Theoretical Study of Low-Lying Electronic States of PtX (X= F, Cl, Br

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Theoretical Study of Low-Lying Electronic States of PtX (X = F, Cl, Br, and I) including Spin-Orbit Coupling Wenli Zou, and Bingbing Suo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b05730 • Publication Date (Web): 27 Jul 2016 Downloaded from http://pubs.acs.org on July 27, 2016

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The Journal of Physical Chemistry

Theoretical Study of Low-Lying Electronic States of PtX (X = F, Cl, Br, and I) including Spin-Orbit Coupling Wenli Zou†,‡ and Bingbing Suo∗,†,‡ †Institute of Modern Physics, Northwest University, Xi’an, Shaanxi, 710069, P. R. China ‡Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi’an, Shaanxi, 710069, P. R. China E-mail:[email protected] Phone: 86(029)88303540

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July 25, 2016 Abstract The low-lying electronic states of platinum ion (Pt+ ) and platinum monohalides (PtX; X = F, Cl, Br, and I) are calculated using the multireference configuration interaction method with relativistic effective core potentials. The spin-orbit coupling is taken into account through the perturbative state-interaction approach. For the Ω states of PtX below 35000 cm−1 , the potential energy curves and the corresponding spectroscopic constants are reported. It is found that the lowest Ω=3/2 state is the ground one for the four species of PtX. Overall, the theoretical results are in reasonable agreement with the available experimental data.


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INTRODUCTION The open-shell molecules containing heavy transition elements are challenging for both experimental measurements (for example, see Ref. 1,2 and references therein) and theoretical models. 3 In experiments, numerous nearly-degenerate states make the assignment rather involved, and in theory their complicated electronic structure, often multireference dominated, requires the proper inclusion of both electronic (static and dynamic) correlations and relativistic (scalar and spin-orbit) effects. In the last two decades, lots of relativistic multireference methods have been developed 4–6 and successfully applied to the low-lying electronic states of heavy-element containing molecules like PtH 4 and UO2, 7 but they are far from adequate to meet the requirement, mainly due to their lack of efficiency an d th e missing capability to compute multiple roots. From an application’s point of view, scalar relativistic multireference calculation plus a cheaper perturbative treatment of spin-orbit (SO) coupling (SOC) is desirable since a large number of spinor states can be obtained simultaneously but only spending a little more time than non-relativistic calculations. This kind of combination method has been widely applied to plenty of compounds of 3d and 4d metals like NiX (X = H, F, Cl, Br, I, and At), 8,9 CuCl2, 10 ZrN, 11 RhO, 12 PdH, 13 CdH0/+1, 14,15 and so on. For the applications to 5d or heavier element systems, however, its accuracy may be worse since the perturbative treatment of SOC in general does not work well for the strong coupling between SO interactions and dynamic correlations. 6 Nevertheless there have been some successful applications in the literature (MRPT2 and MRCI+Q results of AuH 16 and UH, 17 for example). In the present work, the low-lying Ω electronic states of the PtX (X = F, Cl, Br, and I) molecules are studied theoretically using also the perturbation approach to deal with SOC since multiple states are desired as much as possible, but through a variety of rigorous tests. In addition to examine the performance of the method, another main purpose of this work is intended to provide abundant spectral data to guide future experimental measurements of PtX. To the best of our knowledge, the first experimental and theoretical studies of PtX were 3 ACS Paragon Plus Environment


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carried out by Bridgeman et. al. 18 (PtCl) and Liu and Franke 19 (PtF and PtCl) in 2001, respectively, whereas the other studies were performed only in the recent several years, 20–26 which focus mainly on PtF and less on PtCl. In experiments, the spectra of PtF 21–25 and PtCl 18,23 were detected, and the spectroscopic constants of their ground states as well as two excited states of PtF were reported before 2015. While the present paper is being reviewed, four new electronic states of PtF were published by Ng, Southam, and Cheung. 26 The ground and several lowest excited states of PtF and PtCl were also theoretically studied by relativistic wavefunction 19,20 and density functional theory (DFT) 18,19 methods. Yet, PtBr and PtI have not been investigated either experimentally or theoretically. In this connection, the experimental and theoretical investigations of the homologous molecules PtH 4,19,27–29 and PtCN 30,31 have to be mentioned. The similarity of these molecules is that, to some extent, the platinum atom shows highly ionic character in the short-distance range of the Pt-X distance, therefore the PtX molecules can be described by Pt+X− and exhibit analogous electronic structures. This theoretical work of PtX (X = F, Cl, Br, and I) will be presented in three sections. In Section II the computational details are described, in Section III the results are discussed, and the final section s ummarizes the conclusions.

COMPUTATIONAL DETAILS Basis sets used in this research are aug-cc-pwCVQZ-PP for Pt 32 and aug-cc-pVQZ-PP for F, 33 Cl, 33 Br, 34 and I 34 (denoted as AVQZ), where the 60, 2, 10, 10, and 28 core electrons are respectively replaced by relativistic effective core potentials (RECPs) with SO potentials. The aug-cc-pVQZ-PP basis functions of Br and I have been recontracted 33 since the semicore (n-1)d orbitals were not correlated in the original functions, 34 which may degrade the accuracy. PtX is calculated at the state-averaged complete active space multiconfigurational self-consistent field 35,36 (SA-CASSCF) and the subsequent internally-contracted multirefer-


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ence configuration interaction with single and double excitations 37–39 and Davidson’s cluster correction with relaxed coefficients 40 (MRCISD+Q) levels of theory by MOLPRO. 41 The active space is composed of Pt 5d6s and X np, i.e., 15 electrons in 9 orbitals. All the or-bitals except Br 3s3p and I 4s4p are correlated at the MRCISD+Q level. SA-CASSCF can maintain the degeneracy of orbitals and electronic states if proper orbitals and states are selected, but it often fails to describe the states with different occupations on ndor Rydberg orbitals, i.e., the orbital bias problem. 42 Therefore the spin-free Λ-S states of the platinum systems from the 5d9 and 5d8 superconfigurations are averaged and calculated separately. By default, SOC is treated at the SA-CASSCF level via the state-interaction (SI) approach 43 with SO-RECP, that is, after the SO matrix being calculated at the SA-CASSCF level, the diagonal elements are then replaced by the precalculated MRCISD+Q energies (denoted as CI+Q/SO). In general, the accuracy of SI combined with the SA-CASSCF wavefunctions is much worse in electronic properties than in SO splitting energies, thus SI with the MRCISD wavefunctions is also performed at some selected points to compute transition dipole moments (Rtot ; see the Supporting Information for details), which can be used to predict the intensities of spectroscopic transitions between Ω states in a given energy range. It has been found that in some strong transitions the former approach may underestimate or overestimate Rtot by about 50% or 100%, respectively, and the error becomes significant larger in weaker transitions. The latter approach is expected to produce much more accurate Rtot results but at the expense of much longer computational time (about three orders of magnitude more expensive). Therefore, the former approach is used to calculate potential energy curves (PECs) throughout this work, whereas the latter is performed to evaluate Rtot only. For comparison, two methods have also been tested. (1) The graphical unitary group approach (GUGA) based double-group SO-MRCISD method 44 (denoted as SOCI) is performed using COLUMBUS 45 with the same active space. As a variational method of SOC, SOCI is much more costly than the perturbative CI+Q/SO method, thus all the semi-core orbitals



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have to be frozen, and smaller triple-ζ basis sets with the same SO-RECPs as in AVQZ are used (denoted as VTZ), i.e., the standard cc-pWCVTZ-PP and cc-pVTZ-PP for Pt 32 and Br and I, 34 respectively, and Pitzer’s cc-pVTZ-PP for F and Cl. 46,47 (2) Pt+is treated by SI with the full Breit-Pauli SO-operator, where the diagonal elements in the SO matrix are replaced by the all-electron scalar relativistic MRCISD+Q energies with the second-order DouglasKroll-Hess (DKH2) approach, 48,49 but there are no significant improvements com-pared with the corresponding SO-RECP results of Pt+. Therefore, this method is not used in the present work. The C2v subgroup of C∞v is used throughout the calculations of PtX, where the doublegroup irreducible representation (irrep) is E1/2. In order to identify the double-group irreps of the Ω states in C∞v from the CI+Q/SO results, we perform the procedure outlined in Ref. 8, which has been implemented in a local program. The situation in the SOCI method is different where an additional noninteracting electron with the spin irrep E1/2 in C2v is added into the odd-number-electron system PtX, 44 therefore the doubly degenerate irrep E1/2 of an Ω state in C2v becomes to four irreps through E1/2 ⊗ E1/2 = { A1} + A2 + B1 + B2. 50 In this case the Ω value in C∞v can be determined by analyzing the symmetries of the SA-CASSCF reference orbitals and the dominant electronic configurations. After the PECs of Ω states being obtained, spectroscopic constants are calculated by numerically solving the one-dimensional Schrödinger equation using the LEVEL program, 51 including the adiabatic excitation energy (Te), equilibrium bond length (Re), vibrational frequency (ωe), and rotational constant (Be). In order to estimate the missing experimental Re from the measured B0 values, a function defined in Eq. (1) is fitted through the theoretical Re (in Å) and B0 (in cm−1) data of all the bound Ω states, Re = C0 + C1 B0 + C2 B0 2

(1)

where the coefficients C0 , C1 , and C2 are respectively 3.63172, -9.28442, and 10.56481 for


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PtF, 4.21697, -25.05326, and 66.84159 for PtCl, 4.78426, -68.12057, and 428.12145 for PtBr, and 4.06234, -53.12632, and 244.42820 for PtI with the average error being smaller than 0.002 and the maximum absolute error being 0.007 .

RESULTS AND DISCUSSION Atomic levels of Pt+ To evaluate the accuracy of the CI+Q/SO results of PtX, at first we calculate the atomic levels of Pt+ by CI+Q/SO. In the SI perturbation approach, SOC includes the first-order SOC (splitting of one Λ-S state) and the second-order SOC (couplings between the Λ-S states with the same Ω), 52 and it assumes that the first order SOC is dominant whereas the second order SOC between different spin-free states is weak. However, this is not true for heavy-element systems starting from 5dtransition metals since some very high spin-free states may also strongly interact with the lower-lying ones. This problem shows that special care must be taken of the completeness of the spin-free states, that is, whether all the important spin-free states have been included in the SI treatment. We have tried the wavefunctions of, for example, the lowest 4, 5, 6, and 7 LS states of Pt+ to construct the SO matrix, but the J-term energies are calculated wrongly, which reveals that some important spin-free states are still missing. Only after including all the eight low-lying L-S states of Pt+ below 40000 cm−1 into the SO matrix, reasonable term energies can be obtained. Table 1 shows the theoretical and experimental 53,54 term energies of Pt+as well as the molecular states derived from Pt+X−, whereas the higher levels above 50000 cm−1 are ignored. It can be seen that the J-terms of Pt+ below 20000 cm−1 can be accurately calculated by the SI procedure. Therefore it is expected that the molecular states of PtX below 20000 cm−1 can also be accurately described. The errors of the J-terms between 20000 and 35000 cm−1 become a little larger, but can be significantly r educed i n P tX s ince S OC w ill be 7 ACS Paragon Plus Environment


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partially quenched in molecules. Only the J-terms higher than 35000 cm−1 may be not reliable because of not only the orbital bias (spin-free states from Pt+ 5d8 and 5d7 are always averaged together in SA-CASSCF since they cannot be significantly distinguished) but also the insufficient higher-lying L-S states in the SI perturbation approach. Therefore all the Ω states of PtX given in Table 1 have to be computed by CI+Q/SO but only the Ω states below 35000 cm−1 are reported in this paper. The lowest five levels of Pt+computed by the SOCI/VTZ method are also listed in Table 1. One can see that the agreement of the energies is good, thus SOCI can provide reliable reference results of PtX in the next subsection. However, this method cannot calculate dozens of J or Ω states because of technical difficulties, which limits its practical application. Because of very strong SOC, the assignment of J-terms to L-S states may be not obvious. Based on our theoretical results, the experimental assignments of (II)2 D3/2 and (I)2 P3/2 in Ref. 53,54 should be exchanged (see Table 1). It is also found that the so-called (I)4 P5/2 state is (I)4 F dominant instead whereas (I)4 P is only a secondary dominant component. However, if this J-term is reassigned to (I)4 F5/2 as done in Ref. 55,56, there will be more other problems. Therefore, the assignment of Pt+ collected in Ref. 55,56 is not taken here.

Low-lying states of PtX due to Pt+ 5d9 The ground 2 D state of Pt+ with the 5d9 occupation leads to the lowest three Λ-S states (I)2 Σ+ , (I)2 Π, and (I)2 ∆ of PtX. As shown in Table S1 in the Supporting Information, these states can be expressed approximately by Pt+q X−q (q = 0.5 - 0.8) with the occupations Pt 5dqd 6sqs and X ns2 npq p (qd = 8.5 - 9.0, qs = 0.3 - 0.6, and qd + qs + q p ≈ 14.8), so the Pt+ X− model system is a good reference. For a given Λ-S state, the gross atomic charge q on Pt decreases from F to I, but the population on Pt 6s, ie. qs , is nearly not affected by the halogen a toms. As a consequence, q d + q p is fixed at 14.5 for (I)2 Σ+ , 14.2 for (I)2 Π, or 14.1 for (I)2 ∆. Those electrons populated on Pt 5d, 6s, and X np indicate three different m echanisms i n t he P t-X b onding, i ncluding ( 1) 5 dσ -6s h ybridization, ( 2) covalent 8 ACS Paragon Plus Environment

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interactions between X npσ and Pt 5dσ (or the hybrid 5dσ-6s) as well as X npπ and Pt 5dπ , and (3) back-donation from X−npto Pt+5d6s. Similar to the 3dσ-4s and 4dσ-5s hybridizations, 57 the 5dσ-6s hybridization can effectively reduce the repulsion between Pt 6s and X np and enhance the Pt-X bonding. On the other hand, according to the orbital overlaps with the X− ligands, the order of repulsion for the platinum 5dorbitals with X−is 5dσ (6s-hybridized) > 5dπ > 5dδ, or more strictly speaking, the molecular orbitals 2σ+ > 2π> 1δ (see Figure 1). It can be expected that the (I)2Σ+ state is the most stable one since the singly occupied 5dσ can minimize the Pauli repulsion, and similarly (I)2Π should be the first excited state. However, they are true only for PtF. For PtCl, the orders of (I)2Σ+ and (I)2Π are exchanged, whereas for PtBr and PtI, (I)2Σ+ lies above the ground (I)2Π and the first excited (I)2∆ states (cf. Table S2 in the Supporting Information). This can be attributed to the decreasing of electronegativity from F to I, which leads to the weakening of 5dσ-6s hybridization in the axial direction (see Ref. 58 for more examples) and thereby the increasing of the covalent character between X and Pt. The backdonation from X to Pt increases the Pauli repulsion in the Pt 5d orbitals. Obviously, it becomes to more easy to excite one electron from the doubly-occupied 5dπ and 5dδ to the singlyoccupied hybrid 5dσ-6s, which stabilize the (I)2Π and (I)2∆ states, respectively.

The aforementioned three Λ-S states of PtX split into five Ω states through SOC, i.e. (1)1/2, (1)3/2, (1)5/2, (n)1/2, and (n)3/2 (n= 2 for PtI or 3 otherwise), which is similar to the case of PtH where the first three and the latter two Ω states correspond to a hole in the Pt 5d5/2 and 5d3/2 spinors, respectively. 4,19 Higher states of PtX as well as (2)1/2 and (2)3/2 of PtF, PtCl, and PtBr arise from Pt+ 5d8 and 5d7 (see Table 1). For CI+Q/SO, the SI approach is combined with either SA-CASSCF or more accurate MRCISD wavefunctions, and the single point excitation energies calculated at the theoretical equilibrium bond lengths of the (1)3/2 states are listed in Table 2. It can be seen that the two groups of CI+Q/SO energies of PtX are fairly close (but this is not true for electronic properties). To verify the accuracy of the perturbative CI+Q/SO method further,



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the vertical excitation energies of the lowest several Ω states of PtX are also double-checked by the variational SOCI method, and the results are collected in Table 2. The (2)1/2 and (2)3/2 states of PtF cannot be obtained by SOCI because of convergence problems whereas the (3)1/2 state is accidentally obtained instead. One can see that the CI+Q/SO energies of PtX agree with the SOCI ones in reasonable precision nevertheless in the latter method there are some defects: (1) the level of basis set is lower, (2) the semi-core orbitals are not correlated, and (3) Davidson correction for size-consistency is missing. The agreement indi-cates that the CI+Q/SO results should be reliable at least for the states of PtX below 35000−1. Note that the Λ-S states resulting from the 5d8 and 5d9 asymptotes of Pt+ must be calculated separately in SA-CASSCF followed by MRCISD+Q because of orbital bias, otherwise the excitation energies of the Ω states from 5d9 become much worse (for example, 129 and 1230 vs. 517 and 766 cm−1 for (1)1/2 and (1)5/2 of PtF, respectively). However, the SOCI results do not suffer from this problem since in its SA-CASSCF reference wavefunction only the Pt+5d9 derived Λ-S states are averaged. The PECs of the lowest three Ω states (1)1/2, (1)3/2, and (1)5/2 of PtX are shown in Fig. 2. It can be found that the ground state is identically (1)3/2 in the four species of PtX, but their orders depend very much on the electronegativities of halogens: (1)1/2 increases whereas (1)5/2 decreases gradually in energy from PtF to PtI. (1)1/2 and (1)3/2 of PtF are nearly degenerate, and yet in PtI (1)3/2 and (1)5/2 become nearly degenerate instead. It has been found that in PtH the ground Ω state is (1)5/2 instead of (1)3/2 4,19 because of different strengths of SOC and ligand fields of hydrogen and halogens. 19 Since the electronegativities of astatine and hydrogen are very close (being about 2.2 59), it is expected that the ground state of PtAt may be also (1)5/2, which is confirmed by our preliminary calculations. Nevertheless, PtAt is not studied in this work since some low-lying Λ-S states resulting from the asymptotic limit Pt + At make the calculations more complex.

In the next subsections the results of PtX will be discussed in more detail. The PECs


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of Ω states below 35000 cm−1 are plotted in Figures 3 (PtF), 4 (PtCl), 5 (PtBr), and 6 (PtI), and the spectroscopic constants with available experimental values as well as the square of total transition dipole moment (R2tot) are summarized in Tables 3 (PtF), 4 (PtCl), 5 (PtBr), and 6 (PtI), where the dominant Λ-S states in the components can be found in Table S2 in the Supporting Information. For the sake of identification, the odd- and even-number’th states with Ω = 1/2, 3/2, 5/2, or 7/2 in the figures are shown in black and red, respectively. Since Λ and S are not good quantum numbers for heavy element Pt, the PECs and spectroscopic constants of Λ-S states given in the Supporting Information are not very important in physics and will not be discussed here unless necessary.

PtF In the five Pt+ 5d9 (2 D) characterized Ω states of PtF in the ordering of (1)3/2 < (1)1/2 < (1)5/2 ≪ (3)1/2 < (3)3/2, the latter two states are even much higher in energy than the Pt +5d8

characterized (2)1/2 and (2)3/2 states, being different from the case of PtH. 4 Except

(1)5/2 which is nearly a pure (I)2∆ state, the other four states are heavy mixtures of two of three Λ-S states (I)2Σ+, (I)2Π, and (I)2∆. In a recent paper by one of the author, the ground state at the CI+Q/SO level was calculated to be (1)1/2 by mistake. 20 The reason is that the interactions from the Pt+5d8 (4F) characterized quadruple states also play important roles in the (1)3/2 and (1)1/2 states, but they were completely neglected. After introducing the four lowest quartet Λ-S states (see Table 1) into the SO matrix, the correct ground state (1)3/2 can be obtained instead (not shown in Ref. 20), nevertheless the relative proportions of the quartet states are very small in (1)3/2 and (1)1/2. Again, this reveals the importance of including enough basis Λ-S states in the SI approach. Among the above five Ω states of PtF due to Pt+5d9, only the ground state (1)3/2 has been fully studied in experiments, 21,23,24 while (1)1/2 and (1)5/2 were reported only recently. 25,26 For the ground state, the calculated bond length differs from the experimental value only by 0.003 Å, and the calculated vibrational frequency is in better agreement with 11 ACS Paragon Plus Environment


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the most recent experimental ∆G1/2 value of 594 cm−1 than the old ωe one. For the rotational constant, only B0 = 0.2772 cm−1 was experimentally measured, being close to the theoretical B0 value of 0.2791 cm−1. For the (1)1/2 and (1)5/2 states, the bond lengths estimated from the experimental B0 values 25,26 by Eq. 1 are close to the corresponding theoretical ones, and the vibrational frequency (∆G1/2) of (1)5/2 was also experimentally measured, 26 being in excellent agreement with the calculated one within the error bounds. Since the available experimental spectroscopic constants of (1)1/2 and (1)5/2 are scarce, we have to compare our results with the full-relativistic DFT ones in the literature. 19 The bond length and vibrational frequency values by DFT are only about 0.01 Å and 10 cm−1 larger, respectively, but the excitation energy of (1)1/2 is nearly 800 cm−1 too high, which may be due to the defects of the singlereference method. The higher two states (3)1/2 and (3)3/2 were not reported before. Compared to the lower three ones, the bond length of (3)1/2 is basically the same whereas the one of (3)3/2 becomes much longer. In addition, both of their vibrational frequencies are about 40 cm−1 smaller, which may be ascribed to complicated avoided crossings and strong state interactions between Ω states. The higher Ω states as well as (2)1/2 and (2)3/2 are composed of Pt+5d8 and possible 5d7 superconfigurations. Their bond lengths are significantly longer than the ones of the aforementioned five Ω states from Pt+5d9, indicating weaker bonding capability in 5d8 than in 5d9. The same has been found in the states resulting from the 3dn and 3dn+1 superconfigurations of some first-row transition metal systems, 8,9,60 which is due to the more diffuse radial extension and thereby the larger radial correlations of the 3dorbitals with n + 1 occupation than that with n occupation. 61 Based on the results in this work and in the literature, 16,62 this explanation also holds for second- and third-row transition metal compounds. Two transitions have been observed in absorption spectra until 2015, i.e. X3/2 — [11.9]3/2 21,24 and X3/2 — [12.5]2Σ+

22

but the latter was reassigned to (1)1/2 — [12.5]2Σ+

recently. 25 The upper states of the two transitions correspond to our theoretical (4)3/2 and


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(5)1/2, respectively, and their theoretical spectroscopic constants of (4)3/2 and (5)1/2 are in very good agreement with the experimental ones. The two transitions are also supported by the rather large R2tot values of (1)3/2 — (4)3/2 and (1)1/2 — (5)1/2. On the contrary, R2tot of the (1)3/2 — (5)1/2 transition (i.e. the early suggested X3/2 — [12.5]2Σ+

22)

is ten times

much smaller than the one of (1)1/2 — (5)1/2, meaning that the spectrum of the former transition will be covered by the latter one and therefore is difficult to detect. Most recently, Ng et. al. detected and analyzed four new transitions, 26 which lead to three newfound Ω states due to Pt+5d8, i.e., (7)3/2 (namely [18.9]2Π3/2), (6)5/2 ([19.9]2∆5/2), and (7)5/2 ([23.2]2∆5/2). As can be seen in Table 3, the agreement between theoretical and experimental spectroscopic constants of the three states is moderate. The R2tot values also suggest some other very strong transitions with R2tot ≥ 0.1, for example, (1)1/2 — (2,4)1/2, (1)5/2 — (4,6,7)5/2, and (1)5/2 — (3)7/2, which may be observed in future experiments.

PtCl The Ω states of PtCl derived from Pt+5d9 are (1)3/2, (1)5/2, (1)1/2, (3)1/2, and (3)3/2 in ascending order, where the first excited state becomes to (1)5/2 instead of (1)1/2, being different from the case of PtF. All of them except (1)5/2 are mixtures of the Λ-S states (I)2Σ+, (I)2Π, and (I)2∆, whereas (3)1/2 is also contaminated with some (I)4Σ− component. Among the five Ω states, only the ground (1)3/2 state has been experimentally measured. 18,23 Its latest experimental vibrational frequency 23 is in excellent agreement with our theoretical one, whereas the fitted bond length from experimental B0 is 0.025 Å shorter. The first three Ω states were also theoretically studied using relativistic four-component DFT by Liu and Franke. 19 Their bond length of the ground state is 2.158 Å, lying between our 2.174 Å and the experimentally estimated 2.149 Å. For the first and the second excited states, their bond lengths and vibrational frequencies are in good agreement with ours, but their excitation energies are about 600 and 1100 cm−1 too high because of the singlereference nature of DFT.



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The next two states (3)1/2 and (3)3/2 have a little longer bond lengths. The vibrational frequency of (3)1/2 is significantly l arger t han t he o nes o f t he o ther f our s tates b ecause of an avoided crossing between (2)1/2 and (3)1/2 at about the equilibrium bond length. As in PtF, the higher excited Ω states as well as (2)1/2 and (2)3/2 are derived from Pt+ 5d8 and possible 5d7 superconfigurations. O n t he w hole, t heir b ond l engths a re much longer than the ones of the above Pt+ 5d9 characterized states, and their vibrational frequencies decrease accordingly. This indicates again different b onding c haracters i n Pt+ 5d9 and 5d8 since bond strength is directly related to force constant k and k ∝ ωe 2 . None of these states have been detected experimentally, but some large R2tot values show that the following transitions would most likely be experimentally found: (1)1/2 — (4,5,7)1/2, (1)3/2 — (4,7,10)3/2, (1)5/2 — (3,4,6-8)5/2, and (1)5/2 — (3)7/2.

PtBr Since there is no theoretical or experimental work to compare, we will only briefly discuss the results for PtBr. Similar to PtF and PtCl, the five Ω s tates o f P tBr r esulting from Pt+ 5d9 are ordered as (1)3/2 < (1)5/2 < (1)1/2 ≪ (3)1/2 < (3)3/2, whereas the higher Ω states as well as (2)1/2 and (2)3/2 come from Pt+ 5d8 and possible 5d7 superconfigurations. The bond lengths in the former group are about 0.1 shorter than the ones in the latter group because of stronger bonding characters in Pt+5d9. All the Ω states in the former group except (1)5/2 are mixtures of (I)2Σ+, (I)2Π, and (I)2∆, and in (3)1/2 there is also some (I)4Σ− component, again, being the same as in PtF and PtCl. It also can be seen from Figure 5 and Table 5 that some states lying above 28000 cm−1 are repulsive. This is not surprising since it can be ascribed to the much weaker Pt-Br bond than Pt-F and Pt-Cl, and therefore some excited states may be higher than the asymptotic limit Pt + Br in energy and become unstable. Some potential strong transitions can be predicted by the R2tot values: (1)1/2 — (4-7,9,13)1/2, (1)1/2 — (10)3/2, (1)3/2 — (4,7,8,10,11)3/2, (1)5/2— (3,4,6,7,9)5/2, and (1)5/2 — (3)7/2, where the transition from bound (1)5/2 to repulsive 14 ACS Paragon Plus Environment

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(9)5/2 will lead to a continuum absorption spectrum. 63

PtI Experimental and theoretical works on PtI have not been carried out so far. Different from the three lighter analogs, the Pt+5d9 and Pt+5d8 derived Ω states of PtI are well separated in energy, that is, the lowest five Ω states (1)3/2 < (1)5/2 < (1)1/2 ≪ (2)1/2 < (2)3/2 correspond to the former superconfiguration, whereas the higher Ω states come from the latter superconfiguration as well as Pt+5d7. It is calculated that (1)5/2 of PtI is higher than (1)3/2 by only 4 cm−1, however, which may be a little underestimated considering the deviation between the SI treatments with SA-CASSCF and MRCISD wavefunctions (see Table 2). Except the pure (I)2∆ state (1)5/2, all the other four Ω states are composed of (I)2Σ+, (I)2Π, and (I)2∆, whereas the mixtures from quadruple states are negligible. In general, the bond lengths of Pt+5d8 and 5d7 derived Ω states are 0.1 Å or more longer than the ones due to Pt +5d9,

which again can be attributed to stronger bonding capability in Pt+5d9. There are much

more repulsive states than in PtBr, showing that the I atom is more weakly bonded to Pt than F, Cl, and Br. The R2tot values suggest some strong transitions of PtI which may be detected in future spectroscopic experiments: (1)1/2 — (6-12,14)1/2,(1)1/2 — (10)3/2, (1)3/2 — (4,6,8-10,12)3/2, (1)5/2 — (7-9,11)5/2, and (1)5/2 — (3)7/2.

CONCLUSIONS PtX is a rather difficult ki nd of sy stem be cause a va riety of ne arly-degenerate st ates require multireference character, dynamic electron correlation, and relativistic effects (including scalar relativistic effects a nd S OC) b eing t aken i nto a ccount i n a n a dequate manner. Especially, SOC is so strong that the frequently used perturbative SI approach often fails if the selected basis of Λ-S states are not complete (see above the failed examples of Pt+ and PtF 20). On the other hand, the two- or four-component variational approaches, including



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SOCI, are more robust and reliable but with much higher computational effort to calculate dozens of (or more) states. Therefore, the SI approach is still applicable but with an extremely careful selection of contributing Λ-S states, as demonstrated in the present work of PtX. The low-lying electronic Ω states of PtX (X = F, Cl, Br, and I) below 35000 cm−1 are systematically studied by the CI+Q/SO method with the AVQZ basis set for the first time in this work, where all the valence orbitals and the important semi-core orbitals are correlated. By including all the important low-lying atomic L-S or molecular Λ-S states into the SO matrix, in which the Pt+ 5d9 derived states must be treated separately, the overall performance of the perturbative CI+Q/SO method can be confirmed by both the experimental energy levels of Pt+ and the theoretical SOCI/VTZ results of PtX. It is found that (1)3/2 is their ground states whereas the first excited state is (1)1/2 (PtF) or (1)5/2 (PtCl, PtBr, and PtI). Although there are similarities in the electronic structure of PtX, the ordering of low-lying Ω states and bonding characters are a little different because of the trend of F > Cl > Br > I in electronegativity. Thus it can be expected that the ground and the first excited states of PtAt turn out to be (1)5/2 and (1)3/2, respectively. In addition, this study shows clearly that the bonding capability of the 5d9 superconfiguration is much stronger than that of 5d8 . Our theoretical results are grossly in good agreement with the available experimental values of PtF and PtCl. The potential energy curves and the corresponding spectroscopic constants of PtX are reported, and some potential ultraviolet-visible spectroscopic transitions are predicted, which help spectroscopists to reassign the uncertain experimental spectra and detect new spectrum bands of PtX. This work provides useful guidance for future experimental and theoretical studies of PtX and related molecules.


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ACKNOWLEDGMENTS This work is supported by grants from the National Natural Science Foundation of China (NSFC 21173166 and NSFC 21203147). We thank the authors and some expert users of the COLUMBUS program for kindly technical help about the SOCI calculations and Profs. L. C. O’Brien and A. S.-C. Cheung for helpful discussions.

SUPPORTING INFORMATION The Supporting Information is available free of charge which includes: (1) definitions of the total transition dipole moment (Rtot ) between degenerate electronic states and the corresponding total oscillator strength (ftot ), molar extinction coefficient (ε), and radiative lifetime (τ); (2) NPA charges and natural electron configurations of (I)2 Σ+ , (I)2 Π, and (I)2 ∆; and (3) potential energy curves and spectroscopic constants of Λ-S states of PtX.

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3 σ

6 s 2 σ 2 π 1 δ

5 d P t

n p X

-

+

1 π 1 σ

P tX

Figure 1: Schematic diagram of active molecular and fragment orbital levels of PtX.



(1 )1 /2

(1 )3 /2

3 5 0 0

3 5 0 0

3 0 0 0

3 0 0 0

2 5 0 0

2 5 0 0

2 0 0 0

2 0 0 0

1 5 0 0

1 5 0 0

1 0 0 0

1 0 0 0

5 0 0

(1 )5 /2

5 0 0 P tF

-1

E n e rg y / c m

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P tC l

0

0 1 .7

1 .8

1 .9

2 .0

2 .1

3 5 0 0

3 5 0 0

3 0 0 0

3 0 0 0

2 5 0 0

2 5 0 0

2 0 0 0

2 0 0 0

1 5 0 0

1 5 0 0

1 0 0 0

1 0 0 0

5 0 0

2 .0

2 .1

2 .2

2 .3

2 .3

2 .4

2 .5

2 .6

2 .4

5 0 0 P tI

P tB r 0

0 2 .1

2 .2

2 .3

2 .4

2 .5

2 .7

R (P t-X ) / Å

Figure 2: Potential energy curves of the (1)1/2, (1)3/2, and (1)5/2 states of PtX.


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3 0 0 0 0

2 0 0 0 0

-1

1 0 0 0 0

Ω= 1 / 2

E n e rg y / c m

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


Ω= 3 / 2

0

3 0 0 0 0

2 0 0 0 0

1 0 0 0 0 Ω= 7 / 2 Ω= 9 / 2

Ω= 5 / 2 0 1 .6

1 .7

1 .8

1 .9

2 .0

2 .1

2 .2

2 .3

2 .4

2 .5

1 .6

1 .7

1 .8

1 .9

2 .0

2 .1

2 .2

2 .3

R (P t-F ) / Å

Figure 3: Potential energy curves of PtF below 35000 cm−1 .


2 .4

2 .5


3 0 0 0 0

2 0 0 0 0

-1

1 0 0 0 0

E n e rg y / c m

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0

Ω= 1 / 2

Ω= 3 / 2

Ω= 5 / 2

Ω= 7 / 2 Ω= 9 / 2

3 0 0 0 0

2 0 0 0 0

1 0 0 0 0

0 1 .9

2 .0

2 .1

2 .2

2 .3

2 .4

2 .5

2 .6

1 .9

2 .0

2 .1

2 .2

2 .3

2 .4

R ( P t- C l) / Å

Figure 4: Potential energy curves of PtCl below 35000 cm−1 .


2 .5

2 .6

Page 29 of 37

3 0 0 0 0

2 0 0 0 0

-1

1 0 0 0 0

E n e rg y / c m

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


Ω= 1 / 2

Ω= 3 / 2

Ω= 5 / 2

Ω= 7 / 2 Ω= 9 / 2

0

3 0 0 0 0

2 0 0 0 0

1 0 0 0 0

0 2 .0

2 .1

2 .2

2 .3

2 .4

2 .5

2 .6

2 .0

2 .1

2 .2

2 .3

2 .4

R (P t-B r) / Å

Figure 5: Potential energy curves of PtBr below 35000 cm−1 .


2 .5

2 .6


3 0 0 0 0

2 0 0 0 0

1 0 0 0 0 Ω= 1 / 2

Ω= 3 / 2

-1

E n e rg y / c m

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 30 of 37

0

3 0 0 0 0

2 0 0 0 0

1 0 0 0 0 Ω= 5 / 2

Ω= 7 / 2 Ω= 9 / 2

0 2 .3

2 .4

2 .5

2 .6

2 .7

2 .8

2 .9

2 .3

2 .4

2 .5

2 .6

2 .7

R (P t-I) / Å

Figure 6: Potential energy curves of PtI below 35000 cm−1 .


2 .8

2 .9

Page 31 of 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


Table 1: Atomic levels of Pt+ (in cm−1 ) and the corresponding Λ-S and Ω states of PtX. config.

term

J

5d9

(I)2 D

5d8 6s

(I)4 F

5d8 6s

(I)4 P

5d8 6s

(I)2 F

5d8 6s

(II)2 D

5d7 6s2

(II)4 F

5d8 6s

(I)2 P

5d8 6s

(I)2 G

5/2 3/2 9/2 7/2 5/2 3/2 5/2 3/2 1/2 7/2 5/2 3/2 c) 5/2 9/2 7/2 5/2 3/2 3/2 c) 1/2 7/2 9/2

a)

expt. a)

SOCI

0 8420 4787 9356 13329 15791 16821 21169 21718 18098 23462 32238 32919 24880 34647 36484 37878 23876 27256 29031 29262

0 7963 3567 8839 12936

Pt+ CI+Q/SO b) 0 7241 4175 8664 13289 17141 16267 21051 24219 17705 23255 32239 32607 27054 34866 39930 43617 24400 28905 29120 29878

components (≥ 10%)

Λ-S states

(I)2 D (97) (I)2 D (74) + (I)4 F (10) + (II)2 D (10) (I)4 F (97) (I)4 F (69) + (I)2 F (27) (I)4 F (37) + (II)2 D (31) + (I)4 P (30) (I)4 F (37) + (II)2 D (27) + (I)2 D (25) (I)4 F (53) + (I)4 P (30) + (I)2 F (12) (I)4 P (49) + (I)4 F (29) + (I)2 P (19) (I)4 P (96) (I)2 F (67) + (I)4 F (30) (I)2 F (49) + (I)4 P (31) + (II)2 D (20) (II)2 D (58) + (I)2 P (25) + (I)4 F (15) (II)2 D (43) + (I)2 F (38) + (I)4 F (10) (II)4 F (57) + (I)2 G (41) (II)4 F (99) (II)4 F (99) (II)4 F (99) (I)2 P (45) + (I)4 P (44) (I)2 P (96) (I)2 G (93) (I)2 G (56) + (II)4 F (43)

2 Σ+ , 2 Π, 2 ∆

Reference 53,54.

b) The underlined value indicates an error of 0.2 eV (about 1600 cm−1) or larger. c)

According to the components, the two experimental J=3/2 levels in Reference 53,54 should be exchanged.


4 Σ− , 4 Π, 4 ∆, 4 Φ

4 Σ− , 4 Π

2 Σ− , 2 Π, 2 ∆, 2 Φ 2 Σ+ , 2 Π, 2 ∆ 4 Σ− , 4 Π, 4 ∆, 4 Φ

2 Σ− , 2 Π 2 Σ+ , 2 Π, 2 ∆, 2 Φ, 2 Γ

PtX Ω states 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2 1/2, 1/2,

3/2, 3/2 3/2, 3/2, 3/2, 3/2 3/2, 3/2

5/2

3/2, 3/2, 3/2 3/2, 3/2, 3/2, 3/2, 3/2 3/2

5/2, 7/2 5/2

5/2, 7/2, 9/2 5/2, 7/2 5/2 5/2

5/2 5/2, 7/2, 9/2 5/2, 7/2 5/2

3/2, 5/2, 7/2 3/2, 5/2, 7/2, 9/2


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

Table 2: Vertical excitation energies (in cm−1 ) at the minimum of (1)3/2: CI+Q/SO with AVQZ v.s. SOCI with VTZ. The relative energies of (1)3/2 are always 0 cm−1 . states CI+Q/SO a) CI+Q/SO b) SOCI PtF (1.865 Å) c ) (1)1/2 129 76 231 (1)5/2 1230 c) 1049 1288 c ) (3)1/2 8828 8642 8777 PtCl (2.174 Å) (1)5/2 570 478 421 (1)1/2 993 851 628 (2)1/2 9218 8963 8770 (2)3/2 10039 9895 10346 PtBr (2.282 Å) (1)5/2 341 307 382 (1)1/2 1149 1107 1040 (2)1/2 9350 9028 8754 (2)3/2 10032 9757 10199 PtI (2.446 Å) (1)5/2 79 160 253 (1)1/2 1177 1266 1493 (2)1/2 9484 8949 8677 (2)3/2 10013 9553 9917 a) SI with SA-CASSCF wavefunctions. b) SI with MRCISD wavefunctions. c) If the Λ-S states from 5d8 and 5d9 are averaged and calculated together in SA-CASSCF and subsequent MRCISD+Q, the energies of PtF become to 517, 766, and 8944 cm−1 .


Page 32 of 37

Page 33 of 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


Table 3: Spectroscopic constants of Ω states (1)1/2 Expt. c,d) (2)1/2 (3)1/2 (4)1/2 (5)1/2 Expt. c,d,e) (6)1/2 (7)1/2 (8)1/2 (9)1/2 (10)1/2 (11)1/2 (12)1/2 (13)1/2 (14)1/2 (15)1/2 (16)1/2

Te (cm−1 ) 79 x 6649 8825 11578 13569 (x+12512) 14672 18398 19730 21363 23635 25454 26842 29575 30306 32942 34582

Re (Å) 1.887 (1.899) 1.939 1.872 1.947 1.997 (2.001) 1.915 1.929 1.938 1.928 1.934 1.938 1.919 1.939 1.976 1.962 1.959

ωe (cm−1 ) 610.6

(1)3/2 Expt. c, f ,g,h) Expt. c,i) (2)3/2 (3)3/2 (4)3/2 Expt. c, f ,h) (5)3/2 (6)3/2 (7)3/2 Expt. c,i) (8)3/2 (9)3/2 (10)3/2 (11)3/2 (12)3/2 (13)3/2 (14)3/2

0 0 0 6712 10405 12520 11936 15687 16103 20173 (18861) 21417 23487 26109 27736 28850 30368 33993

1.865 1.868

0.2801 (0.2772)

1.942 1.924 1.950 (1.940) 1.947 1.929 1.957 (1.935) 1.929 1.919 1.950 1.918 1.943 1.972 1.949

599.2 582 (594) 572.3 552.8 538.8 556.4 603.9 598.4 548.3 551 582.3 588.1 545.0 564.1 618.2 571.1 593.7

(1)5/2 Expt. c,i) (2)5/2 (3)5/2 (4)5/2 (5)5/2 (6)5/2 Expt. c,i) (7)5/2 Expt. c,i) (8)5/2 (9)5/2

1105 (375) 7467 11919 17946 19976 20531 (19944) 25140 (23158) 29199 32517

1.901 (1.877) 1.953 1.973 1.955 1.955 1.967 (1.968) 1.915 (1.938) 1.934 1.945

595.3 (591) 560.8 569.1 555.7 553.0 581.7

597.6 577.4

0.2696 (0.2750) 0.2552 0.2501 0.2548 0.2548 0.2517 (0.2507) 0.2655 (0.2584) 0.2603 0.2575

9219 13124 21355 32261

1.987 1.959 1.952 1.941

550.0 562.1 559.9 565.3

0.2467 0.2537 0.2555 0.2585

(1)7/2 (2)7/2 (3)7/2 (4)7/2

564.6 574.7 589.3 557.6 (558) 689.4 582.2 552.0 648.0 603.3 594.5 599.3 514.3 555.7 542.7 606.6

576.2

Be (cm−1 ) 0.2735 (0.2690) 0.2590 0.2784 0.2570 0.2444 (0.2426) 0.2652 0.2618 0.2593 0.2621 0.2604 0.2592 0.2645 0.2589 0.2494 0.2529 0.2537

0.2583 0.2632 0.2560 0.2585 0.2568 0.2618 0.2543 0.2610 0.2616 0.2645 0.2560 0.2646 0.2580 0.2503 0.2564

(1)1/2

R2tot (a.u.) a) (1)3/2 (1)5/2

0.127 0.017 0.149 0.176

0.017 0.015

0.011 0.084 0.019 0.036 0.016 0.006 0.024 0.048 0.022

0.019 0.067

0.037

0.018

0.007

0.045 0.050 0.153

0.016

0.035

0.038

0.280

0.005 0.053 0.025 0.020

0.012 0.045

0.006 0.016

0.022 0.012 0.015 0.019 0.012 0.039 0.041 0.021 0.012 0.011

195 Pt19 F.

components b) (%) (I)2 Σ+ (64) + (I)2 Π (24) A2 Σ+ (I)4 Π (38) + (I)4 Σ− (33) + (I)2 Π (14) (I)2 Π (43) + (I)2 Σ+ (25) + (I)4 Σ− (22) (I)4 Π (55) + (III)2 Π (13) (II)2 Σ+ (42) + (I)4 Σ− (16) + (I)4 Π (14) [12.5]2 Σ+ (II)2 Π (42) + (II)4 Π (18) + (II)2 Σ+ (11) (I)4 Π (39) + (III)2 Π (30) + (I)4 ∆ (12) (I)2 Σ− (39) + (I)4 ∆ (23) + (I)4 Σ− (13) (II)4 Π (36) + (I)4 ∆ (20) + (I)4 Π (18) + (II)2 Σ+ (11) (II)4 Π (75) (II)4 Π (27) + (II)2 Π (20) + (I)4 ∆ (12) (I)2 Σ− (26) + (III)2 Π (25) + (V)2 Π (12) (IV)2 Π (39) + (III)2 Σ+ (30) (II)4 Σ− (50) + (IV)2 Π (18) + (II)4 Π (15) (II)2 Σ− (39) + (IV)2 Π (29) + (III)2 Σ+ (15) (II)2 Σ− (34) + (III)2 Σ+ (26) + (II)4 Σ− (16) (I)2 Π (74) + (I)2 ∆ (18) X2 Π3/2 X2 Π3/2 (I)4 Π (52) + (I)4 Σ− (27) + (I)4 ∆ (13) (I)2 ∆ (55) + (I)2 Π (21) (I)4 Σ− (29) + (I)4 ∆ (20) + (I)2 ∆ (17) + (II)2 ∆ (10) [11.9]3/2 (I)4 Π (26) + (I)4 ∆ (26) + (II)2 ∆ (13) + (II)2 Π (12) (II)4 Π (40) + (I)4 Σ− (16) + (II)2 Π (12) (III)2 Π (37) + (I)4 ∆ (17) + (II)2 ∆ (12) [18.9]2 Π3/2 (I)4 Φ (34) + (III)2 ∆ (17) (III)2 Π (26) + (II)2 Π (23) + (II)4 Π (23) (IV)2 Π (41) + (I)4 Φ (23) + (I)4 ∆ (11) (III)2 ∆ (48) + (V)2 Π (16) (III)2 ∆ (26) + (V)2 Π (17) + (II)2 ∆ (14) + (II)4 Σ− (14) (II)4 Σ− (46) + (IV)2 Π (17) (V)2 Π (35) + (II)4 Σ− (21) + (IV)2 Π (14)

0.018

0.006 0.064 0.261 0.046 0.160

0.073

0.098

0.007 0.012

0.054 0.027

(I)2 ∆ (93) [0.04]2 ∆5/2 (I)4 Π (65) + (I)4 ∆ (26) (I)4 ∆ (38) + (II)2 ∆ (24) + (I)4 Π (15) (I)4 Φ (43) + (II)4 Π (36) (II)4 Π (29) + (I)4 ∆ (26) + (I)4 Φ (19) + (I)2 Φ (16) (II)2 ∆ (49) + (I)4 Φ (15) + (II)4 Π (10) [19.9]2 ∆5/2 (III)2 ∆ (57) + (I)2 Φ (21) [23.2]2 ∆5/2 (IV)2 ∆ (34) + (III)2 ∆ (32) + (I)2 Φ (26) (II)2 Φ (78) + (IV)2 ∆ (11)

0.051 0.100 0.052

(I)4 ∆ (73) + (I)4 Φ (24) (I)4 Φ (46) + (I)2 Φ (33) + (I)4 ∆ (17) (I)2 Φ (62) + (I)4 Φ (28) (II)2 Φ (94)

0.008

(1)9/2 9775 1.957 553.5 0.2543 (I)4 Φ (97) a) Calculated at the minimum of (1)3/2. Only the values larger than 0.005 a.u. are shown. b) Calculated at R for each state. Contributions smaller than 10% are not shown. e c) R in parentheses is estimated using B (see Eq. 1). Other values in parentheses in the T , ω , and B columns are the experimental T , ∆G and B0, e e e e 0 0 1/2, respectively. d)

Reference 25. Reference 22. f ) Reference 21. g) Reference 23. h) Reference 24. i) Reference 26. e)



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

Table 4: Spectroscopic constants of Ω states (1)1/2 (2)1/2 (3)1/2 (4)1/2 (5)1/2 (6)1/2 (7)1/2 (8)1/2 (9)1/2 (10)1/2 (11)1/2 (12)1/2 (13)1/2 (14)1/2 (15)1/2 (16)1/2

Te (cm−1 ) 942 8956 9839 13378 15117 16244 20446 21394 23680 25124 27004 28226 29575 30969 33448 34924

Re (Å) 2.201 2.260 2.209 2.286 2.302 2.245 2.276 2.284 2.272 2.258 2.271 2.251 2.253 2.330 2.293 2.296

ωe (cm−1 ) 392.3 285.0 413.0 338.6 369.0 380.7 318.9 325.0 336.4 341.1 348.6 339.3 317.2 300.9 296.8 379.4

Be (cm−1 ) 0.1174 0.1114 0.1165 0.1089 0.1072 0.1129 0.1098 0.1090 0.1101 0.1116 0.1103 0.1122 0.1120 0.1047 0.1082 0.1081

(1)3/2 Expt. c,d) Expt. e) (2)3/2 (3)3/2 (4)3/2 (5)3/2 (6)3/2 (7)3/2 (8)3/2 (9)3/2 (10)3/2 (11)3/2 (12)3/2 (13)3/2 (14)3/2

0 0 0 9351 10250 13847 17127 18215 21318 22170 24788 27007 28552 29454 31110 34333

2.174 (2.149)

0.1203 (0.1227)

2.282 2.222 2.293 2.275 2.281 2.286 2.267 2.269 2.279 2.243 2.264 2.322 2.272

393.9 394 399.1 315.0 385.6 326.1 324.2 354.1 310.0 345.3 314.2 310.9 330.3 358.8 304.7 354.9

(1)5/2 (2)5/2 (3)5/2 (4)5/2 (5)5/2 (6)5/2 (7)5/2 (8)5/2 (9)5/2

459 10151 13960 18670 21254 21781 25390 30066 31964

2.213 2.294 2.315 2.284 2.289 2.308 2.232 2.261 2.261

395.9 338.0 344.0 313.8 319.9 330.8 338.0 356.6 339.4

0.1161 0.1078 0.1061 0.1090 0.1086 0.1066 0.1142 0.1113 0.1117

(1)7/2 (2)7/2 (3)7/2 (4)7/2

11378 14485 22171 31274

2.326 2.295 2.286 2.247

332.8 340.5 305.7 353.3

0.1052 0.1078 0.1088 0.1130

0.1092 0.1152 0.1081 0.1098 0.1093 0.1088 0.1107 0.1105 0.1095 0.1130 0.1109 0.1055 0.1104

(1)1/2 0.020 0.097 0.130 0.214 0.018 0.112 0.026 0.095 0.031 0.016 0.066 0.086 0.055 0.012 0.006

0.005 0.012 0.028 0.048 0.056 0.073 0.009 0.005

R2tot (a.u.) a) (1)3/2 (1)5/2

0.050 0.013 0.013 0.053 0.059 0.008 0.044

0.007 0.019

0.009 0.066 0.253 0.041 0.425 0.038 0.017 0.110 0.067 0.014 0.024

0.011 0.006 0.007 0.027 0.091 0.011 0.014

195 Pt35 Cl.

components b) (%) (I)2 Σ+ (60) + (I)2 Π (36) (I)4 Σ− (37) + (I)4 Π (36) + (I)2 Π (14) (I)2 Π (30) + (I)2 Σ− (28) + (I)4 Σ− (26) (I)4 Π (48) + (I)2 Σ− (14) + (III)2 Π (12) (II)2 Σ+ (46) + (I)4 Σ− (17) + (I)4 Π (13) (II)2 Π (49) + (II)4 Π (21) (I)4 Π (47) + (III)2 Π (30) (I)4 ∆ (33) + (I)2 Σ− (32) + (I)4 Σ− (16) (II)4 Π (48) + (I)4 ∆ (15) + (I)4 Π (14) (II)4 Π (70) + (II)2 Σ+ (10) (II)2 Π (20) + (II)4 Π (18) + (I)4 Π (13) + (I)4 ∆ (12) (III)2 Π (28) + (V)2 Π (19) + (III)2 Σ+ (15) + (I)2 Σ− (13) (IV)2 Π (42) + (III)2 Σ+ (34) (II)4 Σ− (56) + (I)4 Π (17) (II)2 Σ− (37) + (IV)2 Π (26) + (III)2 Σ+ (13) + (V)2 Π (11) (II)2 Σ− (28) + (III)2 Σ+ (21) + (II)4 Σ− (19) + (II)2 Σ+ (11)

0.059 0.029 0.079 0.010 0.016 0.014 0.008

(I)2 Π (77) + (I)2 ∆ (19) X2 Π3/2 X2 Π (I)4 Π (49) + (I)4 Σ− (31) + (I)4 ∆ (12) (I)2 ∆ (69) + (I)2 Π (21) (I)4 Σ− (27) + (II)2 Π (21) + (I)4 ∆ (20) + (II)2 ∆ (11) (II)4 Π (29) + (III)2 Π (22) + (I)4 ∆ (11) (I)4 Π (21) + (II)2 ∆ (20) + (II)4 Σ− (17) + (II)4 Π (14) (II)2 Π (22) + (I)4 ∆ (22) + (III)2 Π (16) + (I)4 Σ− (14) (I)4 Φ (46) + (III)2 ∆ (15) (III)2 Π (38) + (II)4 Π (30) + (II)2 ∆ (17) (IV)2 Π (35) + (I)4 Φ (20) + (V)2 Π (19) + (I)4 ∆ (10) (III)2 ∆ (40) + (V)2 Π (12) + (II)2 Π (11) + (II)2 ∆ (10) (III)2 ∆ (25) + (V)2 Π (21) + (II)2 ∆ (11) + (I)4 Φ (11) (II)4 Σ− (54) + (IV)2 Π (11) + (II)2 ∆ (10) (V)2 Π (21) + (II)4 Σ− (21) + (II)2 Π (19) + (IV)2 Π (17)

0.007 0.128 0.295 0.035 0.269 0.169 0.111 0.032

(I)2 ∆ (97) (I)4 Π (61) + (I)4 ∆ (30) (I)4 ∆ (30) + (II)2 ∆ (27) + (I)4 Π (15) + (I)4 Φ (12) (II)4 Π (50) + (I)4 Φ (27) (I)4 Φ (32) + (I)4 ∆ (26) + (II)4 Π (24) + (I)2 Φ (12) (II)2 ∆ (48) + (I)4 Φ (16) + (I)4 Π (14) + (I)2 Φ (10) (III)2 ∆ (57) + (I)2 Φ (17) + (II)4 Π (12) (I)2 Φ (29) + (III)2 ∆ (26) + (IV)2 ∆ (25) (II)2 Φ (84)

0.090 0.131 0.060

(I)4 ∆ (66) + (I)4 Φ (31) (I)2 Φ (38) + (I)4 Φ (36) + (I)4 ∆ (22) (I)2 Φ (56) + (I)4 Φ (30) + (I)4 ∆ (12) (II)2 Φ (94)

0.045 0.028

Page 34 of 37

(1)9/2 11227 2.293 327.8 0.1082 (I)4 Φ (97) a) Calculated at the minimum of (1)3/2. Only the values larger than 0.005 a.u. are shown. b) Calculated at R for each state. Contributions smaller than 10% are not shown. e c) R in parentheses is estimated using B (see Eq. 1). Value in parentheses is the experimental B . e 0 0 d) Reference 23. e) Reference 18.


Page 35 of 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


Table 5: Spectroscopic constants of Ω states (1)1/2 (2)1/2 (3)1/2 (4)1/2 (5)1/2 (6)1/2 (7)1/2 (8)1/2 (9)1/2 (10)1/2 (11)1/2 (12)1/2 (13)1/2 (14)1/2 (15)1/2 (16)1/2

Te (cm−1 ) 1089 8959 9718 13099 15136 15800 19846 20890 22964 24190 26190 26603 27661 31532 c) 32204 34842 c)

Re (Å) 2.312 2.378 2.305 2.398 2.418 2.365 2.388 2.400 2.397 2.378 2.398 2.390 2.375

ωe (cm−1 ) 265.6 215.1 318.7 232.2 240.2 249.3 220.7 226.9 235.0 236.2 236.5 214.0 230.6

Be (cm−1 ) 0.0559 0.0530 0.0563 0.0522 0.0513 0.0537 0.0526 0.0521 0.0523 0.0531 0.0522 0.0526 0.0533

2.409

225.0

0.0519

(1)3/2 (2)3/2 (3)3/2 (4)3/2 (5)3/2 (6)3/2 (7)3/2 (8)3/2 (9)3/2 (10)3/2 (11)3/2 (12)3/2 (13)3/2 (14)3/2

0 9400 10102 13594 16407 18026 20395 21171 23687 25695 27363 27949 31898 c) 33699 c)

2.282 2.391 2.319 2.402 2.388 2.402 2.378 2.403 2.390 2.398 2.393 2.391

277.7 235.6 286.0 223.3 227.7 240.7 222.3 231.8 216.2 196.2 215.1 243.6

0.0576 0.0525 0.0559 0.0520 0.0526 0.0520 0.0531 0.0520 0.0526 0.0522 0.0525 0.0525

(1)5/2 (2)5/2 (3)5/2 (4)5/2 (5)5/2 (6)5/2 (7)5/2 (8)5/2 (9)5/2

254 10322 14005 17898 20407 21228 23704 28879 c) 30606 c)

2.318 2.414 2.434 2.394 2.403 2.435 2.368

274.8 231.7 234.0 225.0 229.0 217.0 237.5

0.0558 0.0515 0.0507 0.0523 0.0520 0.0507 0.0535

(1)7/2 (2)7/2 (3)7/2 (4)7/2

11578 14118 21135 28447 c)

2.438 2.420 2.400

225.1 228.8 222.4

0.0505 0.0512 0.0521

(1)1/2 0.020 0.087 0.104 0.128 0.174 0.115 0.062 0.173 0.059 0.022 0.090 0.129 0.082 0.011 0.008

0.006 0.016 0.033 0.051 0.048 0.102

R2tot (a.u.) a) (1)3/2 (1)5/2

195 Pt79 Br.

0.005

components b) (%) (I)2 Σ+ (59) + (I)2 Π (38) (I)4 Σ− (47) + (I)4 Π (38) (I)2 Π (40) + (I)2 Σ+ (33) + (I)4 Σ− (16) (I)4 Π (46) + (I)2 Σ− (17) + (III)2 Π (14) (II)2 Σ+ (45) + (I)4 Π (18) + (I)4 Σ− (14) (II)2 Π (49) + (II)4 Π (23) (I)4 Π (47) + (III)2 Π (27) + (I)2 Σ− (14) (I)4 ∆ (30) + (I)2 Σ− (27) + (I)4 Σ− (16) + (I)4 Π (10) (II)4 Π (44) + (I)4 ∆ (16) + (II)2 Π (11) + (I)4 Π (11) (II)4 Π (68) + (II)2 Σ+ (12) (II)2 Π (24) + (I)4 ∆ (19) + (V)2 Π (14) + (I)4 Π (10) (III)2 Π (24) + (III)2 Σ+ (20) + (IV)2 Π (12) + (V)2 Π (12) (III)2 Π (47) + (III)2 Σ+ (30) (II)4 Σ− (26) + (IV)2 Π (18) + (III)2 Σ+ (16) + (II)4 Π (14) (V)2 Π (26) + (III)2 Σ+ (22) + (II)4 Σ− (11) (V)2 Π (35) + (II)4 Σ− (29) + (III)2 Π (13)

0.078 0.288 0.038 0.005 0.434 0.219 0.053 0.116 0.148 0.005 0.023 0.021

0.007 0.009 0.005

(I)2 Π (79) + (I)2 ∆ (19) (I)4 Π (48) + (I)4 Σ− (35) + (I)4 ∆ (10) (I)2 ∆ (71) + (I)2 Π (21) (I)4 Σ− (27) + (II)2 Π (20) + (I)4 ∆ (18) + (I)4 Π (10) (II)4 Π (35) + (III)2 Π (21) + (II)2 Π (10) (I)4 Π (21) + (II)2 ∆ (19) + (I)4 ∆ (16) + (I)4 Σ− (14) (III)2 ∆ (24) + (I)4 Σ− (15) + (II)2 Π (14) + (I)4 ∆ (14) (I)4 Φ (38) + (III)2 Π (15) (III)2 Π (34) + (II)4 Π (29) + (II)2 ∆ (16) (V)2 Π (51) + (I)4 Φ (19) (IV)2 Π (31) + (III)2 ∆ (22) + (II)2 ∆ (20) (III)2 ∆ (32) + (I)4 Φ (19) + (V)2 Π (12) + (II)2 ∆ (10) (II)4 Σ− (46) + (II)2 ∆ (13) + (IV)2 Π (12) (II)4 Σ− (45) + (IV)2 Π (15) + (II)2 Π (15)

0.005 0.145 0.207 0.059 0.357 0.315 0.080 0.107

(I)2 ∆ (98) (I)4 Π (48) + (I)4 Σ− (34) + (I)4 ∆ (10) (I)4 ∆ (31) + (II)2 ∆ (25) + (I)4 Φ (16) + (I)4 Π (13) (II)4 Π (55) + (I)4 Φ (21) + (III)2 ∆ (10) (I)4 Φ (38) + (I)4 ∆ (24) + (II)4 Π (23) (II)2 ∆ (43) + (I)4 Π (16) + (I)2 Φ (15) + (I)4 ∆ (10) (II)2 Φ (59) + (I)2 Φ (11) (II)2 Φ (60) + (I)2 Φ (12) + (II)2 ∆ (10) (I)2 Φ (33) + (II)2 Φ (32) + (IV)2 ∆ (18) + (III)2 ∆ (13)

0.007 0.093 0.143 0.055

(I)4 ∆ (54) + (I)4 Φ (41) (I)2 Φ (38) + (I)4 ∆ (31) + (I)4 Φ (27) (I)2 Φ (54) + (I)4 Φ (29) + (I)4 ∆ (13) (II)2 Φ (79)

0.066 0.027 0.078 0.049 0.006 0.012 0.040

0.011 0.005 0.010 0.039 0.090 0.022

0.055 0.038 0.006 0.053 0.047 0.087

(1)9/2 10737 2.396 233.2 0.0523 (I)4 Φ (98) a) Calculated at the minimum of (1)3/2. Only the values larger than 0.005 a.u. are shown. b) Calculated at R for bound state or the minimum of (1)3/2 for repulsive state. Contributions smaller than 10% are not shown. e c) Repulsive state. Calculated at the minimum of (1)3/2.



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

Table 6: Spectroscopic constants of Ω states (1)1/2 (2)1/2 (3)1/2 (4)1/2 (5)1/2 (6)1/2 (7)1/2 (8)1/2 (9)1/2 (10)1/2 (11)1/2 (12)1/2 (13)1/2 (14)1/2 (15)1/2 (16)1/2 (17)1/2

Te (cm−1 ) 1110 9482 10433 13939 15699 16700 19876 20807 23384 c) 22953 24366 26289 c) 25814 30368 c) 31322 c) 33144 c) 34187 c)

Re (Å) 2.481 2.453 2.532 2.552 2.542 2.565 2.561 2.608

ωe (cm−1 ) 208.9 204.7 212.5 209.0 197.3 202.3 155.6 153.6

Be (cm−1 ) 0.0356 0.0365 0.0342 0.0337 0.0339 0.0334 0.0336 0.0324

2.630 2.626

125.3 163.3

0.0317 0.0316

2.587

209.8

0.0329

(1)3/2 (2)3/2 (3)3/2 (4)3/2 (5)3/2 (6)3/2 (7)3/2 (8)3/2 (9)3/2 (10)3/2 (11)3/2 (12)3/2 (13)3/2 (14)3/2 (15)3/2

0 9951 11065 14811 16035 18811 20349 22203 c) 21915 24733 c) 26808 c) 29114 c) 30070 c) 32637 c) 33677 c)

2.446 2.480 2.543 2.544 2.556 2.563 2.595

214.3 215.0 202.4 201.3 162.8 142.3 168.6

0.0367 0.0357 0.0339 0.0339 0.0336 0.0332 0.0325

2.617

137.5

0.0320

(1)5/2 (2)5/2 (3)5/2 (4)5/2 (5)5/2 (6)5/2 (7)5/2 (8)5/2 (9)5/2 (10)5/2 (11)5/2

4 11888 15667 18227 19418 21336 22650 25706 c) 29776 c) 31592 c) 34384 c)

2.482 2.573 2.576 2.570 2.584 2.588 2.590

217.9 199.7 174.8 179.3 174.4 141.5 198.2

0.0356 0.0332 0.0331 0.0332 0.0329 0.0327 0.0330

(1)7/2 (2)7/2 (3)7/2 (4)7/2 (5)7/2

13247 15529 20664 c) 23946 c) 29395 c)

2.564 2.597

190.9 189.5

0.0334 0.0325

(1)1/2 0.037 0.028 0.057 0.033 0.202 0.125 0.100 0.474 0.200 0.172 0.263 0.030 0.107

R2tot (a.u.) a) (1)3/2 (1)5/2

0.006 0.063 0.020 0.009 0.091 0.035 0.005 0.024 0.005

0.012

0.018 0.040 0.028 0.021 0.014 0.113

0.057 0.274 0.093 0.309 0.018 0.700 0.281 0.115 0.074 0.164 0.015

0.054 0.007 0.056 0.030 0.059 0.027

0.011 0.016 0.096 0.013 0.008

0.086 0.049 0.083 0.026 0.988 0.419 0.139 0.045 0.244 0.039 0.049 0.118 0.042

Page 36 of 37

195 Pt127 I.

components b) (%) (I)2 Σ+ (60) + (I)2 Π (40) (I)2 Π (58) + (I)2 Σ+ (39) (I)4 Σ− (54) + (I)4 Π (22) (I)4 Π (41) + (III)2 Π (25) + (I)2 Σ− (17) (II)2 Π (44) + (II)4 Π (28) + (III)2 Π (10) (I)4 Π (38) + (II)2 Σ+ (37) (I)4 Π (39) + (I)2 Σ− (21) + (III)2 Π (13) + (II)2 Π (11) (II)4 Π (18) + (I)2 Σ− (17) + (I)4 Σ− (14) + (III)2 Π (12) (II)4 Π (41) + (II)2 Π (12) + (I)4 ∆ (10) (II)2 Σ+ (29) + (II)4 Π (28) + (III)2 Σ+ (10) + (I)4 ∆ (10) (II)4 Π (24) + (I)2 Σ− (16) + (I)4 ∆ (12) + (III)2 Π (11) + (V)2 Π (11) (III)2 Σ+ (38) + (V)2 Π (24) + (III)2 Π (13) + (II)4 Π (14) (I)4 ∆ (29) + (IV)2 Π (12) + (III)2 Π (11) + (II)4 Π (10) (V)2 Π (27) + (III)2 Σ+ (20) + (II)4 Σ− (13) (IV)2 Π (52) (II)2 Σ− (52) + (II)4 Σ− (29) (II)4 Σ− (35) + (II)2 Σ− (32) + (II)2 Σ+ (10) (I)2 Π (81) + (I)2 ∆ (18) (I)2 ∆ (78) + (I)2 Π (19) (I)4 Π (47) + (I)4 Σ− (38) (I)4 Σ− (32) + (I)4 Π (19) + (III)2 Π (14) + (I)4 ∆ (10) (II)4 Π (43) + (II)2 Π (26) + (IV)2 Π (14) (II)2 ∆ (26) + (I)4 ∆ (25) + (I)4 Π (13) (III)2 ∆ (34) + (I)4 Φ (21) + (V)2 Π (19) (III)2 Π (27) + (I)4 ∆ (26) + (IV)2 Π (18) + (I)4 Φ (16) (II)2 Π (32) + (V)2 Π (17) + (III)2 Π (14) + (II)4 Π (13) (IV)2 Π (36) + (II)2 Π (20) + (I)4 Φ (18) + (V)2 Π (15) (II)2 ∆ (25) + (V)2 Π (24) + (I)4 ∆ (14) + (IV)2 Π (10) (III)2 ∆ (55) + (I)4 Φ (20) (III)2 Π (22) + (II)2 ∆ (19) + (II)2 Π (15) + (I)4 ∆ (12) (II)4 Σ− (65) + (III)4 Π (15) + (II)4 ∆ (13) (II)4 ∆ (57) + (II)4 Σ− (26) (I)2 ∆ (99) (I)4 Π (77) + (I)4 ∆ (14) (I)4 ∆ (40) + (II)2 ∆ (26) + (I)4 Φ (21) (I)4 Φ (50) + (I)4 ∆ (15) + (II)4 Π (12) + (II)2 ∆ (12) (I)4 Φ (51) + (I)4 ∆ (15) + (II)4 Π (12) + (II)2 ∆ (11) (II)2 ∆ (44) + (I)4 ∆ (19) + (I)4 Π (11) (III)2 ∆ (52) + (I)2 Φ (27) (II)2 Φ (74) + (III)2 ∆ (10) (II)4 ∆ (33) + (I)2 Φ (20) + (II)2 Φ (17) + (III)2 ∆ (11) + (III)4 Π (10) (II)4 ∆ (43) + (I)2 Φ (21) + (III)2 ∆ (13) (III)4 Π (62) + (IV)2 ∆ (17) (I)4 Φ (65) + (I)4 ∆ (17) + (I)2 Φ (17) (I)4 ∆ (69) + (I)2 Φ (22) (I)2 Φ (52) + (I)4 Φ (26) + (I)4 ∆ (13) (II)2 Φ (68) + (II)4 ∆ (30) (II)4 ∆ (57) + (II)2 Φ (26)

(1)9/2 11412 2.551 187.9 0.0337 (I)4 Φ (99) (2)9/2 31670 c) (II)4 Φ (99) a) Calculated at the minimum of (1)3/2. Only the values larger than 0.005 a.u. are shown. b) Calculated at the R for bound state or the minimum of (1)3/2 for repulsive state. Contributions smaller than 10% are not shown. e c) Repulsive state. Calculated at the minimum of (1)3/2.


Page 37 of 37

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TOC


Theoretical Study of Low-Lying Electronic States of PtX (X= F, Cl, Br

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