Low-Lying Electronic States of CuAu - The Journal of Physical

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Low-Lying Electronic States of CuAu Davood Alizadeh Sanati, and Dirk Andrae J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b05522 • Publication Date (Web): 05 Jul 2016 Downloaded from http://pubs.acs.org on July 9, 2016

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The Journal of Physical Chemistry

Low-Lying Electronic States of CuAu Davood Alizadeh Sanati†,‡ and Dirk Andrae∗,† †Physikalische und Theoretische Chemie, Institut f¨ ur Chemie und Biochemie, Freie Universit¨ at Berlin, 14195 Berlin, Germany ‡Previous address: School of Chemistry, College of Science, University of Tehran, 14176 Tehran, Iran E-mail: [email protected] Phone: +49 30 83850958. Fax: +49 30 83854792

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Abstract Coinage metal diatomic molecules are building blocks for nanostructured materials, electronic devices, and catalytically or photochemically active systems currently receiving lively interest in both fundamental and applied research. This theoretical work elucidates the electronic structure in the ground and several low-lying excited states of the diatomic molecule CuAu that result from the combination of the atoms in their ground states nd10 (n + 1)s1 2 S and lowest excited d-hole states nd9 (n + 1)s2 2 D (n = 3 for Cu, n = 5 for Au). Full and smooth potential energy curves, obtained at the multi-reference configuration interaction (MRCI) level of theory, are presented for the complete set of the thus resulting 44 Λ−S terms and 86 Ω terms. Our approach is based on a scalar relativistic description using the Douglas-Kroll-Hess (DKH) Hamiltonian, with subsequent perturbative inclusion of spin-orbit coupling via the spin-orbit terms of the Breit-Pauli (BP) Hamiltonian. The Ω terms span an energy interval of about 7 eV at the ground state’s equilibrium distance. Spectroscopic constants, calculated for all terms, are shown to accurately reproduce the observation for those nine terms that are experimentally known.

Introduction “As we attempt to understand the chemical bonding of transition metal compounds, a major unresolved question concerns the role of the d orbitals in the bonding of these species. To what extent do the d orbitals take part in the chemical bond, and how does the extent of their participation vary as one moves through the Periodic Table?” 1 Such questions are of paramount importance for the understanding of chemical bonding between transition metal atoms. Nevertheless, little attention has been paid to the nature of bonding, to electronic transitions, and to the optical properties of these species. From an experimental point of view, the rather limited detailed information on these systems is due to the experimental hardships, for instance the great difficulties in the synthesis of a species like diatomic AgAu. 2 2


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From a theoretical point of view, several pertinent computational difficulties exist and are briefly outlined in the following. In order to obtain a reliable description of the electronic structure of these species, it has been widely recognized that inclusion of both electron correlation and relativistic effects is necessary. Therefore, one has to employ theoretical methods that are able to account for dynamic correlation, not only in a non-relativistic limit, but also with inclusion of the scalar relativistic and spin-orbit (SO) coupling effects either as a priori or as a posteriori contributions. 3 Despite highly developed tools for this task, the understanding of the physical and chemical properties of the smallest building blocks of clusters, i. e., dimers and trimers, still remains a significant and difficult issue. In general, it is still not possible to predict the electronic ground state and the correct sequence of potential energy curves (PECs) or potential energy surfaces (PESs) of low-lying excited electronic states for such systems. Reasons for this include a high density of electronic states, compared to main group compounds, and a high sensitivity of the results of a calculation with respect to the finer details of the theoretical methods applied. Nevertheless, during the last two decades, progress has been made in studying homo- and heteronuclear diatomic molecules built up from atoms of d-block elements. We mention, in particular, the systematic experimental studies conducted by Morse and coworkers 1,2,4–12 and the theoretical studies by Mavridis and coworkers. 13–17 On the other hand, bimetallic clusters are of great interest for basic science and applications, 18 due to their particular and unique structural, 19–25 electronic, 19,20 optical, 26–28 and magnetic 29–31 properties. Most of the interest and research has concentrated on bimetallic clusters of the late transition metals. In particular, those formed between group 11 elements (Cu, Ag, and Au) are of considerable interest. The study of these clusters recently became an active field of research because of their novel catalytic behavior 25,32 and their potential applications in nanoelectronics and nanosensors. 33 The fact that the group 11 atoms have a filled d subshell in their ground states has important consequences for the structural and optical properties of their compounds. The

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filled d subshell may be considered as being inert in many situations, and the d orbitals are not taking part in chemical bonding, or are only very little involved in it. To be sure, this view requires modification as soon as one steps down in group 11: both Ag and Au can form stable compounds in higher oxidation states (certainly up to III for Ag, and up to V for Au). 34 Therefore, with respect to complexity of molecular electronic structure, the group 11 compounds can be considered as intermediate cases between the compounds of main group elements and those of the other d block elements. Several experimental 1,37–39 and theoretical 40–42 investigations have been reported for CuAu. On the experimental side, Bishea et al. studied jet-cooled CuAu with resonant two-photon ionization spectroscopy. 1 They observed and analyzed eight band systems of this diatomic molecule. They also assigned Ω values to the nine states associated with these band systems, and reported spectroscopic constants (harmonic vibrational frequency ωe , first anharmonicity constant ωe xe ), oscillator strength (f ), and electronic term energy (T0 ) for these states. Ackerman et al., using high-temperature mass spectrometric studies of the dimerization equilibrium, measured the bond strength of all coinage metal diatomic molecules. 38 The bond strength was subsequently reinvestigated by Kingcade and coworkers. 39 Ruamps identified four emission band systems associated with the CuAu molecule. 37 Theoretical approaches have not provided so much detail on excited electronic states to CuAu. The set of detailed theoretical studies appears to consist of three papers. 40–42 Among them, Kellö and Sadlej calculated electric properties of heteronuclear coinage metal diatomics within the quasirelativistic CCSD(T) approximation. 42 These rather limited theoretical investigations show that detailed and thorough quantum chemical calculations are needed, in order to obtain a description as accurate as possible of the ground and excited electronic states of CuAu to complement the experimental studies. We have recently investigated the low-lying electronic states of the heteronuclear diatomic molecules AgAu 35 and CuAg. 36 Here, we present a study of the electronic ground and lowlying excited states of CuAu. In this work, the low-lying electronic states of CuAu have

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been obtained by all-electron methods based on the scalar relativistic Douglas-Kroll-Hess (DKH) Hamiltonian. Complete-active-space self-consistent field (CASSCF) and subsequent multi-reference configuration interaction (MRCI) calculations have been performed. Spinorbit (SO) effects are calculated perturbatively on the basis of the MRCI eigenvalues and eigenstates. Regardless of the large number of states, or to put it in different form, the large size of the energy sub-space being dealt with, the chosen level of theory allows to obtain reliable spectroscopic properties and can bring in, at the same time, a sufficient amount of dynamic electron correlation and scalar relativistic or spin-orbit coupling effects (vide infra).

Computational Details The all-electron calculations for CuAu (108 electrons) were carried out with a valence quadruple zeta Gaussian basis set for copper (dubbed def2-QZVPP) 43 and with a segmented all-electron relativistically contracted (SARC) Gaussian basis set, again of valence quadruple zeta quality, for gold (QZVP-DKH). 44 The SARC basis sets are adopted to the Douglas-Kroll-Hess (DKH) Hamiltonian that has been used for the scalar relativistic calculations in the present study. In order to adequately balance the Au basis with respect to the one for Cu, we augmented the Au basis with two g functions (taken from the def2QZVPP basis for Au of ref. 43). Thus, the generally contracted basis sets finally used are (24s18p10d4f2g)/[11s6p5d4f2g] for Cu, and (22s15p11d6f2g)/[17s11p8d3f2g] for Au. All of the aforementioned basis sets can be readily obtained from the Basis Set Exchange website. 45,46 As zeroth-order ansatz a wavefunction of CASSCF type was used, constructed by allotting 22 valence electrons to a total of 12 molecular orbitals transforming as the set of 4sCu ⊕ 3dCu ⊕ 6sAu ⊕ 5dAu atomic orbitals at the separated atom limit. CASSCF wavefunctions for forty-four Λ − S terms (see Table 1) arising from the interaction of Cu(2 S) + Au(2 S), Cu(2 D) + Au(2 S), Cu(2 S) + Au(2 D), and Cu(2 D) + Au(2 D) asymptotes were computed with

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the state-averaged CASSCF (SA-CASSCF) method. 47–49 A set of state-averaged orbitals was obtained via optimizing the energy average for the six 1 Σ+ states lowest in energy (equally weighted). The SA-CASSCF molecular orbitals thus obtained were used for the subsequent MRCI calculations. We used the internally contracted variant of the multi-reference configuration interaction (MRCI) approach 50,51 as implemented in the MOLPRO program package. 52,53 The Davidson corrections of the rotated reference 54 were used for the Λ − S MRCI energies (diagonal elements for the subsequent spin-orbit coupled diagonalization). Core correlation effects were partly taken into account by including three outer core molecular orbitals in the MRCI treatment (cMRCI). These molecular orbitals have mainly the atomic character of s and p and they correlate with the 5p orbitals of Au in the separated atom limit. Jansen and Hess examined this differential 5p–5d correlation by MRCI methods for the Au atom. 55 They have shown that correlating the 5p subshell improves (decreases) the 2 S → 2 D excitation energy by 0.12 eV. Pizlo et al. recalculated this core correlation effect with a more flexible basis set and obtained this value to be about 0.3 eV. 56 In this work, all calculations were performed within point group C2v . In order to reduce the MRCI symmetry breaking of the ∆ and Γ states (for which one component appears in the A1 and the other in the A2 irreducible representations), non-degenerate states (Σ+ and Σ− states) were calculated separately from doubly degenerate ones (∆ and Γ states). This allowed us to considerably reduce errors due to symmetry breaking. For example, for the 11 ∆ state, this kind of separate treatment reduces the symmetry breaking error in total energies from 137 cm−1 to 1 cm−1 at the ground state’s equilibrium internuclear distance. For states with spatial symmetry A1 and singlet spin symmetry (six 1 Σ+ states), calculated simultaneously in the same MRCI run, the MRCI expansion (cMRCI expansion) contains approximately 1 × 107 (3 × 107 ) uncontracted and 3 × 106 (5 × 106 ) contracted configurations at the ground state’s equilibrium distance. Scalar relativistic effects are taken into account by means of the Douglas-Kroll-Hess (DKH) Hamiltonian. 57,58 It is worth to mention that in the present work the two-electron

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operators, gij , are the same as in the non-relativistic treatment, and the one-electron integrals are replaced with their relativistic counterparts. The cost of transforming gij , in other words, bringing in the relativistic kinematics corrections also to the two-electron terms, is very high and there is little evidence of its importance. The full spin-orbit Breit-Pauli operator 59 is used to compute matrix elements between internal configurations (no electrons in external orbitals), while a mean-field one-electron Fock operator is employed for contributions of external configurations. The SO eigenstates were obtained by diagonalization of the SO matrix in the basis of non-rotated MRCI wavefunctions. The diagonal elements of the resulting matrix were replaced by the rotated Λ − S cMRCI energies mentioned above. The ab initio calculations were performed with both the MOLPRO 53 and the ORCA 60,61 program packages. The spectroscopic constants were calculated with LeRoy’s LEVEL program. 62

Results and Discussion General Aspects For the Cu atom the ground state is 2 S (3d10 4s1 ), and the excited states 2 D (3d9 4s2 ) and 2

Po (3d10 4p1 ) lie at 12019.7 cm−1 and 30700.9 cm−1 , respectively (J-averaged energies derived

from experimental data). 63 The ground state of Au is 2 S (5d10 6s1 ) and the excited states 2

D (5d9 6s2 ) and 2 Po (5d10 6p1 ) lie at 14070.8 cm−1 and 39902.7 cm−1 , respectively (J-averaged

energies). 63 All molecular states correlating with the Cu(2 S) + Au(2 S), Cu(2 D) + Au(2 S), Cu(2 S)+Au(2 D), and Cu(2 D)+Au(2 D) Λ−S asymptotes have been calculated. Accordingly, there are forty-four Λ−S terms 1,3 [Σ+ (6), Σ− (2), Π(6), ∆(5), Φ(2), Γ]. These give rise, after inclusion of SO coupling, to eighty-six Ω terms, i. e., 0+ (14), 0− (14), 1(25), 2(18), 3(10), 4(4), 5. In addition to these valence states, there are two ion-pair states with symmetry 1 Σ+ (0+ ), formally denoted as Cu+ Au− and Cu− Au+ , whose respective separated atom limits are at 43697 cm−1 and 64506 cm−1 (see Table 1). The Λ − S potential energy curves (PECs) for the forty-four Λ − S terms and the spin-orbit coupled potential energy curves for the 7



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eighty-six Ω terms, based on the DKH scalar relativistic approach at the cMRCI level of theory, are displayed in Figures 1 and 2, respectively. All PECs have been calculated in a pointwise manner by performing single-point calculations for 27 internuclear distances in the range from 1.70 ˚ A to 8.00 ˚ A. Table 2 summarizes the associated spectroscopic constants — including equilibrium bond length (re ), vibrational constants (ωe and ωe xe ), electronic term energy (Te ) and dissociation energy (De ) — for the fourteen Λ − S terms correlating to the separated atom limits Cu(2 S) + Au(2 S), Cu(2 D) + Au(2 S), and Cu(2 S) + Au(2 D). This table also gives the main electronic configurations of these terms, as found at the equilibrium bond length of the ground state. Table S2 presents results for thirty higher-lying Λ − S terms resulting from the asymptote Cu(2 D) + Au(2 D).

Description without spin-orbit coupling (Λ − S terms) As in all coinage metal diatomic molecules, the ground state of CuAu based on SR-MRCI wavefunctions is a 1 Σ+ state with the dominant closed-shell electron configuration (dπ)4 (dδ)4 (dδ ∗ )4 (dπ ∗ )4 (dσ)2 (dσ ∗ )2 (sσ)2 (sσ ∗ )0 . The calculated spectroscopic constants of the ground state 11 Σ+ at the SR-MRCI (SR-cMRCI) level of theory are re = 2.35 ˚ A (2.34 ˚ A), ωe = 245.5 cm−1 (250.9 cm−1 ), ωe xe = 0.77 cm−1 (0.83 cm−1 ), and De = 18104 cm−1 (18677 cm−1 ). A and D00 = 18906(153) cm−1 ) 1 Comparison with available experimental data (r0 = 2.3302(6) ˚ reveals that the Λ − S results are already in good agreement with experiment. This could have been expected, since SO coupling effects on the energetically “well isolated” 1 Σ+ ground state are negligible. The data in Tables 2 and S2 also show effects on spectroscopic constants of Λ − S states in CuAu due to correlation of the Au 5p orbitals. For instance, correlation A) and increases the dissociation energy of the Au 5p shell shortens the bond length (−0.01 ˚ (+ 573 cm−1 ) of the 11 Σ+ ground state. In addition, Figure 3 displays the dipole moment curves of the six 1 Σ+ states of CuAu. As can be seen from this figure, the ground state 11 Σ+ at its equilibrium distance (re = 2.34 ˚ A) has a molecular dipole moment that is oppositely oriented to the one found for the state 8


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31 Σ+ : µ(11 Σ+ , re ) = −2.56 D (corresponding to (corresponding to

δ−

δ+

Cu − Auδ− ) vs. µ(31 Σ+ , re ) = +0.12 D

Cu − Auδ+ ). Hence, the Λ − S transition from the ground state 11 Σ+

to the excited state 31 Σ+ has a large charge transfer character and is very intense. The oscillator strength calculated for this electronic transition is f = 0.17. Figure 1 displays, however, also a curve crossing of the 31 Σ+ state with the Cu+ Au− ion-pair curve at r ≈ 4 ˚ A. Consequently, at larger internuclear distance, the charge polarization of the 31 Σ+ state is inverted, compared to the situation at and around the ground state’s equilibrium distance: µ(31 Σ+ , 4 ˚ A) = −0.45 D (corresponding to

δ+

Cu − Auδ− ).

In all three heteronuclear coinage metal diatomic molecules, states of symmetry 1 Σ+ (in Hund’s case (a) coupling scheme), resulting from like separated atom limits, are more strongly bound than other states. As an example, the differences in dissociation energies De (21 Σ+ ) − De (11 ∆) calculated at the SR-MRCI level of theory for CuAg, AgAu, and CuAu are +1129 cm−1 , +5404 cm−1 , and +2436 cm−1 , respectively. This may be rationalized on the basis of the intersection of the ion-pair Cu+ Au− state and the 31 Σ+ state in the case of CuAu (see Figure 1), or more generally stated, the correlation of the ion-pair state(s) with the low-lying valence 1 Σ+ states of these diatomic molecules. In the Λ − S notation, the ion-pair states (both Cu+ Au− and Cu− Au+ ) may correlate with six d-hole states having the same symmetry as the ground state: spatial symmetry Σ+ and spin symmetry singlet. However, they may correlate with fourteen d-hole states, all of which are 0+ , in the spinorbit coupled representation. Therefore, analyzing the correlation of the ion-pair state(s) and valence states is easier in the Λ − S framework. Aside from that, the Λ − S terms were treated variationally within the present work, whereas the SO coupling was included perturbatively. Thus, coupling of states with identical symmetry and the analysis of the results with respect to the effect of this coupling make more sense in the Λ − S regime. This may be the rudimentary reason that we were to some extent better able to track down the ion-pair-valence correlation in the Λ − S calculations than in the SO coupled calculations. It is also worth to compare ground state dipole moments and dissociation energies of the

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three molecules CuAg, AgAu, and CuAu, as calculated at the SR-MRCI level of theory. The dipole moments at the respective equilibrium distances are µ (Cuδ− − Agδ+ at 2.39 ˚ A) = +0.50 D, 36 µ (Cuδ+ − Auδ− at 2.33 ˚ A) = −2.56 D, and µ (Agδ+ − Auδ− at 2.56 ˚ A) = −3.28 D. 35 The magnitude of the formal partial charge, |δ|, as derived from these data for the dipole moments at equilibrium distance, is only about one fifth of an elementary charge in the case of CuAg, but larger than one elementary charge in the cases of CuAu and AgAu. The corresponding dissociation energies are De (CuAg) = 13550 cm−1 , De (CuAu) = 18104 cm−1 , and De (AgAu) = 16534 cm−1 , so that De (CuAu) > De (AgAu) > De (CuAg). One can infer that quite some ionic contribution is present in the bonding in CuAu, in close similarity to the situation previously found for AgAu. 35 In contrast to the Λ − S states resulting from the Cu(2 D) + Au(2 S) separated atom limit, all states asymptotically correlating with the Cu(2 S) + Au(2 D) separated atom limit are only weakly bound, with one exception: the 31 Σ+ state. This suggests that, no matter whether SO coupling is considered or not, the lower excited electronic states of CuAu should possess significant d-hole character on copper. This was first experimentally observed by the electronic isotope shift techniques. 1 As can be seen from the data given in Tables 2 and S2, the 13 Φ term is the only one that is noticeably symmetry contaminated, through minor contributions from configurations (AF), (AG), and (AJ), see Table 3 for more details. This symmetry contamination is due, firstly, to the neglect of the p-hole states, and secondly, to slight shortcomings in the treatment of electron correlation and symmetry (C2v instead of C∞v ), but see also below.

Description with spin-orbit coupling (Ω terms) The spin-orbit eigenstates were obtained in the basis of the wavefunctions associated with the forty-four

2S+1

Λ terms, which leads to eighty-six Ω terms in Hund’s case (c) coupling. 64

Table 1 presents the necessary details to switch from (Λ, S) to Ω states for all molecular states arising from the separated atom asymptotes Cu(2 S1/2 ) + Au(2 S1/2 ), Cu(2 S1/2 ) + Au(2 D5/2 ), 10


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Cu(2 D5/2 )+Au(2 S1/2 ), Cu(2 D3/2 )+Au(2 S1/2 ), Cu(2 D5/2 )+Au(2 D5/2 ), Cu(2 S1/2 )+Au(2 D3/2 ), Cu(2 D3/2 ) + Au(2 D5/2 ), Cu(2 D5/2 ) + Au(2 D3/2 ), and Cu(2 D3/2 ) + Au(2 D3/2 ). We remark that the p-hole states correlating to the separated atom limits Cu(2 Po1/2 ) + Au(2 S1/2 ) and Cu(2 Po3/2 )+Au(2 S1/2 ) (see Table 1), energetically lying between the Cu(2 D3/2 )+ Au(2 D5/2 ) and Cu(2 D5/2 ) + Au(2 D3/2 ) channels, were not considered in our calculations. The Λ−S separated atom limit Cu(2 Po )+Au(2 S) gives rise to 1,3 [Σ+ , Π] states. Inclusion of these states in our study would have forced us to add the Cu 4p orbitals to the active space in the SA-CASSCF calculations, i. e., a CAS(22,15). This increase in size of the problem, even though it is desirable, would have made the calculations unfeasible for us. Therefore, our results for the states asymptotically correlating to the Λ − S separated atom channel Cu(2 D) + Au(2 D) give only a (reliable) qualitative description, as some of the Λ − S d-hole states may overlap with p-hole states somewhere along the potential energy curves. This potential overlap may be the main reason for the symmetry contaminations (in both Λ − S and SO results) mentioned above. The spin-orbit splitting of the

2S+1

Λ states is schematically illustrated in Figures 4, 5,

and 6. The spin-orbit coupled PECs for each symmetry (Ω values 0+ , 0− , 1, 2, 3, 4 and 5) are separately displayed in Figures 7–12. These full PECs enabled us to determine spectroscopic parameters such as the equilibrium bond length (re ), vibrational constants (ωe and ωe xe ), electronic term energy (Te ), dissociation energy (De ), and oscillator strength (f ) for the Ω states. The results are collected in Tables 4 and S4, together with experimental data where available. The lowest Ω state is X0+ with the same wavefunction as the Λ − S ground state 11 Σ+ . Similar to the diatomic molecules AgAu 35 and CuAg, 36 the SO coupling has no influence on the ground state of CuAu. However, for the excited states, SO coupling does substantially affect the spectroscopic constants. The SO coupling mixes electronic states of different spin multiplicities, thus allowing forbidden electronic transitions to gain intensity. For the CuAu molecule in the SO representation, the allowed transitions are those for which ∆Ω = 0, ±1. 65

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Bishea et al. experimentally analyzed the eight excited states a1, A′′ 1, A′ 1, A0+ , B0+ , C1, D′ 1, D0+ , which lie above the ground state with electronic term energies of (theoretical values from our present work in parentheses) 17803 (18098), 19154 (20247), 20202 (20877), 20211 (21175), 20650 (21943), 22165 (22786), 23309 (24657), 23915 (25269) cm−1 , respectively. In addition to these states, our theoretical study reveals several more states (ten of symmetry 0+ and eighteen of symmetry 1) that might be experimentally observable if one scans to higher energies.

Analysis of the absorption spectrum and of the spin-orbit coupled eigenstates of CuAu As just mentioned, the spin-orbit coupling mixes electronic states of different spin multiplicities, thus allowing forbidden electronic transitions to gain intensity. In addition to the excitation energies for the electric-dipole allowed transitions (0+ → 0+ , 0+ → 1), the spinorbit eigenfunction compositions of all states are reported in Tables 4 and S4. A detailed breakdown of the eight experimentally known low-lying allowed transitions is being explained in the following paragraphs. The a1 ← X0+ transition The first transition, both in experiment and from theory, is the a1 ← X0+ transition. Bishea et al. reported an absorption with f ≈ 5×10−5 for this system. The corresponding computed value is 2.68 × 10−6 . Based on the small value, both from experiment and from theory, it is evident that this transition is nominally forbidden in some sense. The SO eigenfunction of the a1 state is dominated by the Λ − S 13 Σ+ state (98% of weight). As can be seen from Figure 9, this state correlates with the lowest asymptotic level, Cu(2 S1/2 ) + Au(2 S1/2 ), and its experimental (computational) dissociation energy is 1157 cm−1 (646 cm−1 ). Within the set of diatomic molecules AgAu, CuAg, and CuAu, the differences between the electronic energies of Λ − S terms 13 Σ+ and 21 Σ+ , or in other words, 12


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the energy differences between the 13 Σ+ and the nearest electric-dipole allowed (Λ, S) state, Te (21 Σ+ ) −Te (13 Σ+ ), calculated at the SR-MRCI level of theory, are ≈ 8600 cm−1 (AgAu), 8000 cm−1 (CuAg), and 4700 cm−1 (CuAu). This makes CuAu the best (or presumably the only) candidate among these diatomic molecules for which off-diagonal spin-orbit coupling can mix the 13 Σ+ state with other states. However, the spin-orbit eigenfunction analysis of the a1 state exposes the existence of only less than one percent of 1 Π contribution. The A′′ 1 ← X0+ transition According to Table 4, the second state with non-zero oscillator strength is A′′ 1. It is computed to lie 20247 cm−1 above the ground state. Based on the extremely short experimental vibrational progression of this system, which may be accounted for by the Franck-Condon principle, Bishea et al. predicted the bond lengths in the upper and lower states to be nearly the same. This view is confirmed by the calculated bond lengths 2.34 ˚ A and 2.36 ˚ A for X0+ and A′′ 1 states, respectively. The eigenvector of this state is composed of 13 Π (77%), 23 Σ+ (12%), and 11 Π (7%) Λ − S terms. Hence, this state derives from the Λ − S term 13 Π, and is consequently expected to correlate to the first Λ − S excited channel, i. e., Cu(2 D) + Au(2 S). Figure 9 shows, however, that the A′′ 1 correlates to the first spin-orbit excited channel, i. e., Cu(2 S1/2 ) + Au(2 D5/2 ). This comes as no surprise and one might have expected this because of the known large SO coupling effects on excited states of gold and also gold-containing systems. The A′′ 1 state is dominated (50%) by the configuration (AC) with symmetry 3 Π and dπ ∗ → sσ ∗ electron promotion. It is reasonable here to make a comparison between the dissociation energies of the A′′ 1 state and the parental Λ − S term 13 Π term, which are calculated here as 6988 cm−1 and 10370 cm−1 , respectively. This downward trend in dissociation energies after inclusion of SO coupling is somewhat obvious for almost all states in heteronuclear coinage metal diatomic molecules. It is due to the fact that SO splitting is usually larger in the free atoms than in the molecules, where it is largely quenched.

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The A′ 1 ← X0+ transition Both from experiment and from theory (present work), this band system is the third electricdipole allowed transition and the computed electronic energy for this transition is 20877 cm−1 (only 630 cm−1 to the blue with respect to the A′′ 1 ← X0+ system). The A′ 1 state is mainly composed of the 23 Σ+ (81%), 11 Π (12%), and 13 Π (5%) Λ − S terms. Thus, this state originates from Λ − S term 23 Σ+ , and similar to the A′′ 1 state, it correlates with the first excited SO coupled asymptotic channel Cu(2 S1/2 ) + Au(2 D5/2 ), as shown in Figure 9. According to lifetime measurements, Bishea et al. indicated that the A′ 1 state is predissociating through interaction with another electronic state. 1 Figure 9 displays a threecontributor perturbation of the a1, A′′ 1, and A′ 1 states around the equilibrium distance. As mentioned, the A′ 1 and A′′ 1 states are very similar with respect to eigenfunction compositions (symmetry requirements for avoided crossings), being both dominated by the 23 Σ+ , 11 Π, and 13 Π contributors. Figure 9 shows that, in addition, the energetic criterion for an avoided crossing is also fulfilled and met at re ≈ 2.4 ˚ A. Therefore, our theoretical results show that the A′ 1 and A′′ 1 states undergo avoided crossing at this point. This avoided crossing might be viewed however as a predissociation of either states, A′′ 1 or A′ 1, through interaction with the a1 state. This view points into an interesting direction for future investigations of coupled quantum dynamics in the excited electronic states of CuAu. The A0+ ← X0+ transition The fourth transition involves the state A0+ , which is found to lie at 20211 cm−1 (21175 cm−1 ) above the ground state. Experimentally and computationally, the A0+ ← X0+ transition is the second most intense transition in the spectrum of CuAu. For instance, the experimental and computational oscillator strengths are 0.01 and 0.00862, respectively. The A0+ state is dominated by the 13 Π (78%), 21 Σ+ (17%), and 31 Σ+ (4%) states. Hence, this state derives from the Λ − S term 13 Π, and Figure 7 shows that it correlates asymptotically with the SO coupled asymptote Cu(2 S1/2 ) + Au(2 D5/2 ). 14


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The B0+ ← X0+ transition Slightly above the A0+ state one finds the B state of symmetry 0+ . As can be seen in Figure 7, although the A0+ and B0+ states originate from two different separated atom limits, i. e., Cu(2 S1/2 ) + Au(2 D5/2 ) and Cu(2 D5/2 ) + Au(2 S1/2 ), respectively, they are energetically very close to each other over a considerable range of internuclear distances and undergo an avoided crossing at r ≈ 2.65 ˚ A. In general, states correlating to the third separated atom limit Cu(2 D5/2 ) + Au(2 S1/2 ) are more bound than states resulting from the second channel Cu(2 S1/2 ) + Au(2 D5/2 ), see Figures 7–10. As a result, almost all Ω states from Cu(2 S1/2 ) + Au(2 D5/2 ) are either perturbed or have undergone avoided crossing through interactions with states descending from the asymptote Cu(2 D5/2 ) + Au(2 S1/2 ). The B0+ state is composed of the 21 Σ+ (80%), 13 Π (15%), and 31 Σ+ (4%) Λ − S terms, and it derives from the parental 21 Σ+ state. The B0+ state is the second most bound excited state, its dissociation energy has been calculated to be 8465 cm−1 . The C1 ← X0+ transition This band system has an absorption oscillator strength of f = 3.6 × 10−3 (from experiment 1 ) and f = 3.37 × 10−3 (from SO-SR-cMRCI calculations), respectively. The eigenvector of the C1 state is mainly composed of the 11 Π (77%), 13 Π (15%), and 23 Σ+ (6%) Λ − S terms. The 11 Π character allows this state to be optically observable and shows that the C1 state is the only such component of the 11 Π state. The D′ 1 ← X0+ transition This band system has an absorption oscillator strength of f = 4 × 10−4 (from experiment 1 ) and f = 2.09 × 10−4 (from SO-SR-cMRCI calculations), respectively. The eigenvector of the D′ 1 state is dominated by the 13 ∆ (96%) and 11 Π (2%) Λ − S terms. According to Figure 9, the C1 and D′ 1 states derive from the separated atom limit Cu(2 D5/2 )+Au(2 S1/2 ). Although the C1 and D′ 1 states are notably different from each other with respect to SO eigenstate 15



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Page 16 of 43

composition at equilibrium distance, i. e., the C1 state is dominated by 11 Π (77%) and the D′ 1 state by 13 ∆ (96%), they are both heavily perturbed by other state(s) with symmetry Ω = 1 descending from the asymptote Cu(2 D3/2 ) + Au(2 S1/2 ) at r ≈ 2.70 ˚ A (see Figure 9). The D0+ ← X0+ transition This transition is the most intense transition among those observed up to now in the spectrum of CuAu. 1 It is associated with a band system at the highest observed frequencies. Excited states of the heteronuclear coinage metal dimers AB with symmetry Ω = 0+ (or 1 Σ+ in 2S+1

Λ coupling scheme) all tend to have some ion-pair character, which derives from the

− 10 2 + 1 + 10 0 separated-ion asymptote M+ A (d s ) + MB (d s ), from which arises only one 0 (or Σ )

state. The transition from the X0+ ground state to this 0+ ion-pair state is a charge transfer transition and should be very intense. 4 Similar to CuAg, 36 the Cu+ + Au− (Cu− + Au+ ) separated atom limit generates an Ω = 0+ state that experiences a long-range Coulomb attraction that will certainly pull it into the energy subspace considered in the present work (see the red and green dashed curves in Figures 1 and 2). It mixes with other Ω = 0+ states, and undergoes avoided crossings as it descends from the asymptotic limit. Maybe it makes a significant contribution even to the ground state. This ion-pair state will show up as having a dipole moment that increases linearly with internuclear separation. As it undergoes avoided crossing, the state that is dominated by this character may change, but a clear linear curve should be observed. The D0+ ← X0+ transition is extremely intense and has an absorption oscillator strength of 0.11 (from experiment 1 ) and 0.14 (from theory, present work), respectively. Moreover, similar to the Λ − S transition 31 Σ+ ← 11 Σ+ , the transition D0+ ← X0+ is a charge transfer transition and it completely changes the dipole moment orientation at the equilibrium distance: from µ(X0+ ) = −2.60 D (oriented from Cu towards Au, i. e. µ(D0+ ) = 3.31 D (oriented from Au towards Cu, i. e.

δ−

δ+

Cu − Auδ− ) to

Cu − Auδ+ ). Therefore, the best

excited Ω candidate corresponding to an ion-pair state is the D0+ state and it is dominated

16


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by the ion-pair Cu− + Au+ contribution. Therefore the D0+ state correlates adiabatically to the separated atom limit Cu(2 D3/2 ) + Au(2 S1/2 ) and diabatically to the ion-pair Cu− + Au+ limit. However, with the large intensity of the D − X system and the asymptotic energy levels of the ion-pair states in mind, Bishea et al. indicated that the D0+ state should be identified with the ion-pair state Cu+ +Au− being more favored than Cu− +Au+ . Obviously, after the detailed analysis presented here, such considerations are, at best, of limited validity (only over some range of internuclear distance r).

Summary and Conclusion Forty-four Λ − S and eighty-six Ω electronic terms of the diatomic molecule CuAu were studied by means of multi-configurational approaches. Scalar relativistic effects were treated on an equal footing with electron correlation whereas spin-orbit (SO) coupling was calculated a posteriori from the MRCI eigenvalues and eigenstates as zeroth-order solutions. Full potential energy curves (PECs) are provided for all states in both Λ − S and SO representations. The calculated SO coupled PECs show a quite considerable number of avoided crossings and predissociations, as could have been expected from the fact that both the Λ − S and the SO asymptotes in CuAu are closer in energy than in the diatomic molecules CuAg or AgAu. In addition to accurately reproducing the spectroscopic constants of the experimentally observed states, results for all d-hole electronic states are presented. Although SO coupling does not affect the properties of the ground state, it is of particular importance for the excited states. Not only the spectroscopic constants, but also the order and nature of the excited states are noticeably changed by the inclusion of SO coupling. As predicted by experimental measurements, in some limited range of internuclear distances, the ion-pair states (Cu+ Au− and Cu− Au+ ) correlate strongly with the low-lying valence states of CuAu and play a dominant role in the low-energy states of this molecule. In addition, it is shown that core correlation effects decrease the electronic excitation energies and increase the bonding

17



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strength for most of the states.

Supporting Information Available Table S2 (complementing Table 2): spectroscopic constants for thirty higher-lying Λ − S terms of CuAu correlating with the separated atom limit Cu(2 D) + Au(2 D); Table S4 (complementing Table 4): spectroscopic constants for sixty-four higher-lying Ω terms of CuAu correlating with the separated atom limits Cu(2 D5/2 ) + Au(2 D5/2 ), Cu(2 S1/2 ) + Au(2 D3/2 ), Cu(2 D3/2 ) + Au(2 D5/2 ), Cu(2 D5/2 ) + Au(2 D3/2 ), and Cu(2 D3/2 ) + Au(2 D3/2 ). This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This work was partly supported by the Center for International Cooperation (CIC) of the Freie Universität Berlin and by the German Academic Exchange Service (DAAD, research grant ID 57129429). Support by the High-Performance Computing (HPC) facilities at the Freie Universität Berlin (ZEDAT), in particular by Dr. Boris Proppe and Dr. Loris Bennett, is gratefully acknowledged.

References (1) Bishea, G. A.; Pinegar, J. C.; Morse, M. D. The ground state and excited d -hole states of CuAu. J. Chem. Phys. 1991, 95, 5630–5645. (2) Bishea, G. A.; Morse, M. D. Spectroscopic studies of jet-cooled AgAu and Au2 . J. Chem. Phys. 1991, 95, 5646–5659. (3) Roos, B. O.; Malmqvist, P.-˚ A. Relativistic quantum chemistry: the multiconfigurational approach. Phys. Chem. Chem. Phys. 2004, 6, 2919–2927.

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(65) Geethalakshmi, K. R.; Ruipérez, F.; Knecht, S.; Ugalde, J. M.; Morse, M. D.; Infante, I. An interpretation of the absorption and emission spectra of the gold dimer using modern theoretical tools. Phys. Chem. Chem. Phys. 2012, 14, 8732–8741.

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Page 25 of 43

Table 1: Correlation Table between Terms of the Separated Atoms and Terms of the Diatomic Molecule CuAu. Energies of the Asymptotes in cm−1 .

25

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Cu

Au

energya

Λ − S termsb

Cu

d10 s1 , 2 S d 9 s2 , 2 D

d10 s1 , 2 S d10 s1 , 2 S

0.0 12019.7

1,3 [Σ+ ]

2S

1,3 [Σ+

⊕ Π ⊕ ∆]

d10 s1 , 2 S

d9 s2 , 2 D

14070.8

1,3 [Σ+

d 9 s2 , 2 D

d9 s 2 , 2 D

26090.5

1,3 [Σ+ (3)

d10 p1 , 2 Po

d10 s1 , 2 S

30700.9

1,3 [Σ+

d10 s0 , 1 S d10 s2 , 1 S

d10 s2 , 1 S d10 s0 , 1 S

43697d 64506d

1 Σ+ (Cu+ Au− )

a b c d

J-averaged energies Eavg = From ref. 64. From ref. 63. From ref. 1.

P

⊕ Π ⊕ ∆]

⊕ Σ− (2) ⊕ Π(4) ⊕ ∆(3) ⊕ Φ(2) ⊕ Γ] ⊕ Π]

1 Σ+ (Cu− Au+ ) J (2J

+ 1)EJ /

P

J (2J

1/2 2D 5/2 2D 3/2 2S 1/2 2S 1/2 2D 5/2 2D 3/2 2D 5/2 2D 3/2 2 Po 1/2 2 Po 3/2 1S 0 1S 0

Au

energyc

Ω termsb

2S

1/2

2S

1/2

0.0 11202.6 13245.4 9161.3 21435.3 20363.9 22406.7 32637.9 34680.7 30353.3 30783.7 43697d 64506d

0+ ⊕ 0− ⊕ 1 0+ ⊕ 0− ⊕ 1(2) ⊕ 2(2) ⊕ 3 0+ ⊕ 0− ⊕ 1(2) ⊕ 2 0+ ⊕ 0− ⊕ 1(2) ⊕ 2(2) ⊕ 3 0+ ⊕ 0− ⊕ 1(2) ⊕ 2 0+ (3) ⊕ 0− (3) ⊕ 1(5) ⊕ 2(4) ⊕ 3(3) ⊕ 4(2) ⊕ 5 0+ (2) ⊕ 0− (2) ⊕ 1(4) ⊕ 2(3) ⊕ 3(2) ⊕ 4 0+ (2) ⊕ 0− (2) ⊕ 1(4) ⊕ 2(3) ⊕ 3(2) ⊕ 4 0+ (2) ⊕ 0− (2) ⊕ 1(3) ⊕ 2(2) ⊕ 3 0+ ⊕ 0− ⊕ 1 0+ ⊕ 0− ⊕ 1(2) ⊕ 2 0+ 0+

2S

1/2 2D 5/2 2D 3/2 2D 5/2 2D 5/2 2D 3/2 2D 3/2 2S 1/2 2S 1/2 1S 0 1S 0

+ 1), with EJ taken from ref. 63.



Table 2: Calculated Bond Lengths re (˚ A), Harmonic Frequencies and Anharmonicity Constants ωe , ωe xe (cm−1 ), −1 Dissociation Energies De (cm ), Term Energies Te (cm−1 ), and Wavefunction Main Configuration Weights of the Lowest Fourteen Λ − S Terms of CuAu. no. 1

2

3

4

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Page 26 of 43

5

6

7

8

9

term 11 Σ+ SR-MRCI SR-cMRCIb 3 1 Σ+ SR-MRCI SR-cMRCI 23 Σ+ SR-MRCI SR-cMRCI 3 1 Π SR-MRCI SR-cMRCI 1 2 Σ+ SR-MRCI SR-cMRCI 1 1 Π SR-MRCI SR-cMRCI 13 ∆ SR-MRCI SR-cMRCI 11 ∆ SR-MRCI SR-cMRCI 31 Σ+ SR-MRCI SR-cMRCI

main configuration weightsa

re

ωe

ωe xe

De

2.35 2.34

245.5 250.9

0.77 0.83

18104 18677

0 0

3.10 3.07

503 627

17597 18063

46%(C)+25%(B)+8%(W)+6%(K)+2%(J) 50%(C)+23%(B)+7%(W)+5%(K)+2%(J)

2.91 2.90

61.10 71.77

Te

80%(A)+2%(B)+3%(C) 81%(A)+2%(B)+3%(C)

2.42 2.43

274.7 262.4

1.20 0.32

10131 10525

20733 20565

31%(C)+30%(B)+21%(K)+3%(L)+2%(J) 28%(C)+33%(B)+21%(K)+3%(L)+2%(J)

2.33 2.31

241.3 250.0

1.26 1.21

9665 10370

21427 20949

65%(AC)+9%(AD)+5%(AF)+2%(AN)+2%(AJ)+2%(AG)+2%(AL) 65%(AC)+9%(AD)+5%(AF)+3%(AN)+2%(AJ)+2%(AG)+2%(AL)

2.35 2.33

224.8 233.5

1.28 1.40

8599 9114

22260 21968

50%(C)+16%(B)+11%(D)+5%(E)+3%(L)+3%(J) 50%(C)+15%(B)+11%(D)+5%(E)+3%(L)+3%(J)

2.35 2.33

226.9 236.9

1.36 1.42

7994 8653

23093 22658

61%(AC)+10%(AD)+6%(AF)+3%(AN)+2%(AG)+2%(AL) 62%(AC)+10%(AD)+6%(AF)+3%(AN)+2%(AG)+2%(AL)

2.41 2.39

207.3 214.8

1.45 1.45

7077 7592

24021 23733

43%(N)+26%(M)+4%(O)+3%(T)+3%(Q)+3%(R)+3%(S) 43%(N)+26%(M)+4%(O)+4%(T)+3%(Q)+3%(R)+3%(S)

2.42 2.40

197.6 205.4

1.52 1.58

6163 6634

24937 24686

41%(N)+25%(M)+5%(O)+4%(P)+4%(Q)+4%(R)+4%(T)+3%(S) 41%(N)+25%(M)+5%(O)+4%(P)+3%(Q)+3%(R)+4%(T)+3%(S)

2.54 2.54

166.5 162.3

0.96 1.08

6976 6467

26195 26042

53%(B)+20%(C)+6%(J)+4%(A)+3%(K) 53%(B)+19%(C)+7%(J)+4%(A) Continued on next page


Page 27 of 43

Table 2 – Continued from previous page no.

term

10

23 ∆ SR-MRCI SR-cMRCI 1 2 ∆ SR-MRCI SR-cMRCI 23 Π SR-MRCI SR-cMRCI 21 Π SR-MRCI SR-cMRCI 33 Σ+ SR-MRCI SR-cMRCI

11

12

13

14

27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Te

main configuration weightsa

1960 2048

31458 30594

44%(M)+33%(N)+6%(S)+2%(T) 44%(M)+33%(N)+6%(S)+2%(T)

1.69 1.66

1748 1822

31548 30798

42%(M)+34%(N)+6%(S)+3%(T) 42%(M)+34%(N)+6%(S)+3%(T)

re

ωe

ωe xe

2.67 2.65

108.2 111.0

1.60 1.57

2.67 2.66

104.6 107.2

De

2.92 2.92

85.63 84.86

1.58 1.53

1300 1281

32005 31344

36%(AD)+17%(AC)+13%(AG)+13%(AM)+4%(AG)+3%(AL)+2%(AF) 36%(AD)+17%(AC)+13%(AG)+13%(AM)+4%(AG)+3%(AL)+2%(AF)

2.93 2.93

75.15 75.63

2.06 2.01

861 855

32425 31737

32%(AD)+20%(AC)+14%(AG)+13%(AM)+4%(AG)+3%(AL) 32%(AD)+20%(AC)+14%(AG)+13%(AM)+4%(AG)+3%(AL)

3.23 3.24

56.58 56.13

1.47 1.48

693 670

32488 31858

52%(W)+24%(K)+6%(C)+5%(J)+2%(B) 52%(W)+24%(K)+6%(C)+5%(J)

. . .c a b c

Configuration labels are defined in Table 3. These weights correspond to the ground state equilibrium distance. SR-cMRCI stands for inclusion of the 5p orbitals of Au in MRCI excitations. See Table S2 for data on further thirty higher-lying terms.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 43

Table 3: Electron Configurations Contributing Significantly to the Ground and Low-lying Excited Electronic States of CuAu. label (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) (L) (M) (N) (O) (P) (Q) (R) (S) (T) (U) (V) (W) (AC) (AD) (AE) (AF) (AG) (AH) (AI) (AJ) (AK) (AL) (AM) (AN) a b

dπ

dδ

4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 3 4 4 3 4 3 4 3 3 4 3

4 4 4 4 4 4 4 2 4 4 4 4 3 4 4 4 3 3 4 3 3 4 4 4 4 4 4 4 3 4 4 3 4 4 4

electron configurationa dδ ∗ dπ ∗ dσ dσ ∗ sσ 4 4 4 4 4 4 2 4 4 4 4 4 4 3 3 3 4 4 3 4 3 4 4 4 4 3 4 4 4 3 4 4 4 4 4

4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4 3 3 4 3 4 3 4 4 3 4

2 2 1 0 2 2 2 2 2 1 2 2 2 2 1 2 1 2 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1

2 1 2 2 0 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 1 2 2

electron promotionb sσ ∗ 0 1 1 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2

— sσ → dσ → (dσ)2 → (sσ)2 → (dπ ∗ )2 → (dδ ∗ )2 → (dδ)2 → (dπ)2 → dσ,dσ ∗ → dσ ∗ → ∗ dσ ,sσ → dδ → dδ ∗ → dδ ∗ ,dσ → dδ ∗ ,sσ → dδ,dσ → dδ,sσ → dδ ∗ ,dσ ∗ → dδ,dσ ∗ → dδ,dδ ∗ → dπ, dπ ∗ → dσ,sσ → dπ ∗ → dπ → ∗ dδ , dπ ∗ → dπ ∗ ,dσ → dπ,dσ → dδ, dπ ∗ → dπ,dδ ∗ → dπ ∗ ,sσ ∗ → dπ,dδ → dπ, sσ → dπ ∗ , dσ ∗ → dπ, dσ ∗ →

Valence electron configurations (core shells have been suppressed). With respect to electron configuration (A).

28


sσ ∗ sσ ∗ (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 sσ ∗ (sσ ∗ )2 sσ ∗ sσ ∗ (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 sσ ∗ sσ ∗ (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2 (sσ ∗ )2

Page 29 of 43

Table 4: Calculated Bond Lengths re (˚ A), Harmonic Frequencies and Anharmonicity Constants ωe , ωe xe (cm−1 ), −1 Dissociation Energies De (cm ), Term Energies Te (cm−1 ), Oscillator Strengths (f ), and Wavefunction Composition of the Lowest Twenty-two Ω Terms of CuAu. no.

term

re

ωe

ωe xe

De a

Te

f

main state weightsb

1

X0+ Expt.c 0− a1 Expt.c 2 A′′ 1 Expt.c 0− A′ 1 Expt.c A0+ Expt.c 0− B0+ Expt.c C1 Expt.c 3 2 D′ 1 Expt.c 2 D0+ Expt.c 3 2

2.34 2.3302(6)c 2.89 2.39e 2.428(23) 2.30 2.36 2.336(5) 2.43 2.38 2.419(8) 2.34 2.350(3) 2.36 2.32 2.340(2) 2.35 2.392(5) 2.39 2.39 2.39 2.398(4) 2.40 2.53 2.478(6) 2.64 2.52

250.6 250c,d 72.1 72.0 109.23(58) 252.0 193.0 – 236.8 317.9 234.18(68) 231.5 190.71(257) 288.0 238.9 259.11(–) 246.0 237.17(160) 214.8 212.6 215.7 220.81(113) 195.2 218.8 177.28(63) 121.4 290.5

0.82 0.7d 2.93 2.93 0.890(93) 1.21 −0.56 – 2.78 6.09 1.263(111) 1.48 −1.781(500) 3.86 2.66 2.038(–) 1.20 1.345(330) 1.39 1.48 1.67 0.934(220) 22.17 1.25 −0.993(86) −3.52 19.18

18730 18906(153)c 648 646 1157(150) 7469 6988 – 6979 6570 – 6110 – 8641 8465 – 7628 – 4508 4136 5901 – 5353 7357 – 5192 4830

0 0.000 18097 18098 17803.027(5) 19864 20247 19154.026(3) 20300 20877 20201.638(5) 21175 20211.274(2) 21781 21943 20650.002(1) 22786 22164.887(4) 22846 23212 24657 23308.867(3) 25222 25269 23914.936(3) 25374 25842

– – – 2.68×10−6 5×10−5 – 3.43×10−4 5.8×10−4 – 7.18×10−4 ≤0.0056 8.62×10−3 0.01 – 6.12×10−4 0.005 3.37×10−3 3.6×10−3 – – 2.09×10−4 4×10−4 – 1.37×10−1 0.11 – –

100%(11 Σ+ ) – 98%(13 Σ+ ) 98%(13 Σ+ ) – 96%(13 Π) 77%(13 Π) + 12%(23 Σ+ ) + 7%(11 Π) – 71%(23 Σ+ ) + 28%(13 Π) 81%(23 Σ+ ) + 12%(11 Π) + 5%(13 Π) – 78%(13 Π) + 17%(21 Σ+ ) + 4%(31 Σ+ ) – 70%(13 Π) + 28%(23 Σ+ ) 80%(21 Σ+ ) + 15%(13 Π) + 4%(31 Σ+ ) – 77%(11 Π) + 15%(13 Π) + 6%(23 Σ+ ) – 99%(13 ∆) 73%(13 ∆) + 25%(11 ∆) 96%(13 ∆) + 2%(11 Π) – 73%(11 ∆) + 25%(13 ∆) 84%(31 Σ+ ) + 7%(23 Π) + 6%(13 Π) + 1%(21 Σ+ ) – 99%(23 ∆) 98%(21 ∆)

2 3 4 5 6 7

29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


8 9 10 11 12 13 14 15 16 17 18

Continued on next page



Table 4 – Continued from previous page no.

term

re

ωe

19

1

2.70

236.0

5.88

20 21 22 . . .f

2 1 0−

2.68 2.86 2.87

244.7 219.9 191.4

5.99 5.33 3.01

a

b c

d e

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 30 of 43

f

ωe xe

De a

Te

f

main state weightsb

5201

27302

1.02×10−3

5239 4142 4163

27355 28458 28471

– 1.33×10−3 –

33%(23 Π) + 32%(23 ∆) + 31%(21 Π) + 1%(13 Π) +1%(11 Π) 65%(23 Π) + 16%(21 ∆) + 15%(23 ∆) + 2%(13 Π) 40%(33 Σ+ ) + 28%(21 Π) + 27%(23 Π) + 3%(43 Σ+ ) 55%(23 Π) + 39%(33 Σ+ ) + 4%(43 Σ+ )

For terms undergoing avoided crossings and resulting from distinct separated atom channels, dissociation energies are calculated with respect to the lower/lowest asymptotic level. These weights correspond to the ground state equilibrium distance. Unless stated otherwise, all experimental values are from ref. 1, and given with 1σ error limits in parentheses. The bond length for X0+ is r0 , not re . The bond strength for X0+ is D00 = 2.344(19) eV, which has been converted to wavenumber units. No harmonic frequencies ωe and anharmonicity constants ωe xe are given in ref. 1 for X0+ and A′′ 1, but instead ∆G′′1/2 = 248.35(−) cm−1 and ∆G′1/2 = 238.4476(41) cm−1 . All experimental term energies are T0 , not Te . From ref. 37. The a1 state has two wells. The local and global minima are located at 2.39˚ A and 2.89˚ A, respectively. See Table S4 for data on further sixty-four higher-lying terms.


Page 31 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: Potential energy curves of the ground and low-lying excited Λ − S terms of CuAu obtained at the SR-cMRCI level of theory. Experimental asymptotic energies are shown as horizontal dashed lines in black. The ion-pair curves for Cu+ Au− and Cu− Au+ are plotted as dashed lines in red and green, respectively, without any corrections accounting for Pauli repulsion setting in at short distances or attractions due to polarization of the ions or formation of chemical bonds.

31



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: Potential energy curves of the ground and low-lying excited Ω terms of CuAu obtained at the SR-cMRCI level of theory with inclusion of spin-orbit coupling.

32


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Page 33 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: Dipole moment curves of the six 1 Σ+ terms included in the present study (the vertical dashed line marks the equilibrium bond length re of the 11 Σ+ ground state).

33



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E (cm-1 ) 57500

52500

47500

5, 6 3 Σ+ .................................... .................................... 1, 2 1 Σ− .................................... 5, 6 1 Σ+ .................................... 1, 2 3 Σ−



4 3 Σ+ 4 1 Σ+

42500

.................................... ....................................

.. ... ... ... .... .......... . . . . . ... ...... ........ ..... ..... ... .............. ... .. ....... ...... .... ............................. . . .... ...... ........ .... ..................... .... .... ....... ....... ... ...... ....... ...... .............. ................... . ......... ............ . ............ .... ............. ...... ............ ..... ....... ... ................ .. ......... .... ... ...... ..... .......... ... ... . ........ .... .. ... ........ .. ... .... .... ..... . .... .... .... ...... ..... ... . .... .... ... .... .... .... .... .... .... .... .... .. . ... .... . .......... .. .... . . . . . .... .. ..... ..... .. .... . .... .. .. .... .... .. .. ...

.... .... ....

.................................... .................................... .................................... .................................... ....................................

.................................... .................................... ........................................................................ .................................... .................................... ....................................

3 3 Σ+

.................................... .... .... .... .... .... .... .... .... ....

3 1 Σ+

.................................... .... .... .... .... .... .... .... .... .... ....

2 1 Σ+ 2 3 Σ+

.................................... .... .... .... .... .... .... .... .... .... .... .... .................................... .......... B0+ .................................... .... .... .... .... .... ........ ........ ........ ........ ........ ........ ........................................................................ .......... ′ A1 .................................... .... .... .... .... .... .... .... .... .... .... .... .................................... ......... a1

37500

32500

27500

22500

1 3 Σ+

....

.................................... ......... D0+

17500

Figure 4: Correlation diagram for low-lying excited Λ − S terms of Σ+ and Σ− symmetry (left) and corresponding Ω terms (right) in CuAu at the equilibrium bond length of the electronic ground state. The correspondence between terms is indicated by dashed lines.

34


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E (cm-1 ) 57500

52500

47500

1, 2 1 Φ 4, 5, 6 1 Π .................................... 4, 5, 6 3 Π ........................................................................ 1, 2 3 Φ



3 1Π 3 3Π

........................................................................

.. ... ... .... ................ . . . . . . . . .. ... ... ...... .. ... ........ .. .... .. ..................... . ......... ................ ........... . . . . .. ... ... .......... ................ ....... ....... ......... .... ... ............ ... .............................. . . . . . ....... . ....... .. ...... ........ .... ........... ...................... .................. ............. .... . . ............. ..... ....... .. ............. ..... ........... ........ ..... .... ........ ................. .... ........ ........................ ......... .......................... ......... .. ............................... ....... . ......... ................. .. ... ......... .............. .... .... ...... ............ ... ................................... .... .... .... ............ ................. . ..... .............. . . .. .... ... .............. ................ .. . ..... .. ..... .... .......................... . ..... .. . ...... . ...

.................................... ........................................................................ .................................... .................................... .................................... ....................................

........................................................................ .................................... ........................................................................ .................................... ............................................................................................................ ....................................

42500

37500

2 1Π 2 3Π

o

....................................

.... ....... ...... .. ....... .. .... ... ..... .... .. . . . . . .. ...... .... .. ............ .... . ............ ............... .... .... .... .... .... .... .... .... ....

.................................... .................................... ....................................

32500

27500

22500

1 1Π 1

3Π

1 3 Σ+

.................................... .... .... .... .... .... .... .... .... .... .... .... .................................... ......... C1 . .... .... .... .... .................................... + .................................... .... ........ .......... ............ ................................ ............ ........ ........ ..... .... .................................... ......... A0 .... .... .... ...... .... .................................... ......... ′′ . .... .................................... A 1 .................................... .... .... .... .... .... .... .... .... .... .... .... .................................... ......... a1

17500

Figure 5: Correlation diagram for low-lying excited Λ − S terms of Π and Φ symmetry (left) and corresponding Ω terms (right) in CuAu at the equilibrium bond length of the electronic ground state. The correspondence between terms is indicated by dashed lines.

35



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E (cm-1 ) 57500

52500

47500

1 3 Γ .................................... 1 1 Γ .................................... 4, 5 1 ∆ .................................... 4, 5 3 ∆ ....................................



.. ... ... .... ....... . . .. .. .... ... ...... .... ........ .... ........... . .. .. .. .. .... .. ............. .... .. ....... ... .... ........... ... ....... .............. ..... . .. . . . . ...... .... . ... .... ...... . ........ ...... .... .. ... ... ...... .. . . . ..... .. .............. ........... .. .. ...... .............. ...... .......... ..... .... ... ......... .... .... ........ .... ............... ........ ....... .... .... . .... .... ..... .... .... ... ....... .... ..... .... .... . ....... ...... ...... ... .. . .... .... ....... .............. ........ . .... ..... ...... .... .......... ......... .... . ... .... .... ........ ..... ... .... .. ... .... ........... ....... . .... ... .. ..... ... .......... ................. . .... .. .... ... ...... .. ... ... . ....

3 1∆ 3 3∆

o

.................................... ....................................

2 1∆ 2 3∆

o

........................................................................ .............. .... .... .... .... .... .... .... .. ....

.................................... .................................... .................................... ........................................................................

.................................... .................................... .................................... .................................... ........................................................................ .................................... ....................................

42500

37500

32500

.. .... ........ ........ ........ ....... . ..... ....... ....... ....... ..... ...... ..... ..

27500 1 1∆ 1 3∆ 22500 1 3 Σ+

.................................... ....................................

.. .... .... .... .... .... .... .... .... .... .... ... .... .... ... ... .... .... ... .... ........ ........ ........ ..... .... .... . ... .... .... ....... ...... .... .... .. .... ....

....................................

.................................... .................................... .................................... ......... D′ 1 ........................................................................

.................................... .... .... .... .... .... .... .... .... .... .... .... .................................... ......... a1

17500

Figure 6: Correlation diagram for low-lying excited Λ − S terms of ∆ and Γ symmetry (left) and corresponding Ω terms (right) in CuAu at the equilibrium bond length of the electronic ground state. The correspondence between terms is indicated by dashed lines.

36


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7: Spin-orbit coupled potential energy curves of CuAu for the ground state X0+ and for the higher-lying terms with Ω = 0+ .

37



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8: Spin-orbit coupled potential energy curves of CuAu for the ground state X0+ and for terms with Ω = 0− .

38


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 9: Spin-orbit coupled potential energy curves of CuAu for the ground state X0+ and for terms with Ω = 1.

39



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



41



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 12: Spin-orbit coupled potential energy curves of CuAu for the ground state X0+ and for terms with Ω = 4 or Ω = 5.

42


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Graphical TOC Entry

Correlation diagram of the Ω and Λ − S potential energy curves of the electronic ground state and low-lying excited electronic terms of CuAu.

43


Low-Lying Electronic States of CuAu - The Journal of Physical

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