce the 2P3/22P1/2 splitting as 842 (vs. 920cm1 exp.)and the 2D5/22D3/2 splitting as 4, 302cm1 (vs. 4472cm1

exp.), the relative ordering of these four fine-structure states

was found to be critically dependent on the diagonal ener-gies defining the effective Hamiltonian of the EPCISO algo-rithm. These results show the great difficulty in obtaining thecorrect 2P1/2,2 D5/2,2 P3/2,2 D3/2 mixedexperimentalorder-ing for neutral Ag due to the complexity needed to properlydeal with the d10snpm d9s2 differential correlation effectswhich, ofcourse, can be properly dealtwith atthe atomic level(using larger basis sets), but cannot be easily transferred tothe molecular problem in complex systems like AgX.

3.3 The molecular states

The spectroscopy of all the CuX and AgX molecules can beexplained as transitions from the fine structure states arisingfrom the 3,1+,3,1 and 3,1 parents to the X1+(0+)ground states. The extent of the interactions between theM+X ionic and the covalent MX structures depends on thepossiblemixingsofthediabatic,atomicandionicasymptotesfor each MX couple.

Covalent states: In their ground state, the valence configu-ration of the metal atom corresponds to the 2S state and thehalogen atoms are in their 2P state. The first asymptote isthus correlated only to 3,1+ and 3,1 states. The secondasymptote corresponds to the excitation of the metal atomto a 2D or a 2P state. The gap between the ground and thefirst excited asymptotic state, as well as the nature of thisexcited state, depends on the metal (2D for Cu and 2P forAg). In these low-lying asymptotes, the halogens remain intheir ground state configurationbecause their excitation ener-gies are much larger than for the metal. It is then easy to notethat these two configurations are asymptotically correlatedto a large number of singlet and triplet states: one 3,1, acouple of 3,1, three 3,1, one 3,1+ and two 3,1 forM(2D), and one 3,1, two 3,1, one 3,1+ and two 3,1

for M(2 P).

Ionic states: The configuration of the lowest ionic asymp-totic state is M+(d10)X(p6). The first ionic state is henceof1+ symmetry, as well as the ground covalent electronicstate, so they will strongly interact when their energies comeclose together. This does not happen for the excited statesnear the ground state equilibrium geometry for CuF, CuCland CuBr but for CuI this begins to occur, especially for

the 3,1 ones. For the whole silver halide family, this strongneutralionic mixing gives rise to theoretical problems antic-ipated already by Mulliken in 1937.

Higher ionic excited states M+((n 1)d9ns 1)X(np 6)correspond to the electronic excitation of the M ion in 3Dand 1D states states, which can generate 3,1+, 3,1 and1,3 states.

3.4 The choice of zeroth-order references

There are two issues concerning this point: the definition ofthe active orbital space that can be used and, the question ofwhether state-specific or state-averaged CASSCF wavefunc-

tions are used as references for further correlated descrip-tions.

3.4.1 The choice of the active orbital space

The question of the active orbital space that must be cho-sen to define the reference wavefunctions is not a minor is-sue and can have important consequences for spectroscopicpurposes. The CASSCF calculations of [1] were somewhatlimited, since the authors only included 16 electrons in 10active orbitals, these being the five nd, the (n + 1)s and the(n + 1)p orbitals of the metals, along with the three npof the corresponding halogen atom. Without a doubt, this

active set of orbitals adequately generates the complete ac-tive space of configurations needed for the description of thelowest excited states of copper and gold halides, but it isinsufficient to provide even reasonable zeroth-order CASS-CFwavefunctionsfortheexcitedstatesofsilverhalides,sincethe Ag(2P0)+X(2P) asymptotes (which cannot be properlydescribed with this CAS) lie below theAg(2D)+X(2P) ones.Recall that the Ag(2P0) + X(2P) asymptote is diabatical-ly coupled to 3 +,1+, 3, 1, 3 and 1 configurationsthat will strongly interact with those arising from the otherexcited asymptote, as well as with the lowest ionic ones. Theexclusion of both the Ag(n + 1)p orbitals from the activeset precludes the mixture of the numerous Ag(4d105p1)X

(npsnpt , s+ t= 5), Ag(4dx 4dy 4dz 5s2, x +y+z = 9)

X(npsnpt , s+t= 5) neutralandAg

+(4dx4dy 4d

z 5s

1,x+

y + z = 9) X(ns2np6) ionic structures present in thedescription of the lowest excited states. So, for the silverhalides,theCASSCF(16,10)wavefunctionslacktheessentialeffects brought in by the nondynamic electronic correlationassociated with one of the most important diabatic neutralstructures needed to provide a good zeroth-order referencefor the excited states. The smallest set of active orbitals thenhas to be composed of 12 orbitals, and must imperatively in-clude the other two (n + 1)p orbitals. This generates much


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larger CASSCF wavefunctions, with 17, 495 CSF instead ofonly 187 for the 1+ symmetry, and 28,344 CSF insteadof only 148 for the 3 one; these larger reference CASS-CF wavefunctions generate, of course, much larger MRCIspaces of around 500800 million CSF [35,43,54], insteadof the 10 million considered in [1]. However, only such largevariational calculations can provide truly reliable theoretical

spectroscopic results for the silver halide molecules.

3.4.2 State-averaged versus state-specific orbitaloptimizations

Once the previous point has been satisfactorily solved, thesecond point addresses state-averaged (SA) versus state-spe-cific (SS) orbital optimizations. Our experience is that forthese complex spectroscopic problems, the state-averageddescription provides even qualitatively wrong behavior ofthe CASSCF wavefunctions for the 21+ excited states ofAgX, which are in all cases involved in the BX transitions

of this family; to illustrate this, Fig. 1 shows a comparisonof the SS versus SA descriptions for the two lowest 1+

states of AgCl. Two basic spectroscopic quantities calcu-lated after highly correlated ACPF calculations using thesetwo different CASSCF wavefunctions as reference are as fol-lows: Re(21+) = 4.35a.u., e = 286cm1 fortheSSref-erence and Re(21+) = 4.43a.u., e = 326cm1 for theSA reference; only the experimental vibrational frequencyof 279cm1 has been reported to compare these theoret-ical results. These results highlight the importance of theSS-CASSCF zeroth-order description for spectroscopic pur-poses. The effect of the SS or the SA description on thetransition energies is much less evident, since the dynamic

correlation energy can be quite different on each electronicstate, even within the same spin-space manifold. In [1] theauthors used SA CASSCF(16,10) references, averaging overall the space symmetries only optimizing separately the twodifferent spin situations; doing this rather rough orbital aver-aging introduced such errors as the ones shown above for thefrequencyofthe21+ stateofAgCl,sincetheyalsoobtainedthe e = 324cm1 MRCISD value.

3.4.3 The Spinorbit effects in the molecules

For the CuX and AgX families, two levels of complexity inthe theoretical approach used must be considered. The firstone is to use the purely electronic approximation in the Ham-iltonianandtoneglecttheSOeffectsonthebasisofthesmall-ness of these effects for particular cases; this approximationprovided good enough descriptions for most of the observedtransitions and the experimental spectra could successfullybe explained for CuF [17] and CuCl [24,27]. For CuBr, aswas mentioned in the previous section, the double-group rel-ativistic calculations of [25,26] naturally take into accountthese effects.

However, for CuI, the SO effects arising from both atomshave to be imperatively considered, given the much less

Fig. 1 Comparison of state-specific versus state-averaged (0.50.5)CASSCFdescriptionfortheX 1+ and21+ statesofAgCl.Curvesareidentified by the following notation: state-specific X1+ (down trian-gle); state-specific 21+ (circle); state-averaged X1+ (up triangle);state-averaged 21+ (plus sign). In all cases, 16 active electrons in 12active orbitals were considered, leading to CAS expansions of 17,945CSF. Note the divergence problem of the state-specific calculation forthe 21+ state beyond 4.725a.u

evidentinterplaybetweentheneutralandionicstructurespre-viously discussed. Therefore, the second level of complexityhas to be applied, which means that the SO effects are intro-duced after the electronic descriptionhas beenachieved. Thiswas done in [32] for CuI.

In the very interesting and careful analysis made in [1] itwas shownthat for thecopperhalides,the shapes of thepoten-tial energy curves are almost not modified by the spinorbitinteractions. The molecular fine-structure splitting reportedis below 0.2eV, as expected for a Cu+(3d94s1)X config-uration; nevertheless, the interactions between fine structurecomponents are detected, for example, between the = 1componentsof3+ and 1 statesthatleadstothepresenceofa Q branch and to a substantial -doubling in the 3+1+

system, which are mentioned in a recent experiment [70].For AgX compounds it has been noted [1] that, as ex-

pected from the atomic states, the spinorbit interactions areabout twice as large as for CuX compounds. Strong interac-

tions are expected for these and, as an example, all the differ-ent components arising from the parent electronic states areshown in Fig. 7 of [1] for AgF at the minimum of the groundstate. Their results for AgX(X=F,Cl,Br) show that the mostimportant interactions are, by far, those arising from the 3state, betweenits 0+ componentandthe21+ state, betweenthe = 1 component and the 1, as well as 31 states, anda small interaction between the = 0 component and the3+0 state. Another large interaction was found between the = 2 components of the 3 and 1 states, but this is of noconsequence to the observed spectroscopy up to date.


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650 A. Ramrez-Sols

For AgI, the same type of SO interactions were found[55],buttheseeffectsappearalreadyontopofamorecomplexsituation due to the presence of the double-well 21+ poten-tial that has been previously discussed.

4 Overview: what works fine and what does not

4.1 Equilibrium geometries and harmonic frequencies

Table 3 shows a compilation of the two most basic quantities(equilibrium geometries and frequencies) for which the the-oretical results present important deviations. The CuX mol-ecules have been excluded since for these molecules there isbetter agreement between theory and experiment, therefore,the assignments and the nature of the observed transitionshave generally been successfully achieved.

The MX equilibrium geometries have been measuredexperimentally (sometimes indirectly) only for the ground

states, except very few exceptions, like for the B states ofAgCl and AgI. The theoretical MRCI and ACPF values arefound in very good agreement (within 0.010.015) evenwithout the SO coupling, since the ground states are almostleft unchanged by the SO effects. The correspondingMRCISD, CASSCF+ACPF or CC vibrational frequenciesare also within 2030 cm1 from the experimental values forground states of CuX and AgX. This accuracy has also beenveryrecentlyachievedthroughDFTusingahybridfunctional[71] for the AgX ground states.

For the excited states, much larger errors exist and themost dramatic failure comes from the pathological behav-ior of the 3+ state of AgI, for which a theoretical CASS-CF(16,12)+ACPF value of 867cm1 has been calculated,while the exp. value is only 151 cm1. This, of course, stemsfrom the extraordinarily complex mixing of diabatic neutraland ionic configurations that, for this halogen, happens tooccur just above the ground state equilibrium geometry (seeFig. 2).

Only for a few of theexcitedstates experimental informa-tion exists concerning equilibrium geometries. For instance,for the B0+ state of AgI, the MRES measurements haveprovided the RKR-fitted values of two potential wells. TheACPF+SO results have provided values (2.52 and 4.29)for both wells that compared with the experience (2.69 and3.42) are too short and too long, respectively. This prob-lem is coupled to the rather large errors on the correspond-ing vibrational frequencies, calculated as 351 and 46cm1,compared with the 131 and 124cm1 experimental valuesfor the two minima on this potential. It is quite surprising tofind experimentally such a small vibrational frequency forthe innermost minimum, which is actually quite close to therepulsive core region of the B0+ state, as can seen in Fig. 2.

Unfortunately, there are still no other studies with whichthese ACPF+SO values could be compared. Anyway, it isclear that these quasi-state-specific (weights 1:7) CASSCF+ACPF calculations already including the SO effectsrepresent the current state-of-the-art and no other better

Fig.2 Potential energycurves forthe lowest fine-structure states of AgI

in the 410a.u. range. States are identified by the following notation: = 0+ (dark full lines), = 2 (dotted-dashed curve), = 1 (lightfull line), = 0 (dashed line)

approach seems possible in the near future for two basicreasons:

(a) A DFT approach is out of the question since this B statecontainsadominantcomponentfromthe2 1+ stateand,therefore, it cannot be studied with KohnSham basedtheories. Given the accuracy needed, it seems that time-dependent DFT (TDDFT) is a much too rough approxi-mation to be used for this problem.

(b) The single-reference CC methods are also excluded forthe study of such a complex potential since the pres-ence of a maximum near the equilibrium geometry ofthe ground state clearly shows (see Fig. 2) the strongneutralionic configuration mixing that occurs aroundthis spectroscopically active region. So, no better solu-tion for the time being can be envisaged to improve thedescription already given of this complex B0+ state ofAgI.

4.2 Transition energies and nature of the excited statesof MX

The spectra of the copper halide family can now almost befully understood on the basis of the vast experimental andtheoretical work. It is very important to point out that theexperimental work on radiative lifetimes of the excited statesmeasured from fluorescence decay on CuCl, CuBr and CuIallowed essential insight concerning the singlet and tripletcharacter of the states.

The measured transitions are between the ground stateX1+ (from the Cu+(3d10)X(ns 2np 6) configuration) andthe ionic excited states arising from the Cu+(3d94s1)X(ns 2np 6) configuration. Most of the bands in the spectra


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Table 3 The most important deviations from experimental values (in parentheses) for some of the basic spectroscopic quantities for AgX

AgF AgCl AgBr AgI3+

Re 1.88CASPT2[34], (1.93) No experiment No experimente 553MRCI[1], 564CC[1] (507) 867ACPF[53] (151)21+ 2.52[53] 2.56[54] (2.69) sRe 1.89CASPT2[34], (1.96) 2.34CCSO[1], (2.32) 4.29[53] 4.19[54] (3.42) l

2.30ACPF[43] 532[53] 351[54] (131) se 523MRCI[1], 519CC[1] (455) 324MRCI[1], 256CC[1] (279) 216MRCI[1] (180) 74[53] 46[54] (124) l3

Re 2.06CCSO[1], 1.91[34]

(2.02) No experiment No experiment No experimente 574CASPT2[34] (376)Bond lengths in angstroms, energies in wavenumbers. s and l denote the short and long minima for the B0+ state of AgI

Table 4 Term values (in cm1) and parent state assignments of the observed excited states of AgX

State Exp. Te Previous Assignment () New Theoretical (T00 or adiabatic)AgF

A0 24931 None (0)3+[35] 22773CASPT2[35], 25969CC+SO[1], 25727CC+SO[59]

A

1 24951 None (1

)3

+[35]

26938[34]

, 22773[35]

, 23630MRCI[1]

, 25969CC+SO[1]

A0+ 29280 None (0+)21+[35] 31299[34], 27487[35], 29598MRCI[1], 31130EOMCC[1],30243CC+SO[1], 29195EOMCCSD[59]

B0+ 31664 None (0+)3[35,1] 28866[35], 30969MRCI[1], 32421CC[1],33953[59] {31372(2),31776(1),33792(0),34365(0+)}SO [1]

(1) 1[59] 34356SO[59]

AgClB 31606 3(0+)21+3 31388(21+)[43], 32098MRCI[1], 32663EOMCC[1],

33308(0+)SO[1], 33147SO[59]

C 43525 None (?) 23 43147MRCI[1]

D 48800 None (2) 3[43] (31+)[1] 50496(3)[43], 49357(31+)MRCI[1], 41857SO[59]

AgBrB 31292 None (0+) 21+ 32663MRCI[1], 32340(0+)SO [1], 32501S O[59]

C 43551 None (0) (23)[1] 43309MRCI[1]

AgI

A 23906 None (0, 1) 3+ 23640[54]B 31197 3(0+)21+3 23230[54]

C 44720 None (?) 31

D 46000 None (?) 23E 47500 None (?) 31+33References for the corresponding experimental data are found in each theoretical work cited. T 00 was calculated using the CASSCF+ACPFenergies with zero point energy correction. Experimental values in parentheses

of the heavier copper halides could be assigned to particularexcitations in good agreement with experimental data; how-ever, there is still no consensus [25,26] on the interpretationof some of these transitions for CuI, where the presence of

the neutral configurations is much more important for theexcited states near the equilibrium geometry of the groundstate. In the MCSCF+CIPSI calculations of [32] the neu-tral states, arising from the Cu(3d104s1)I(ns 2np 5) configu-ration, appear in the same energy region as the ionic states,even without the inclusion of spinorbit interaction. In or-der to provide definite answers to these questions concerningCuI, more precise CASSCF calculations (using state-specificorbitals for the excited states that correctly take into accountthis neutralionic competition) plus MRCISD-like descrip-tions are needed now. It should be emphasized that theoreti-

cal radiative lifetimes have also been found to be in excellentagreement withexperiments for some of these copper halides[2729].

Table 4 presents the present situation concerning the

assignment of the parent states to all the known transitionsfor the AgX family, as well as the corresponding theoreticaltransition energies, calculated at various levels of theory.

The use of state-averaged orbital optimization for latercorrelated applications such as MRCISD has to be properlyjustified. For some cases, this state-averaged zeroth-orderdescription leads to important qualitative inaccuracies, suchas the absence of local maxima and exaggerated harmonicfrequencies. For instance, in the AgI case, the double-wellB potential cannot be properly obtained using state-averagedCASSCF for the 21+ state.


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652 A. Ramrez-Sols

The large CASSCF(16,12)+CASPT2 calculations forAgF provide transition energies that are off by +2,000and 1, 700cm1 for the A and B states. The smallCASSCF (16,10)+MRCISD results underestimate by 8001, 600cm1 most of the Te for AgF due to the exclusion ofthe 5p orbitals from the active space.

Inspiteofthefactthatthestate-specificCASSCF +ACPF

+EH(SO) method has allowed the confirmation of the one-state hypothesis for the B state of AgI, this very expensiveapproach yields a transition energy for the B0+ state that is3,000cm1 below the experimental value of 31,197 cm1.

In [1] theauthors point outthat thelargest deviations fromexperiment arise for dissociation energies, since theoreticalvalues are systematically smaller than experimental data by0.2eV on the average. For AgI, the error is also 0.19eV atthe CASSCF+ACPF level [54]. These deviations cannot beexplained by the radical change of the diabatic character ofthe wavefunction (Cu + F Cu+F) upon molecular for-mation, since the energy difference between the covalent andionic asymptotes is very well reproduced by CCSD(T) and

CASSCF+ACPF calculations, with an accuracy better than0.04eV. However, some of the experimental De values havebeen indirectly estimated by means of approximate relations.

Asalastremark,itshouldbesaidthattheextremelycom-plex spectroscopy of CuCl2 has been studied and explainedusing single-reference methods such as SDCI, CPF [72] andCCSD(T)[73];morerecentlystate-of-the-artbenchmarkvar-iational multireference methods [60,74] have been applied tostudy this molecule. However, we have recently shown thatDFT-based methods using some of the new and more refinedfunctionalscanalsoprovidereliableresults,withinthe SCFapproximation, that are of similar accuracy as those painfullyobtained with the CASSCF(21,14)+ACPF +SO approach

[75]. To our knowledge, this has not yet been attempted forany of the CuX or AgX members and perhaps this approachcould provide answers to particular issues that have not yetbeen solved using standard ab initio methods.

5 Conclusions

This overview of the theoretical works devoted to study thespectroscopy of CuX and AgX molecules has shown that:

1. The multireference second order perturbational scheme

(CASPT2) works well to describe the spectroscopy ofCuX family but fail rather badly for the AgX series, dueto the strong change in character arising from the neu-tralionic configuration mixings that occur for this fam-ily. Therefore, these methods should be avoided for thistype of molecule.

2. The molecular active orbital spaces have to be care-fully defined to include in the zeroth-order referencewavefunctions all the relevant asymptotic neutral andionic fragments that will interact in the spectroscopicallyactive region.

3. Many of the single-reference coupled-cluster wavefunc-tions have provided accurate enough results for some(but not all) excited states of these molecules. This isalso valid for the EOM-CCSD(T) method for selectedsinglet excitations.

4. The use of state-averaged orbital optimization for latercorrelated applications such as MRCISD has to be

properly justified and cannot be applied without a care-ful analysis of its consequences on the spectroscopy;this state-averaged zeroth-order description can lead toimportant qualitative (such as topological) inaccuraciesin the potential curves.

5. ThelargeCASSCF+ACPFapproachprovidesharmonicfrequencies for the 21+ and 3+ states of AgI that aredramatically overestimated, and in error by up to morethan 300 and 500% (over 700cm1), respectively.

6. Fundamental contradictions remain between thepredictions made by small CASSCF(16,10)+MRCISDandCCof[1]andthoseoflargeCASSCF(16,12) +ACPF[43], since the former point to the 31+ state while the

latter to 32 as the parent of the D state in AgCl. It is notclear what other ab initio method could shed new lighton this complex problem; the SCF approach of DFTis by nature excluded to deal with such a highly excitedroot of the 1+ manifold and, therefore, it cannot giveadditional insight.

7. Inspiteofthefactthatthestate-specificCASSCF+ACPF+EH(SO) method confirmed the one-state hypothesisof the B state, this very expensive approach yields atransitionenergyfortheAgIB0+ statethatis8,000cm1

below the experimental value of 31,197cm1. Lesssophisticated state-averaged CASSCF(+MRCISD) willnot provide accurate enough zeroth-order wavefunctions

for this complex case. On the other hand, this transi-tion cannot be properly described using single referencemethods (CC for example) due to the presence of strongconfigurationmixing near the ground state Re; therefore,no other theoretical tool from ab initio quantum chemis-try seems able yet to solve this riddle.

8. DFT-based methods (within the SCF approach) usingsome of the new and more refined functionals can per-haps provide alternative answers to particular questionsthat have not yet been solved using standard ab initiomethods, since many of the transitions can be assignedto de-excitations from states that differ in their Squantum numbers from the ground states of the CuX and

AgX series. TDDFT can be a useful tool to study statesof the same spin-space symmetry as the ground state.Also, recent advances in four-component time-depen-dent DFT [76] will become valuable tools to study thekind of complex spectroscopy found in transition metaldimers.

9. The very recent development of more refined scalar-relativistic and spinorbit effective potentials has nothelpedtosolvethemainproblemsassociatedwiththeex-cited state description of these molecules, since the newCu and Ag MCDHF-PP provide less accurate CCSD(T)


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atomic results (using equivalent correlation treatmentandbasissetsaswiththeoldMWBones)butonlyforthed10s1d9s2 andthe d10d9s1 transitions,whereachangein occupation of the d orbitals occurs [61]; the authorsstress that their new CCSD(T) energies lead to errors arerather large, up to 2,180cm1, and explicitly show thatonly a huge fully uncontracted valence 14s13p10d6 f4

g4h4i basis set can reduce these errors to 1,100cm1.However, it is clear that such basis sets cannot be usedfor highly correlated molecular calculations. The linkof this with the spectroscopy of these MX molecules isthat all the excited states of these halides are diabati-cally correlated to the M+(d9s1)X(p6) atomic asymp-totes and that, for the silver ones, these are sometimesmixed with the M(d9s2)X(p5) neutral ones. Unfortu-nately, they have not included CuI and AgI in their firstbenchmark applications of these new RECP and SOEP.

10. Allinall,thelargevarietyoftheoreticaleffortstodescribethe spectroscopy of these molecules has greatly helpedobtain important insights to understand the complex

spectroscopy of these halides and most of the knowntransitions have been explained, especially for the CuXfamily. However, these efforts have also produced fun-damental results concerning some excited states that arestill far from the experimental ones. Therefore, muchwork remains to be done to provide new methods whichareaccurateenoughandcanproperlydealwiththeessen-tial problems that arise from the nondynamic and dy-namic electronic correlation effects on these molecules,since it has been shown that the spinorbit effects fromthe atoms (ions) can quite accurately be transferred tothe molecules.

Acknowledgements The authorthanks PIFI-SESIC(SEP)Mxico andthe French CNRS for support during his sabbatical stay at LPQ-IR-SAMC.

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Theory Success and Failure on Silver Monohalides

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