The Electronic Structure of OsSi Calculated by MS-NEVPT2 with

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

The Electronic Structure of OsSi Calculated by MSNEVPT2 with Inclusion of the Relativistic Effects Bingbing Suo, Yongqin Lian, Wenli Zou, and Yibo Lei J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00825 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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The Journal of Physical Chemistry

The Electronic Structure of OsSi Calculated by MS-NEVPT2 with Inclusion of the Relativistic Effects Bingbing Suo,∗,† Yongqin Lian,† Wenli Zou,∗,† and Yibo Lei‡ †Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710127, China ‡Key Laboratory of Synthetic and Natural Functional Molecule Chemistry of Ministry of Education, The College of Chemistry and Materials Science, Northwest University, Xi’an, Shaanxi 710127, China E-mail: [email protected]; [email protected]

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Abstract The electronic states of OsSi are calculated by Multi-State N-Electron Valence State Second Order Perturbation Theory (MS-NEVPT2) with all-electron basis sets. The relativistic effects are considered comprehensively that allows us to identify the X 3 Σ− 0+ ground state. The theoretical equilibrium bond length 2.103 Å is close to the experimental measurement of 2.1207 Å while the vibrational frequency 466 cm−1 is smaller than the experimental value of 516 cm−1 . Two excited states, namely 3 Π1 (I) and 3Π

1 (II),

3Π

1 (I)

are located at 15568 and 18316 cm−1 above the ground state, respectively. The

← X 3 Σ− transition has been assigned to the experimental spectra at 15729 0+

may produce the bands near 18469 cm−1 . Although cm−1 and 3 Π1 (II) ← X 3 Σ− 0+ the latter transition energy is in accord with the experimental spectra, theoretical calculations give too small oscillator strength. Moreover, plenty of excited states with considerable oscillator strengths are located that could serve as reference data in future experiments. The four low-lying states of OsC are also calculated for comparison.

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Introduction Transition metal complexes have a lot of applications in many areas of science from

catalytic chemistry, metallo biochemical systems, to magnetic, ferro-electric and superconducting materials etc. Among all metal complexes, diatomic molecules are the simplest ones on structure, often serving as the model systems to study metal-ligand bonding. Experimentally, modern molecular spectroscopy technique could give the high-resolution spectra of the diatomic metal compounds. Combining with theoretical analysis and experimental tests, comprehensive information about the electronic structure of metal complexes can be revealed. However, the open d-shell electrons in transition metal elements could give rise to many degenerate or quasi-degenerate states, which pose a great challenge on theoretical calculations. In general, multiconfigurational electronic correlation calculations are necessary to give an even qualitative description of such strongly correlated systems. For theorists, 2


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such comparisons are good benchmarks to check the newly developed methods as indicated by many of publications on Cr2 . 1–8 There are enormous experimental works on diatomic metal silicides, such as FeSi, 9 CoSi, 9 NiSi, 9,10 RuSi, 11 IrSi, 12,13 PdSi, 14 PtSi, 15,16 and OsSi 17 etc. Plenty of band systems have been recorded while the theoretical calculations are far from complete to interpret the available spectra. For instance, the only theoretical calculation on OsSi was performed by Wu and Su via density functional theory (DFT) with the B3LYP functional and the LANL2DZ basis set. 18–20 These authors concentrated mainly on the ground 3 Σ− state and obtained the spectroscopic parameters of Re =2.139 Å and ωe =520 cm−1 . 18 Recently, Johnson and Morse reported the first spectra of OsSi by using resonant two-photon ionization spectroscopy. 17 Two electronic band systems in the scope of 15212 to 18634 cm−1 were recorded in which nine bands had been resolved in rotational resolution, allowing the ground state to be identified 00 −1 as the X 3 Σ− 0+ with the equilibrium bond length of 2.1207 Å and ∆G1/2 = 516 cm . By

comparing with the isovalent ReN molecule, 21,22 Johnson and Morse guessed that the X 3 Σ− 0+ state was the mixture of the 3 Σ− and 1 Σ+ , in which the spin-orbit coupling (SOC) pushed the 3 − X 3 Σ− 0+ down to the Σ1 component. Although the spectroscopic parameters of the ground

state from the DFT calculation were in accord with the experimental measurement, it might be a fortunate result from error cancellation because the SOC effect was fully neglected. 18 Due to lack of the theoretical results on the excited states, two upper states involved in the experimental spectra were tentatively assigned as A3 Π1 and B 1 Π1 by using WO as the reference molecule. 23 To clarify the experimental spectra of OsSi, high level theoretical calculations with intensive consideration the relativistic effects are highly desired. Recently, we have developed a Multi-State (MS-) version of N-Electron Valence State Second-Order Perturbation Theory (NEVPT2) program. 24 NEVPT2 is size consistent 25,26 and less affected by the intruder state problem that is superior to the widely used Multi-State Complete Active Space Second-Order Perturbation Theory (MS-CASPT2). 27–29 Schapiro, Sivalingam, and Neese have assessed the accuracy of NEVPT2 in calculating the vertical

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excitation energies (VEEs) of 28 organic molecules. 30 It is found that NEVPT2 has the similar accuracy as CASPT2 with the IPEA shift. 30,31 Nevertheless, few works have been reported the use of NEVPT2 to calculate transition metal compounds, whereas CASPT2 has been proven very successful in this field. Therefore, MS-NEVPT2 is carried out to calculate the potential energy curves (PECs) of OsSi as well as to give a detailed interpretation of the available spectra. Besides, the SOC calculations are performed to consider the zero-field splitting. 18 This paper is organized as follows: in section 2 we will introduce the methods used in this study. Then, section 3 presents the theoretical results including the atomic levels, the spectroscopic parameters of the Λ − S states as well as the Ω states, and interprets the experimental spectra according to our calculations. The electronic structure and chemical bond of OsSi are also analyzed. Finally, a brief conclusion is given in section 4.

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Methods and computational details The relativistic atomic natural orbital with the polarized valance triple zeta (ANO-

RCC-VTZP) basis set developed by Roos et. al. is used in this study, 32,33 where the [24s21p15d11f4g2h] primitive functions are contracted to (8s7p5d3f2g1h) for Os 32 and [17s12p5d4f] are contracted to (5s4p2d1f) for Si. 33 The scalar relativistic effects are considered via the spin-free second order Douglas-Kroll-Hess (DKH2) Hamiltonian. 34–36 The more precise thirdorder DKH (DKH3) and exact two component (X2C) Hamiltonians are also tested and no substantial differences are observed for the spectroscopic parameters of the Λ − S states as indicated in Table S1 in the supporting document. The State-Averaged Complete Active Space Self Consistent Field (SA-CASSCF) calculation is first performed by the MOLCAS program to take into account the static correlation. 37 Then, the transformed molecular orbital integrals are used by the Xi’an-CI package developed in our group to perform the MS-NEVPT2 calculation. 38–43 For comparison, MS-CASPT2 25,26 in MOLCAS is also performed to calculate the Λ−S states of OsSi. In SA-CASSCF, the active space is composed of

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the Os(5d6s) and Si(3s3p) orbitals, that is, 12 electrons distribute on 10 molecular orbitals in any possible ways. Same active space is used in MS-NEVPT2 and MS-CASPT2. All core electrons of Os and Si are correlated in the multi-reference perturbation calculations, in which both core-core, core-active and active-active correlations are considered. Besides MSNEVPT2 and MS-CASPT2, spin-adapted time-dependent density functional theory (SATDDFT) 44–47 with the B3LYP functional is also performed via Beijing Density Functional package (BDF) 48–51 to calculate VEEs of the triplet states and the oscillator strengths. The SA-TDDFT results are listed in Table S2 of the supporting document. The ground state of Os is 5 D(5d6 6s2 ) with four low-lying states 5 F (5d7 6s1 ), 3 P (5d6 6s2 ), 3

F (5d7 6s1 ) and 3 H(5d6 6s2 ) situated in the range of 0.81 to 1.49 eV higher. 52 The Si atom has

a 3 P (3s2 3p2 ) ground state and the first excited state 1 D(3s2 3p2 ) is 0.76 eV above. 52 Adiabatic coupling of the ground and low-lying excited states of Os and Si may give rise to the singlet, triplet, quintet and septet molecular terms with the Σ− , Σ+ , Π, ∆, Γ spatial symmetries. Despite the C∞v symmetry of OsSi, its subgroup C2v is used in whole calculations, which has four irreducible representations (irreps). To obtain more excited states, the number of roots in each irrep with a given spin symmetry is increased one by one until all the Λ − S states below 30000 cm−1 are included in the MS-NEVPT2 calculation. The number of roots in each spin-spatial symmetry is listed in Table S3 of the supporting information. Moreover, SOC is considered via state-interaction (SI) approach, in which the SOC matrix is calculated at the SA-CASSCF level while the pre-calculated MS-NEVPT2 energies are used to substitute for the diagonal elements. The SOC calculations are performed with the Molpro package. 53,54

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Results and discussion

3.1

The atomic states of OsSi

The accuracy of MS-NEVPT2 is evaluated by comparing theoretical energy splitting of the atomic states with the J-averaged energy levels from National Institute of Standards 5



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and Technology (NIST), which are summarized in Table 1. 52 Analyzing the dominant configurations of OsSi as a supermolecule at the bond length of 10 Å allows us to identify 5 atomic states of Os and 2 states of Si. As seen in Table 1, MS-NEVPT2 gives the correct ground 5 D(5d6 6s2 ) state of Os. For the four excited states, the absolute deviations of the theoretical excitation energies with respect to the J-averaged values are in the range of 0.01 (3 F ) to 0.13 (5 F ) eV, falling into the error bar of the ANO-VTZP basis set optimized for Os. 32 Moreover, MS-NEVPT2 gives the energy gap of 1 D −3 P of Si as 0.68 eV, which is close to the J-averaged value of 0.76 eV from NIST. 52 Overall agreement between the theoretical results and the J-averaged atomic energy levels indicates that MS-NEVPT2 and the basis sets used in this study should produce the sufficiently accurate results for OsSi. Table 1: Atomic Levels of Os and Si Atom

State

Conf.

Os

5D

5d6 6s2 5d7 (4 F )6s 5d6 6s2 5d7 (4 F )6s 5d6 6s2 3s2 3p2 3s2 3p2

5F 3P 3F 3H

Si

3P 1D

a

3.2

∆E(eV)a (NIST) 0.00 0.81 1.28 1.26 1.54 0.00 0.76

∆E(eV) (Theor.) 0.00 0.68 1.17 1.25 1.64 0.00 0.68

Abs. Deviation 0.00 0.13 0.11 0.01 0.10 0.00 0.08

J-averaged value from Ref. 52.

Comparison of spectroscopic parameters of the Λ − S states of OsSi by MS-NEVPT2 and MS-CASPT2

Both MS-CASPT2 and MS-NEVPT2 have been performed to calculate the PECs of the Λ − S states of OsSi, which are drawn in Figure S1-S3 in the supporting document. From these PECs, spectroscopic parameters are calculated by numerically solving the Schrödinger equation using the LEVEL 8.2 program. 55 The fitted spectroscopic parameters are presented in Table 2, including Re for equilibrium bond length, Te for adiabatic excitation energy, ωe for vibrational frequency, and De for dissociation energy, while the leading configurations 6


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are listed in Table 3. Generally speaking, the spectroscopic constants by MS-NEVPT2 are in line with the results of MS-CASPT2. As seen in Table 2, the equilibrium bond length 2.114 Å of the X 3 Σ− state by MS-NEVPT2 is close to the experimental value of 2.1207 Å. 17 MS-CASPT2 produces a slightly longer Re with the value of 2.139 Å. The vibrational frequency 527 cm−1 from MS-CASPT2 agrees well with the experimental value of 516 cm−1 , 17 while MS-NEVPT2 produces a slightly smaller frequency of 493 cm−1 . Table 2: Spectroscopic Parameters of the Λ − S States by the MS-NEVPT2 and MS-CASPT2 (in parentheses) Calculations States X 3 Σ−a 3 ∆(I) 1 Σ+ (I) 1Γ 1 ∆(I) 5 Π(I) 3Φ 3 Π(I) 3 ∆(II) 3 Π(II) 1 Π(I) 5 ∆(I) 5 Σ− 1 ∆(II) 1 Σ+ (II) 5 ∆(II) 1 Φ(I) 5 Π(II) 3 Π(III) 5Γ 3 Σ+ (I) 1 Φ(II) 1 Π(II) 5Φ 3 ∆(III) 3 Σ+ (II) 5 Π(III) 7∆ a

Re (Å) 2.114(2.139) 2.080(2.088) 2.074(2.085) 2.073(2.080) 2.039(2.046) 2.128(2.130) 2.152(2.148) 2.152(2.159) 2.053(2.052) 2.189(2.218) 2.142(2.138) 2.227(2.227) 2.216(2.217) 2.102(2.101) 2.076(2.061) 2.243(2.230) 2.161(2.153) 2.112(2.104) 2.100(2.103) 2.225(2.223) 2.117(2.234) 2.105(2.099) 2.116(2.135) 2.105(2.103) 2.237(2.269) 2.252(2.228) 2.120(2.104) 2.170(2.147)

Te (cm−1 ) 0 2015(3720) 5277(5342) 7314(6982) 11282(13446) 11948(12224) 12501(12931) 13546(13423) 14678(16131) 16009(16986) 16018(16609) 16853(16864) 18675(18877) 18831(19280) 19105(22486) 19381(19508) 19423(19352) 20037(19892) 20819(23059) 20959(22541) 21552(22674) 22547(23718) 22833(24968) 23172(24248) 23966(24251) 24234(25112) 24324(25092) 25449(26495)

ωe (cm−1 ) 493(527) 541(538) 553(559) 545(567) 520(561) 478(475) 512(424) 497(539) 586(573) 428(434) 526(523) 450(451) 440(438) 569(566) 632(535) 442(455) 509(508) 524(546) 461(404) 429(432) 348(425) 490(502) 517(502) 568(505) 542(468) 518(486) 456(523) 450(481)

De (eV) 5.93 6.35 6.15 5.91 5.40 4.49 4.45 4.43 4.78 4.03 4.95 3.77 3.57 4.73 4.74 3.53 4.77 3.48 3.43 3.64 3.82 4.40 4.74 3.09 3.67 3.62 2.97 2.75

Dissociation limit Os5 D(5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os3 P (5d6 6s2 )+Si3 P (3s2 3p2 ) Os3 P (5d6 6s2 )+Si3 P (3s2 3p2 ) Os3 P (5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os5 D(5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si3 P (3s2 3p2 ) Os3 P (5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os3 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os3 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os3 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 F (5d7 6s1 )+Si1 D(3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os3 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os3 H(5d6 6s2 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 F (5d7 6s1 )+Si3 P (3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 ) Os5 D(5d6 6s2 )+Si1 D(3s2 3p2 )

The experimental spectroscopic constants of the X 3 Σ− state: Re =2.1207 Å and ωe =516 cm 0+ −1 . 17 The total energy of MS-NEVPT2 is -17529.060686 Hartree.

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Overall, MS-NEVPT2 tends to underestimate the adiabatic excitation energies compared to MS-CASPT2. Among all the 27 excited states, the absolute energy differences of 21 states between MS-NEVPT2 and MS-CASPT2 are within 0.2 eV. The largest deviation comes from the 1 Σ+ (II) state, in which the excitation energy from MS-CASPT2 is 3381 cm−1 (0.42 eV) higher than the MS-NEVPT2 one. The 1 Σ+ (II) is a mixture of three configurations, ie. 17σ 2 9π 4 4δ 4 (51.1%), 17σ 2 18σ 2 9π 4 4δ 2 (19.5%), and 17σ 1 18σ 1 9π 4 4δ 4 (4.9%). It is a typical doubly excited state and also is multiconfigurational in character. Since the experimental excitation energy of 1 Σ+ (II) is not available at present, it is not clear which result is better, MS-CASPT2 or MS-NEVPT2. It is interesting to compare SA-TDDFT with the multi-reference electronic correlation calculation results. Table S2 in supporting document presents the VEEs calculated by SATDDFT, MS-NEVPT2, and MS-CASPT2. The energy orders of nearly all the triplet states from SA-TDDFT are in agreement with the MS-NEVPT2 results, supporting the assignment of the excited states. An only exception is 3 Σ+ (II), in which a large oscillator strength is obtained by SA-TDDFT while the wave function calculation gives a zero oscillator strength. As seen in Table 3, the 3 Σ+ (II) state has a leading configuration of 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (65.6%) and is a doubly excited state, which has exceeded the ability of SA-TDDFT. As a result, SA-TDDFT produces the incorrect 3 Σ+ (II) state.

3.3

The valence orbitals, bonding, and low-lying states of OsSi

To better understand the chemical bond of OsSi, we present the energy levels and isosurface plots of the valance orbitals in Figure 1, as well as the occupation patterns of the ground state. The orbital energies are obtained by diagonalizing the generalized Fock matrix of the X 3 Σ− state from the SA-CASSCF calculation. The 16σ orbital that is mainly composed of Si(3s), is low in energy and therefore is doubly occupied in the low-lying states of OsSi. Two bonding orbitals 17σ and 9π, which are fully filled in the ground state, are formed by linear combination of Os(5dσ )+Si(3pσ ) and Os(5dπ )+Si(3pπ ), respectively. The anti-bonding 8


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Table 3: Leading Configurations of the Λ − S States of OsSi State X 3 Σ− 3 ∆(I) 1 Σ+ (I) 1Γ 1 ∆(I) 5 Π(I) 3Φ 3 Π(I) 3 ∆(II) 3 Π(II) 1 Π(I) 5 ∆(I) 5 Σ− 1 ∆(II) 1 Σ+ (II) 5 ∆(II) 1 Φ(I) 5 Π(II) 3 Π(III) 5Γ 3 Σ+ (I) 1 Φ(II) 1 Π(II) 5Φ 3 ∆(III) 3 Σ+ (II) 3 Π(IV) 7∆ a

Leading configurationsa 17σ 2 18σ 2 9π 4 4δ 2 (79.6%), 17σ 2 18σ 2 9π 2 10π 2 4δ 2 (5.2%), 17σ 2 18σ 2 9π 3 10π 1 4δ 2 (2.8%) 17σ 2 18σ 1 9π 4 4δ 3 (79.9%), 17σ 2 18σ 1 9π 2 10π 2 4δ 3 (3.9%), 17σ 1 18σ 2 9π 4 4δ 3 (3.3%) 17σ 2 18σ 2 9π 4 4δ 2 (58.4%), 17σ 2 9π 4 4δ 4 (26.5%) 17σ 2 18σ 2 9π 4 4δ 2 (86.3%) 17σ 2 18σ 1 9π 4 4δ 3 (59.1%), 17σ 1 18σ 2 9π 4 4δ 3 (23.5%), 17σ 2 18σ 1 9π 2 10π 2 4δ 3 (3.7%) 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (54.2%), 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (28.4%), 17σ 1 18σ 2 9π 3 10π 2 4δ 2 (3.0%), 17σ 1 18σ 1 9π 4 10π 1 4δ 3 (2.0%) 17σ 2 18σ 2 9π 3 4δ 3 (73.0%), 17σ 2 18σ 1 9π 3 4δ 4 (9.0%), 17σ 2 18σ 2 9π 2 10π 1 4δ 3 (3.9%) 17σ 2 18σ 2 9π 3 4δ 3 (72.5%), 17σ 2 18σ 2 9π 2 10π 1 4δ 3 (5.8%), 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (4.6%) 17σ 1 18σ 2 9π 4 4δ 3 (73.6%), 17σ 1 18σ 2 9π 2 10π 2 4δ 3 (4.6%), 17σ 2 18σ 1 9π 4 4δ 3 (2.6%) 17σ 2 18σ 1 9π 4 10π 1 4δ 2 , (67.0%), 17σ 2 18σ 2 9π 3 4δ 3 (5.6%), 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (3.2%) 17σ 2 18σ 2 9π 3 4δ 3 , (78.7%), 17σ 2 18σ 2 9π 2 10π 1 4δ 3 , (2.9%) 17σ 2 18σ 2 9π 3 10π 1 4δ 2 (84.8%), 17σ 2 18σ 2 9π 1 10π 3 4δ 2 (2.6%) 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (79.2%), 17σ 2 18σ 1 9π 1 10π 3 4δ 3 (3.4%) 17σ 2 18σ 1 9π 4 4δ 3 (59.7%), 17σ 1 18σ 2 9π 4 4δ 3 (20.0%), 17σ 2 18σ 1 9π 2 10π 2 4δ 3 (4.9%) 17σ 2 9π 4 4δ 4 , (51.5%), 17σ 2 18σ 2 9π 4 4δ 2 (19.5%), 17σ 1 18σ 1 9π 4 4δ 4 (4.9%) 17σ 2 18σ 2 9π 3 10π 1 4δ 2 , (68.8%), 17σ 2 18σ 1 9π 3 10π 1 4δ 3 , (19.4%) 17σ 2 18σ 2 9π 3 4δ 3 (57.2%), 17σ 2 18σ 1 9π 3 4δ 4 (14.0%), 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (6.0%), 17σ 2 18σ 2 9π 4 10π 1 4δ 1 (4.2%) 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (31.7%), 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (25.0%), 17σ 1 18σ 1 9π 4 10π 1 4δ 3 (24.3%) 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (62.8%), 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (9.1%), 17σ 2 9π 4 10π 1 4δ 3 (6.1%) 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (89.3%) 17σ 2 18σ 2 9π 3 10π 1 4δ 2 (42.9%), 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (23.8%), 17σ 2 9π 3 10π 1 4δ 4 (21%) 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (21.1%), 17σ 2 18σ 2 9π 4 10π 1 4δ 1 (18.3%), 17σ 2 9π 4 10π 1 4δ 3 (16.0%) 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (13.6%) 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (20.2%), 17σ 2 18σ 2 9π 4 10π 1 4δ 1 (11.4%), 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (10.3%), 17σ 1 18σ 1 9π 4 10π 1 4δ 3 (5.5%) 17σ 1 18σ 1 9π 4 10π 1 4δ 3 (62.7%), 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (18.1%) 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (84.2%) 17σ 2 18σ 1 9π 3 10π 1 4δ 3 (65.6%), 17σ 2 18σ 2 9π 3 10π 1 4δ 2 (9.6%), 17σ 2 9π 3 10π 1 4δ 4 (2.7%) 17σ 1 18σ 2 9π 4 10π 1 4δ 2 (52.9%), 17σ 2 18σ 1 9π 4 10π 1 4δ 2 (18.3%), 17σ 2 18σ 2 9π 4 10π 1 4δ 1 (4.2%) 17σ 1 18σ 1 9π 4 10π 2 4δ 2 (91.2%)

A common occupation is (1 − 16)σ 2 (1 − 8)π 4 (1 − 3)δ 4 1φ4 .

9



combination of Os(5dπ )-Si(3pπ ) and Os(5dσ )-Si(3pσ ) forms the higher 10π and 19σ orbital in energy, being empty in the ground state. The 18σ and 4δ orbitals are non-bonding, in which 18σ is mainly composed of Os(6s) with a small amount of Os(5dσ ) while 4δ is made up of Os(5dδ ). In the ground state of OsSi, the 18σ orbital is doubly occupied while the degenerate 4δ orbital is only half filled by two spin-parallel electrons, giving rise to a triplet state with the Σ− spatial symmetry. The bonding character of OsSi is covalent type, as demonstrated by the gross Mulliken population of Os0.0183 Si−0.0183 . Moreover, a natural bond order (NBO) analysis gives the bond order of the ground state as 2.95, indicating a triple bond. The OsSi molecule is a typical multiconfigurational system, as demonstrated by the main configurations of the electronic states listed in Table 3. The X 3 Σ− state is made up of the 17σ 2 18σ 2 9π 4 4δ 2 (79.6%), 17σ 2 18σ 2 9π 2 10π 2 4δ 2 (5.2%) and 17σ 2 18σ 2 9π 3 10π 1 4δ 2 (2.8%) configurations. The first excited state 3 ∆(I) state lying at 2015 cm−1 is composed of 17σ 2 18σ 1 9π 4 4δ 3 (79.9%), 17σ 2 18σ 1 9π 2 10π 2 4δ 3 (3.9%) and 17σ 1 18σ 2 9π 4 4δ 3 (3.3%). The second excited state 1 Σ+ (I) is 5277 cm−1 higher than the ground state, which consists of two highly mixed configurations of 17σ 2 18σ 2 9π 4 4δ 2 (58.4%) and 17σ 2 9π 4 4δ 4 (26.5%). The 3 ∆(I) state can be obtained by one-electron transition from 18σ to 4δ while the 1 Σ+ (I) state is a mixture of the spin-flip excitation within the 4δ orbital and the double excitation from 18σ to 4δ. The small energy gaps of the first three states suggest that the 18σ and 4δ orbitals are close in energy, as demonstrated in Figure 1. It is interesting to compare OsSi with its isovalent molecules RuC, RuSi and OsC. The RuC molecule has a 1 Σ+ ground state in which the 2δ orbital (mainly Ru 4dδ ) is fully occupied. 56,57 The ground state of RuSi is assigned as 3 ∆ with an open shell 14σ 1 2δ 3 configuration. 58 The ground state of OsC is still controversial: the theoretical calculation predicted a 3

Σ− (16σ 2 4δ 2 ) ground state with the 3 ∆ (16σ 1 4δ 3 ) term being 2200 cm−1 higher, 59 while the

experimental study identified a 3 ∆ ground state. 60 It is found that the occupation patterns of the atom-like δ and σ orbitals determine the ground states of these isovalent molecules. Two connected factors are the relativistic effect and the ligand field strength. From the 4d to

10


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5d metals, the contraction of the (n + 1)s orbital due to strong relativistic effects decreases the energy of the valance (n + 1)s shell, which screens the nd shell and therefore shifts it into a higher energy level. As a result, the energy orders of the δ and σ orbitals interchange from RuX to OsX (X=C,Si) and the non-bonding σ is occupied first in the OsX molecules. Moreover, the electronegativity of the C atom is larger than that of Si, which makes the later capture relatively fewer electric charge as compared to C. The reduction of electron distribution on the metal atom tends to decrease the electronic repulsion on the dδ atom-like orbital, leading to that more electrons are more likely to fill in the δ orbitals of OsC and RuC. Therefore, the OsC molecule may have a 3 ∆ ground state. To check our assumption, SA-CASSCF, MS-NEVPT2 and MS-CASPT2 with the ANORCC-VTZP basis set are performed to calculate OsC. The 3 ∆, 3 Σ− , 1 Σ+ and 1 ∆ states are found as the four lowest states of OsC in all calculations and the spectroscopic parameters are presented in Table 4. Both SA-CASSCF and MS-NEVPT2 give a 3 ∆ ground state, with the 3 Σ− state located about 3600 cm−1 above. However, the energy order of 3 ∆ and 3 Σ− interchanges in MS-CASPT2, in which the 3 Σ− state is 1022 cm−1 lower than the 3 ∆ state. The previous CASSCF calculation by Meloni et. al. indicates that the 3 Σ− state is 1646 cm−1 lower than the 3 ∆ state at the bond length of 1.72 Å. 59 The disagreement between ours and Meloni and coworker’s results may attribute to different basis sets used in two studies: effective core potential is used in the latter work 59 while we use a full-electron basis set. In addition to the correlation effects, SOC should play a significant role in the ground state of OsC and we shall discuss it later.

3.4

Assignment of the experimentally observed spectra

To clearly demonstrate the transitions that may contribute to the experimental spectra, we present the dominant configurations and energy levels of the ground state and its singly excited states in Figure 2. As we have mentioned beforehand, Johnson and Morse had recorded two bands headed 11



Table 4: The Low-lying Λ − S States of OsC Calculated by SA-CASCF, MSNEVPT2 and MS-CASPT2 State

Re (Å)

Te (cm−1 )

3∆

1.685 1.717 1.664 1.706

0 3630 8476 9478

1.631 1.667 1.627 1.624

0 3639 4883 7762

1.668 1.638 1.654 1.620

0 1022 4281 6518

3 Σ− 1∆ 1 Σ− 3∆ 3 Σ− 1 Σ− 1∆ 3 Σ− 3∆ 1 Σ− 1∆

ωe (cm−1 ) Leading configurations SA-CASSCF 1046 15σ 2 16σ 1 8π 4 4δ 3 (86.7%) 1011 15σ 2 16σ 2 8π 4 4δ 2 (84.7%) 1110 15σ 2 16σ 1 8π 4 4δ 3 (84.5%) 1000 15σ 2 16σ 2 8π 4 4δ 2 (44.5%), 15σ 2 8π 4 4δ 4 (32.5%) MS-NEVPT2 1169 15σ 2 16σ 1 8π 4 4δ 3 (85.2%) 1117 15σ 2 16σ 2 8π 4 4δ 2 (86.1%) 1146 15σ 2 16σ 2 8π 4 4δ 2 (43.9%), 15σ 2 8π 4 4δ 4 (37.2%) 1228 15σ 2 16σ 1 8π 4 4δ 3 (86.0%) MS-CASPT2 1142 15σ 2 16σ 1 8π 4 4δ 3 (87.9%) 1152 15σ 2 16σ 2 8π 4 4δ 2 (86.1%) 1151 15σ 2 16σ 2 8π 4 4δ 2 (44.0%), 15σ 2 8π 4 4δ 4 (37.2%) 1215 15σ 2 16σ 1 8π 4 4δ 3 (85.9%)

Figure 1: Orbital Energies, Isosurface Plots of Valence Orbitals and Occupation Patterns of the Ground X 3 Σ− State of OsSi.

12


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25000 (II) (I)

(G)

(II)

(III)

20000

(II) (II)

(F)

(I) (II)

-1

)

(I)

E (cm

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


15000

(I)

(E)

(II)

(D)

(II)

(I)

(C) (I)

10000

(I)

(B) (A)

5000

(I)

(I)

0

X

Figure 2: Leading Configurations, Energy Levels of the Ground State and Its Singly Excited States of OsSi.

near 15000 cm−1 and 18000 cm−1 , respectively. 17 By comparing with the spectra of WO, 23 the two excited states are assigned as A3 Π1 and B 1 Π1 with the same leading configuration of 17σ 2 18σ 2 9π 4 10π 1 4δ 1 , arising from one-electron transition from the non-bonding 4δ orbital to the anti-bonding 10π orbital. However, there is no state with the 4δ → 10π transition below 26000 cm−1 as shown in Figure 2. Instead, three excited states, namely 3 Π(I), 3 Π(II) and 1 Π(I), are situated at 13546 cm−1 , 16009 cm−1 and 16018 cm−1 above the X 3 Σ− state, respectively. The 3 Π(I) and 1 Π(I) states can be generated by a 9π → 4δ excitation from the ground state, giving rise to a 17σ 2 18σ 2 9π 3 4δ 3 configuration. The 3 Π(II) state has a leading 17σ 2 18σ 1 9π 4 10π 1 4δ 2 configuration, which is produced by a 18σ → 10π transition from the ground state. These three states may be involved in the experimentally observed spectra. Besides the excited states below 20000 cm−1 , the 3 Π(III) → X 3 Σ− and 1 Π(II) → X 3 Σ− transitions may also give rise to the observable spectra. If the molecule beam was not cooled down well enough, electronic transitions from the higher lying vibrational levels to the excited 3

∆(I) state were also possible. The dipole allowed transitions include 3 Π(I)/3 Π(II) →3 ∆(I)

and 3 ∆(II) →3 ∆(I), which could produce emission bands below 20000 cm−1 . In particular, transitions to the 3 ∆(I) state will produce the band systems with different rotational-

13



vibrational branches as to the X 3 Σ− state. Resolving such spectra is helpful to interpret the experimental results of OsC in which several band systems related to 3 ∆ have been recorded.

3.5

Results with Spin-orbit coupling

Since the Os atom has a large nuclear number, the zero-field splitting should play a significant role in interpreting the spectra of OsSi. Therefore, state interaction (SI) calculations are performed to take the SOC effects into account. In Table 5, we summarized the spectroscopic parameters of the Ω states below 22000 cm−1 , whereas the ones above 22000 cm−1 are eliminated from the table because only the Λ − S states lower than 30000 cm−1 are included in the SOC calculations, is insufficient to describe the higher-lying Ω states. Moreover, the low-lying Ω states of OsC are listed in Table 6 to compare with OsSi. As shown in Table 5, X 3 Σ− 0+ is identified as the ground state of OsSi. The first two excited −1 3 − Ω states, namely 3 ∆3 (I) and 3 Σ− 1 , lie at 1942 and 3003 cm , respectively. Because the X Σ0+

and 3 ∆3 (I) states are well separated, the assignment of the ground state is unambiguous for OsSi that is different from OsC. 59,60 Moreover, the equilibrium bond length 2.103 Å of the ground state is slightly shorter than the one of 2.114 Å without SOC. Similar to ReN, 21,22 the X 3 Σ− state couples strongly with 1 Σ+ (I), as indicated by the dominant Λ − S states in Table 5. Due to the relatively shorter equilibrium bond length of the 1 Σ+ (I) than that of the X 3 Σ− state, mixing with 1 Σ+ 0+ shorten the bond length and also flatten the PEC of −1 that is smaller the X 3 Σ− 0+ state. Therefore, its vibrational frequency is reduced to 466 cm

than the experimental value. When the SOC effects are considered as the perturbation with the MS-NEVPT2 results as the zero order energies (MS-NEVPT2+SOC), 3 ∆3 is assigned as the ground state −1 higher. However, MS-CASPT2+SOC gives of OsC, with the 3 Σ− 0+ state being 3234 cm 3 −1 a 3 Σ− above. Although MS-NEVPT2+SOC 0+ ground state, and ∆3 locates only 499 cm

assigns the correct ground state 3 ∆3 , it produces a short equilibrium bond length of 1.631 Å. Moreover, MS-CASPT2+SOC gives Re = 1.639 Å for the 3 ∆3 state, which is also sig14


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Table 5: Spectrascropic Parameters of the Ω State of OsSi Ω state

Re (Å)

a X 3 Σ− 0+ 3 ∆ (I) 3 3 Σ− 1 3 ∆ (I) 2 3 ∆ (I) 1 1Γ 4 1 Σ+ 0+ 3 ∆ (II) 3 1 ∆ (I) 2 3Φ 4 5 Π (I) 1 5Π 0− 5Π 0+ 5 Π (II) 1 5Π 2 3 Π (I) 1 1 ∆ (II) 2 5Π 3 3Φ 3 3 ∆ (II) 2 5∆ 4 3 Π (I) 0− 3 Π (II) 1 3 Π (I) 0+ 5∆ 3 3Φ 2 3Π 2 5 Σ− 0− 5 Σ− 1 3 ∆ (II) 1 5∆ 2 3 Π (II) 0− 3 Π (II) 0+

2.103a 2.085 2.116 2.084 2.088 2.114 2.090 2.085 2.078 2.131 2.141 2.136 2.135 2.131 2.138 2.151b 2.109 2.143 2.122 2.108 2.210 2.153 2.144 2.161c 2.193 2.136 2.131 2.223 2.221 2.103 2.191 2.192 2.135

Te (cm−1 ) 0 1942 3003 4273 8145 9191 11009 13405 13435 13888 14203 14277 14282 14668 14687 15568b 15738 16037 16968 17491 17055 18222 18316 18460c 18802 19408 19968 20034 20285 20312 20346 20912 21443

ωe (cm−1 ) 466a 537 497 534 538 441 428 497 445 484 460 465 470 473 441 500b 528 449 545 496 493 463 427 475c 516 478 521 443 436 533 372 438 478

Ftot

Contribution of Λ-S states

0 0 0.000017 0 0.000175 0 0.000199 0 0 0 0.001169 0 0.000449 0.000039 0 0.000406 0 0 0 0 0 0 0.009746 0.000063 0 0 0 0 0.000865 0.005615 0 0 0.000869

3 Σ− (73%),1 Σ+ (I)(24%) 3 ∆(I)(96%) 3 Σ− (94%),3 Π(II)(2%),1 Π(I)(2%) 3 ∆(I)(89%),1 ∆(I)(5%) 3 ∆(I)(92%),3 Π(I)(4%),1 Π(I)(2%) 1 Γ(56%),3 Φ(42%) 1 Σ+ (I)(67%),3 Σ− (18%),3 Π(I)(6%),3 Π(II)(4%) 3 ∆(II)(67%),3 Φ(19%),5 Π(II)(7%) 1 ∆(I)(43%),3 ∆(24%)(II),3 Π(I)(23%) 3 Φ(51%),1 Γ(43%) 5 Π(I)(77%),3 Π(II)(7%),1 Π(I)(2%) 5 Π(I)(87%),3 Π(II)(4%) 5 Π(I)(83%),5 Σ+ (4%),3 Π(I)(2%),1 Σ+ (I)(1%) 5 Π(I)(95%),5 Σ+ (2%),3 Σ− (1%) 5 Π(I)(78%),3 Π(II)(5%),5 ∆(I)(3%),5 ∆(II)(3%) 3 Π(I)(52%),1 Π(I)(30%),3 Π(II)(8%) 1 ∆(I)(39%),3 Π(I)(23%),3 Π(II)(17%) 5 Π(I)(74%),3 Φ(9%),3 ∆(III)(3%) 3 Φ(54%),3 ∆(II)(29%),5 Π(I)(6%) 3 ∆(II)(38%),3 Π(I)(24%),3 Π(II)(14%) 5 ∆(I)(94%) 3 Π(I)(86%),3 Π(II)(6%),3 Σ+ (I)(4%) 3 Π(I)(28%),3 Π(II)(21%),1 Π(I)(18%),3 ∆(II)(12%) 3 Π(I)(76%),3 Π(II)(12%),5 Σ+ (I)(6%) 5 ∆(I)(69%),5 Π(I)(12%),5 Π(I)(8%) 3 Φ(44%),3 Π(II)(12%),1 ∆(I)(12%),1 ∆(II)(10%) 3 Π(II)(37%),3 Φ(26%)(I),3 ∆(II)(11%) 5 Σ− (I)(56%),3 Σ+ (I)(19%),3 Π(II)(8%),5 Π(II)(6%) 5 Σ− (I)(59%),3 Σ+ (I)(16%),5 Π(II)(6%),3 Π(III)(5%) 3 ∆(II)(50%),3 Π(II)(27%),5 Π(II)(6%) 5 ∆(I)(65%),5 Π(II)(15%),3 Π(II)(5%) 3 Π(II)(72%),5 Σ− (I)(9%),3 Π(I)(5%),5 ∆(I)(4%) 3 Π(II)(58%),1 Σ+ (II)(21%),3 Π(I)(7%)

The experimental values of the X 3 Σ− state are Re = 2.1207 Å and ω = 512 cm−1 . 17 0+ b The experimental transition energy is 15729 cm−1 with R = 2.236 Å and ω = 397 cm−1 . 17 e c The experimental transition energy is 18469 cm−1 with R = 2.198 Å and ω = 324 cm−1 . 17 e a

15



nificantly shorter than the experimental result of 1.67267(5) Å. 60 Interestingly, Re of 3 Σ− 0+ calculated by MS-NEVPT2+SOC and MS-CASPT2+SOC are 1.670 and 1.673 Å, being close to the experimental Re , but the possibility of 3 Σ− 0+ as the ground state of OsC has been excluded in the experimental study. 60 Despite the correct ground state being obtained by MS-NEVPT2+SOC, the failure of MS-CASPT2+SOC seems unusual. The intruder state problem could be excluded because different energy level shifts have been tested. In principle, the zero-order Hamiltonian of MS-NEVPT2 is better than the one in MS-CASPT2 that may lead to the different results. However, it is still inadequate to assess MS-NEVPT2+SOC 60 because the energy gap between 3 ∆3 and 3 Σ− 0+ was not reported in the previous study.

Therefore, more experimental works are desired. For the theoretical studies, the controversial results in different calculations and inconsistency with the experimental conclusion indicate OsC is more challenging than OsSi, thus higher level calculation such as the fourcomponent multi-reference configuration interaction is desired to clarify the ground state of OsC as for the IrO molecule. 61 Table 6: Spectrascropic Parameters of the Ω State of OsC Ω state

Re (Å)

3∆

2 3 Σ− 0+ 3∆ 1 3 Σ− 1 1 Σ+ 0+

1.631 1.631 1.670 1.622 1.667 1.633

3 Σ− 0+ 3∆ 3 3∆ 2 3 Σ− 1 3∆ 1 1 Σ+ 0+

1.673 1.639 1.635 1.669 1.648 1.623

3

3∆

Te (cm−1 ) ωe (cm−1 ) Contribution of Λ-S states MS-NEVPT2 with SOC 3 ∆(100%) 0 1170 3 2097 1171 ∆(90%),1 ∆(10%) 3 Σ− (59%),1 Σ+ (41%) 3234 1068 3 ∆(99%),3 Σ− (1%) 6355 1115 3 Σ− (91%),3 ∆(9%) 6719 1117 1 Σ+ (55%),3 Σ− (45%) 11534 1139 MS-CASPT2 with SOC 3 Σ− (73%),1 Σ+ (27%) 0 1163 3 ∆(100%) 499 1150 3 2359 1162 ∆(84%),1 ∆(16%) 3 Σ− (100%) 2487 1140 3 ∆(100%) 6570 1145 1 + 9380 1139 Σ (73%),3 Σ− (27%)

According to our data, two experimental transitions, namely A ← X 3 Σ− 0+ and B ← 17 X 3 Σ− The A − X system should attribute to the 3 Π1 (I) ← X 3 Σ− 0+ , can be assigned. 0+

transition, in which the adiabatic excitation energy 15568 cm−1 agrees well with the exper16


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imental value of 15729 cm−1 . The equilibrium bond length of 2.151 Å of the 3 Π1 (I) state is 0.08 Å shorter than the experimental value of 2.236 Å while the vibrational frequency is overestimated significantly. As shown in Table 5, 3 Π1 (I) is a mixture of the 3 Π(I) and 1

Π(I) states. Both MS-NEVPT2 and MS-CASPT2 predict that the bond lengths of 3 Π(I)

and 1 Π(I) are shorter than 2.160 Å. Notice that the 3 Π(I) and 1 Π(I) states have a common 4δ 3 9π 3 configuration. The equilibrium bond length of the 3 Π1 (I) state should be close to the one of the ground state owning that filling more electrons on the 4δ orbital tends to contract the Os-Si bond. However, if 3 Π1 (I) is perturbed by a nearby state, it will be difficult to determine the spectroscopic parameters and the experimental study may give a too long equilibrium bond length. −1 In the experiment, the B ← X 3 Σ− is much weaker than the 0+ transition at 18469 cm −1 A ← X 3 Σ− 0+ one. At about 18000 cm , two states with the nonzero oscillator strength can be

identified from our data. The 3 Π1 (II) state is composed of the 3 Π(I)(28%), 3 Π(II)(21%),1 Π(I)(18%) and 3 ∆(II)(12%) components with a relatively large oscillator strength (Ftot ) of 0.009746. This value is even larger than that of the 3 Π1 (I) state. Notice that both of the wave function and SA-TDDFT calculations give a larger oscillator strength for the SOC-free 3 Π(II) state than 3 Π(I). A large percentage of 3 Π(II) in 3 Π1 (II) should yield stronger transition of 3

3 3 − 3 + Π1 (II) ← X 3 Σ− 0+ than Π1 (I) ← X Σ0+ . Moreover, the Π0 (I) state has a small oscillator

strength of 0.000063, indicating that the transition of 3 Π0+ (I) ← X 3 Σ0+ is weak. In the experimental study from Johnson and Morse, 17 the upper state is determined to have the same angular moment as the A state. Therefore, the B state is assigned tentatively as 3 Π1 (II). −1 The energy gap of 3 Π1 (II) and X 3 Σ− 0+ is 18316 cm , which is in excellent agreement with

the experimental value of 18469 cm−1 . Unfortunately, the theoretical vibrational frequency 427 cm−1 is much larger than the experimental one. Besides the vibrational frequency, the oscillator strength of 3 Π1 (I) ← X 3 Σ0+ is too large that should lead to stronger transition 3 3 + than the A ← X 3 Σ− 0+ system. However, the Π1 (II) and Π0 (I) states are close in en-

ergy and could coupled via rotational perturbation. 62 Therefore, the real strength of the

17



3

Π1 (I) ← X 3 Σ0+ transition may be weaker than the theoretical result. As seen in Table 5, several other states also have nonzero oscillator strengths. For in-

stance, the 5 Π and 5 Σ− states can mix with some nearby triplet Λ − S states, yielding considerable oscillator strengths between the ground and excited Ω states. In addition, Johnson and Morse detected also some unresolved bands in the range of 15384 to 18406 cm−1 . 17 Our calculation may give some insights to reexamine the unresolved spectra in this region.

3.6

Dissociation Energy of OsSi

Finally, we shall discuss the dissociation energy of OsSi. It can be seen in Table 5 that the X 3 Σ− state dissociates into the asymptote of Os5 D(5d5 6s2 ) + Si3 P (3s2 3p2 ) with the dissociation energy of 5.93 eV. Inclusion of the SOC effect pushes down the dissociation energy to 5.76 eV. There is no experimental dissociation energy of OsSi while the bond dissociation enthalpy of OsC at 298K is estimated to be 6.28±0.15 eV. 59 Since the OsSi bond is weaker than OsC, the calculated dissociation energy of OsSi seems reasonable. Moreover, the experimental dissociation energies of FeSi and RuSi are 3.04 eV, 4.08 eV, respectively, indicating the enhancement of metal-silicon bonding of the group VIII elements as going down the periodic table.

4

Conclusions The electronic states and spectroscopic parameters of OsSi are calculated by MS-NEVPT2

and MS-CASPT2 with the ANO-RCC-VTZP basis set. The spectroscopic parameters of the Λ−S states of OsSi indicate that MS-NEVPT2 yields similar results as MS-CASPT2. Based on the MS-NEVPT2 energies, the SOC effects are added as perturbations that allows us to reveal the electronic structure of OsSi and interpret the available experimental spectra. Besides OsSi, four low-lying states of OsC have also been calculated with the same method to

18


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assign the ground state. The ground state of OsSi is identified as X 3 Σ− 0+ , with the first excited state 3 ∆1 (I) at 1942 cm−1 above, which is in agreement with the experimental assignment. On the other hand, controversial results are obtained for OsC, in which MS-NEVPT2+SOC gives the same 3 ∆3 ground state as the experimental one while MS-CASPT2+SOC prefers a 3

Σ− 0+ ground state as in OsSi. To figure out the electron structure of OsC, more experimental

and theoretical works are required. For the excited states of OsSi, the leading configurations indicate that OsSi has the completely different transitions below 20000 cm−1 from the case of WO, thus the experimental spectra of OsSi should be reassigned. After including the SOC effects, the 3 Π1 (I) state located at 15568 above the ground state can be assigned to the experimental spectra at 15729 while the band headed at 18469 cm−1 may arise from the 3 Π1 (II) ← X 3 Σ− 0+ transition. Moreover, the 3 Π0+ (I) state that is nearly degenerate with 3 Π1 (II) , has a very small os3 3 + cillator strength respect to X 3 Σ− 0+ . The Π1 (II) and Π0 (I) states may perturb strongly

that could reduce the transition strength of 3 Π1 (II) ← X 3 Σ− 0+ and also pose a big challenge to resolve the experimental spectra. In addition, plenty of the Ω states with considerable oscillator strengths are discovered in this study, which may serve as the reference data for the future experiments.

Supporting Information Available The following files are available free of charge. The spectroscopic parameters of Λ − Ω states of OsSi calculated with the DKH3 and X2C Hamiltonian are presented in Table S1. The VEEs and oscillator strengths of the triplet states of OsSi by SA-TDDFT, MS-NEVPT2 and MS-CASPT2 are compared and presented in Table S2. The number of roots in each spin-spatial symmetry in MS-NEVPT2 is listed in Table S3. The PECs of the Λ − S states of OsSi are drawn in Figures S1-S3.

19



Acknowledgement The research was supported by grants from the National Natural Science Foundation of China (Project Nos. 21673174 and 21673175) and from the Double First-class University Construction Project of Northwest University.

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Figure 3: For Table of Contents Only

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The Electronic Structure of OsSi Calculated by MS-NEVPT2 with

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