RelativityâInduced Bonding Pattern Change in Coinage Metal Dimers

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

pubs.acs.org/IC

Relativity−Induced Bonding Pattern Change in Coinage Metal Dimers M2 (M = Cu, Ag, Au, Rg) Wan-Lu Li, Jun-Bo Lu, Zhen-Ling Wang, Han-Shi Hu,* and Jun Li* Department of Chemistry and Laboratory of Organic Optoelectronics & Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: The periodic table provides a fundamental protocol for qualitatively classifying and predicting chemical properties based on periodicity. While the periodic law of chemical elements had already been rationalized within the framework of the nonrelativistic description of chemistry with quantum mechanics, this law was later known to be affected significantly by relativity. We here report a systematic theoretical study on the chemical bonding pattern change in the coinage metal dimers (Cu2, Ag2, Au2, Rg2) due to the relativistic effect on the superheavy elements. Unlike the lighter congeners basically demonstrating ns−ns bonding character and a 0g+ ground state, Rg2 shows unique 6d−6d bonding induced by strong relativity. Because of relativistic spin−orbit (SO) coupling effect in Rg2, two nearly degenerate SO states, 0g+ and 2u, exist as candidate of the ground state. This relativity-induced change of bonding mechanism gives rise to various unique alteration of chemical properties compared with the lighter dimers, including higher intrinsic bond energy, force constant, and nuclear shielding. Our work thus provides a rather simple but clear-cut example, where the chemical bonding picture is significantly changed by relativistic effect, demonstrating the modified periodic law in heavy-element chemistry.

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atomic numbers,25−29 gold and mercury being prominent examples of such.10,30−32 Superheavy elements have especially significant relativistic effects. These elements can be studied by means of the gas-phase chromatography technique33 due to their strong volatilities, whereby they are deposited on the detector surfaces. Pershina and co-workers have performed a series of theoretical calculations to predict the adsorption behavior of many superheavy elements, so as to compare the character of the heavier element with that of lighter homologue in a chemical group.34−38 It is thus interesting to understand how and how much the relativistic effects can affect the conventional chemical bonding pattern and the periodic law.31 Recently, we studied the bond multiplicity change caused by relativistic effect in the group 6 diatomic molecules M2 (M = Cr, Mo, W, Sg) and provided an interesting example that relativity breaks the periodic trend when the element becomes heavier.39 Similar to the group 6 elements with [(n − 1)d5ns1] nonrelativistic configuration, the group 11 elements Cu, Ag, Au, and Roentgenium (Rg) possess [(n − 1)d10ns1] nonrelativistic configurations. Superheavy elements like Rg are synthetic elements not found in nature due to the short half-life period,25,40,41 and their chemical properties are challenging to predict due to enormous relativistic effects. More developed theoretical methods of relativistic quantum chemistry are required for accurate calculations.42 The basic chemical

INTRODUCTION The first recognized periodic table (PT) was developed in 19th century, which has been widely used in illustrating the periodic law or recurring trends in properties of the lighter elements since then.1 The PT has been continuously explored for elements with larger atomic number (Z), with current experimental PT covering element Og (Z = 118) and theoretical ones going much further (e.g., up to Z ≤ 172 by Pyykkö).2−5 Elements falling into the same group (column) generally present similar chemical properties, and to a certain degree d- or f-block elements sometimes tend to have comparable properties as well among some elements in the same period (row). The periodic law of lighter elements is due to nonrelativistic quantum mechanics, as explained by Bohr in 1920s.6−8 For relativistic effect in chemistry, Dirac stated that it would be of little use in the consideration of molecular structures or ordinary chemical reactions in 1929,9 and chemists by and large agreed with his assertion until the 1970s.10,11 Nevertheless, the relativistic effects turn out to be noticeable in all the elements and are significant for the ground states of molecules roughly beginning from the elements in the sixth row (Cs−Rn), especially for lanthanides, actinides, and the superheavy elements of the period table.12−19 For example, the so-called 6s2 inert pair effect refers to a tendency for this pair of 6s2 electrons to resist oxidation due to the stabilization resulting from the dominating direct relativistic ef fects.20−24 Related to relativistic effects, many unexpected and novel properties are brought into the chemistry of the heavier elements with high © XXXX American Chemical Society

Received: February 20, 2018

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DOI: 10.1021/acs.inorgchem.8b00438 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Relativistic effects on the atomic valence-shell orbital energy levels and radial distributions (D(r) = r2R(r)2) of the electron density. (left) The NR, SR, and SO energy levels of Cu, Ag, Au, and Rg all in comparable (n − 1)d10ns1) configuration by using the ZORA-PBE/TZ2P method (more computational details are in Supporting Information); (right) the radial distribution of 7s and 6d orbitals of Rg.

Figure 2. MO energy levels of Cu2, Ag2, Au2, and Rg2 at SR-ZORA PBE/TZ2P level with the HOMOs shown with two dots and all corresponding energy levels connected by short dash lines. The 3D MO contours (isovalue = 0.04 au) are shown in the right panel, and the MO compositions are listed in Table S1. The σ-MOs are singly degenerate, while the π- and δ-MOs are doubly degenerate.

rows of transition metals.49 In fact, the order of AO energies, (n − 1)d < ns, holds for neutral and positively charged elements of all groups 3−18 in all periods 1 to 6, while the somewhat unusual order ns < (n − 1)d often taught in introductory textbooks only holds in groups 1 and 2 and for the d elements of period 7. For Cu, Ag, Au, and Rg, as dominating direct/ indirect relativistic ef fects50 raise the energies of (n − 1)d orbitals and lower ns orbitals, the s−d gap becomes smaller for Au with respect to Ag and Cu. This order is even further reversed in superheavy element Rg. Such phenomenon has been noted in recent papers on the heavy d-elements, such as the particular stability of Hs8+O4 and Hs8+S4.51−53 Illustrated in Figure 1 are the nonrelativistic (NR), scalar-relativistic (SR), and spin−orbit (SO) energy levels of Cu, Ag, Au, and Rg and the electron density radial distribution of the 7s and 6d orbitals of Rg. Clearly, the energy level of the Rg 7s valence-shell orbital is relativistically stabilized so strongly that it stays energetically lower than the destabilized Rg 6d orbitals and becomes significantly contracted radially. Thus, energetically destabilized and radially expanded Rg 6d5/2 orbitals are relativistically put in

properties of Rg with predicted relativistic 6d97s2 electron configuration39,43 are deemed to differ from those of its lighter congeners, gold, silver, and copper to a certain extent, despite lacking of simple examples to directly show the differences.44,45 The chemical properties of Rg have attracted more interest than that of the two former elements Mt and Ds because of the strong relativistic contraction of the Rg 7s subshell.46−48 To explore how the relativistic effect might alter the chemical bonding picture, we here studied the coinage dimer systems Cu2, Ag2, Au2, and Rg2 for comparison and found that the chemical bonding of Rg2 is drastically different from that of its lighter congeners. The bonding pattern change of this series of simple metal dimer thus provides a textbook example of relativistic effects in periodicity.

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RESULTS AND DISCUSSION 1. Different Molecular Orbital Pictures Arising from Distinctive Valence-Shell Energy Levels. According to the common atomic orbital (AO) shell effect, orbital energies of ns orbitals lie above the (n − 1)d ones in third-, fourth-, and fifth B


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Inorganic Chemistry

respectively, and the other MOs are in pairs to show bonding and antibonding cancelation without significantly contributing to the chemical bonding for the whole system. But when it comes to Au2, 6s participation in the σ bonding (HOMO−2 for Au2) is reduced to 80% because of the direct and indirect relativistic effects that cause significant s-d hybridization in gold. When moving down to Rg2, both 2σg (HOMO−4) and 1σu (HOMO−3) MOs dominated by 7s character are occupied, so that the net bonding for Rg−Rg single bond changes to involving HOMO−6. This orbital has bonding interaction between sdz2−sdz2 hybridized orbitals (with 52% 6d and 46% 7s character), with the LUMO acting as its corresponding antibonding orbital. In comparison, the NR and SR MO profiles of Rg2 are plotted in Figure S1. The MO contours of Rg2 based on the NR method are basically similar to these of the Au2 dimer. However, all the σ-type orbitals will be greatly stabilized when the SR effect is taken into account, because the direct relativistic ef fect tremendously lowers the energy of the 7s orbital. As a consequence, the bonding character of Rg−Rg is primarily derived from 6d orbitals rather than 7s orbitals, which is also confirmed in the multiconfigurational CASSCF and DMRG calculations below. It is worth noting that, although SO coupling lowers 7p1/2 energy slightly, 7p participation in bonding seems to be less important in Rg2 dimer. To investigate the possible multiconfigurational features, we performed CASSCF and DMRG calculations. The Löwdin natural orbital occupation number (NOON) of each orbital was determined. With the CASSCF (22e, 12o) calculations, NOONs of the s-σ bonding/antibonding paired orbitals of Cu2, Ag2, and Au2 are 1.94/0.06, 1.98/0.02, and 1.96/0.04, respectively, indicating little occupation of the antibonding σ*(s−s) orbital. While the low-energy natural orbitals are nearly fully occupied, for the d-dominated σ-type bonds of Rg2 the NOON is 1.90/0.11, implying that the ground state has a two-configuration feature. Thus, we performed DMRG-CI calculations with active space extending to (22e, 28o) to see how the NOONs change according to the inclusion of more virtual shells. The natural orbitals and NOONs of Rg2 are shown in Figure 3, while those for Cu2, Ag2, and Au2 are shown in Figures S2−S4. Compared with the CASSCF (22e, 12o) results, the Ag2 and Au2 dimers are not susceptible to the size of active space, where the outer-shell orbitals are practically unoccupied. However, in the Cu2 dimer, the NOONs obtained from the DMRG-CI (22e, 28o) method in the occupied region change a little compared with those from the calculations with the small active space, likely because the 3d orbitals of Cu are so contracted that the inclusion of 4p and 4d orbitals can recover some of the dynamic correlation. Moreover, because of the small HOMO− LUMO gap for Rg2, the single-reference DFT approach does not seem to be reliable enough when high accuracy is sought. From Figure 3 and Figures S2−S4, the effective bond orders (EBOs) are calculated, as listed in Table 2. Especially noteworthy is the EBO of Rg2 calculated to be 1.01, which includes 0.94 from 6d-σ, 0.03 from 7s-σ, 0.02 from 6d-π, and 0.01 from 6d-δ character. Overall, the chemical bonding of Rg2 is primarily a single bond from d-type orbitals, different from other lighter dimers mainly from s-type orbitals. 2. Geometric and Chemical Bonding Analyses. Geometries optimized from CCSD(T) and PBE methods are compared with the experimental data (Table 3). Results from CCSD(T) calculations are within 0.03 Å deviation compared to experimental data, which are reasonably better than those from

the valence region for chemical bonding, while low-energy 7s orbital becomes less valence-active, although 7s is still outside 6d in the valence region as shown by the radial distribution function.29,46,47 Different chemical bonding characters for the Rg2 dimer are therefore expected for the distinctive s2d9 configuration with open-d-shell (rather than s1d10) and inherent electronic structures caused by relativistic effects. The bonding pictures of these M2 dimers are simple and well-known from the qualitative molecular orbital (MO) model. Figure 2 shows the SR MO energy levels of the dimers, with the highest occupied molecular orbitals (HOMOs) illustrated by two dots. Take Cu2 as an example: the 3d orbitals form σ, π, δ bonding MOs (1σg, 1πu, 1δg) and σ*, π*, δ* antibonding MOs (1δu, 1πg, 1σu), while the 4s orbitals form a bonding 2σg and antibonding 2σu MO pair. The energy-level “bands” exert larger expansion from Cu2 to Rg2 due to the stronger orbital interactions between the two coinage metals.54 In contrast with Cu2, Ag2 and Au2 dimers with 1σg mainly formed between (n − 1)dσ orbitals, the 1σg MO of Rg2 has rather low energy because of remarkable mixing with the inert 7s orbital (see Table S1 of the Supporting Information). The HOMO−LUMO (LUMO = lowest unoccupied molecular orbital) gap for Rg2 dimers is rather small, as the LUMO becomes very low in energy due to Rg 7s stabilization, giving rise to multiconfigurational feature of the ground state (vide infra) and complicatedness in assigning the ground state when taking SO coupling relativistic effect into account. We then performed time-dependent density functional theory (TDDFT) calculations corrected with SO coupling effect to estimate the effective vertical singlet excitations of the Au2 and Rg2 dimers to qualitatively compare different electronic structures in the HOMO region. As shown in Table 1, the Table 1. Vertical Singlet Excitation Energies and Oscillator Strengths ( f) of Au2 and Rg2 at the SO-ZORA TD-SAOP/ TZ2P Level peak positionb ( f)

dimers Au2 Rg2

calcd expt55,56 calcd

2.34 (0.022), 2.89 (0.016), 3.28 (0.079), 3.86 (0.002) 2.58 (s), 3.13 (m), 3.30 (m), 3.96 (w)a 2.11 (0.002), 2.56 (0.019), 3.60 (0.004), 4.46 (0.002), 4.65 (0.002), 4.70 (0.050), 5.07 (0.010), 5.20 (0.004), 5.29 (0.001), 5.49 (0.008), 5.53 (0.005), 5.58 (0.002), 5.75 (0.034), 6.09 (0.005), 6.20 (0.102), 6.98 (0.008)

a

The relative intensities from experimental values. s = strong, m = medium, w = weak. bThe energies are in electronvolts, and the oscillator strengths are in atomic units.

theoretical excitation energies and oscillator strengths of Au2 using this approach are comparable with the experiment. We also calculated the excitation energies to predict the electronic spectra of Rg2 for comparison and found that more visiblerange excitations exist due to small HOMO−LUMO gap and the strong SO coupling effect. Moreover, the SO energies of the first excited states of Au2 and Rg2 were calculated to be 1.84 and 0.28 eV at the TD-SAOP/TZ2P level, respectively, suggesting much smaller HOMO−LUMO gap for Rg2 than for the lighter congeners, which are consistent with the fore MO discussions. The 12 frontier valence MOs derived from ns and (n − 1)d orbitals are also shown in the right panel of Figure 2. Especially noteworthy is the bonding pattern change from the lighter dimers to Rg2. In Cu2 and Ag2 molecules, there is a single bond with almost pure (more than 96% s-orbital) s−s σg orbital interactions as shown in Cu2 (HOMO−4) and Ag2 (HOMO), C


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Inorganic Chemistry

Figure 3. Löwdin natural valence orbitals (NOs) of Rg2 from DMRG-CI (22e, 28o), with Löwdin NOONs (isovalue = 0.04 au). For the degenerate π and δ NOs, only one set is shown. The first and third rows are the bonding NOs, and the second and fourth are the corresponding antibonding NOs.

with the canonical MOs and DMRG natural orbitals, strong orbital hybridization occurs in the case of the Rg2 molecule, with 6d (68%) dominating chemical bonding albeit nonnegligible 7s (32%). These results also give evidence to the change of bonding pattern for the Rg2 dimer. We further performed energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) analyses for all dimers, and the results are listed in Table 4 to illustrate the orbital energy contribution to chemical bonding. Consistently, the primary bonding of Cu2, Ag2, and Au2 is derived from s-type σ-bonding, accounting for more than 85% of the total orbital interaction energy, with negligible d-type σ-bonding contribution. Differently, d-character turns out to be the dominant factor in the chemical bonding energy of Rg2, responsible for up to 84% of the orbital interaction. Meanwhile, the s-type σbonding descends dramatically to 11%. Overall, it gives convincing evidence that the single bond between the two Rg is mainly contributed by 6d orbitals, with some 7s hybridization. Interestingly, a little d-type π composition is also involved in the bonding of the Rg2 dimer with a contribution of ∼4%. To elucidate the inherent bonding interaction, the adiabatic force constant (ke) was calculated and shown in Table 5. The

Table 2. Effective Bond Orders of M2 (M = Cu, Ag, Au, Rg) Dimer from DMRG-CI (22e, 28o) Method (n − 1)d-σ (n − 1)d-π (n − 1)d-δ ns-σ total

Cu

Ag

Au

Rg

0.01 0 0 0.99 1.01

0 0 0 0.99 0.99

0 0 0 0.98 0.98

0.94 0.02 0.01 0.03 1.01

PBE. The general trend, albeit nonintuitive, that the M−M distances alter as Cu−Cu < Ag−Ag > Au−Au > Rg−Rg is reproduced, and it is also consistent with the atomic radii and the observed M−C distances of MCN (M = Cu, Ag, Au, Rg) system.57−59 In addition the natural bond orbital (NBO) results based on DFT/PBE and CCSD density matrices listed in Table 3 show the orbital hybridization of atoms in the M−M bond down the periodic table for the coinage metal elements. Results given by these two methods are quite consistent with each other. All the dimers have single σ-bonds while with different AO compositions. Again, NBO analyses reveal that, for the Cu, Ag, and Au dimers, the single bonds are mainly composed of ns-type orbitals, with little (n − 1)d participation. Consistent

Table 3. Calculated Geometric Parameters Compared with Experimental Results and NBO Analyses of Cu2, Ag2, Au2, and Rg2 Diatomic Moleculesa bond lengthb (Å) CCSD(T) Cu2 Ag2 Au2 Rg2

2.221 2.545 2.500 2.480

DFT/PBEd 2.222 2.567 2.523 2.513

(2.252) (2.607) (2.526) (2.561)

NBO analysesc ∑Rp60

expt46

DFT/PBE

CCSD

2.24 2.56 2.48 2.42

2.219 2.534 2.470

Cu [4s3d0.03] Ag [5s4d0.01] Au [6s5d0.06] Rg [6d7s0.59]

Cu [4s3d0.01] Ag [5s4d0.01] Au [6s5d0.05] Rg [6d7s0.47]

a

All calculations are at SR level. bTheoretical bond lengths from both CCSD(T) and DFT/PBE methods compared with the summation of Pyykkö covalent radii (∑Rp) and experimental values (expt). cNBO results analyzed from both DFT/PBE and CCSD density matrix. dThe small frozencore approximation was used for the values without parentheses, that is, [1s2-2p6] for Cu, [1s2-3d10] for Ag, [1s2-4d10] for Au, and [1s2-4f14] for Rg. The numbers in parentheses are obtained by using large core approximation for [1s2-3p6] for Cu, [1s2-4p6] for Ag, [1s2-4f14] for Au, and [1s2-5f14] for Rg. D


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Inorganic Chemistry Table 4. EDA-NOCV Analyses for M2 (M = Cu, Ag, Au, Rg) from SR-PBE/TZ2Pa ΔEσ−s orb ΔEσ−d orb ΔEπ−d orb ΔErest orb ΔEorb a

Cu2

Ag2

Au2

Rg2

−34.4 (89%) −2.0 (5%) 0 −2.2 −38.6

−29.1 (91%) −2.0 (6%) 0 −1.0 −32.1

−46.2 (85%) −3.8 (7%) 0 −4.6 −54.6

−11.5 (11%) −90.3 (84%) −4.3 (4%) −1.4 −107.6

All energies are in kilocalories per mole. The electronic configuration of each fragment is identically taken as (n − 1)d10ns1 for comparison.

Table 5. Scalar-Relativistic Adiabatic Force Constants, Bond Energies and Bond Order Indices of M−M (M = Cu, Ag, Au and Rg) IBDE (eV) Cu2 Ag2 Au2 Rg2 a

bond order a

ke (N/cm)

PBE

CCSD(T)

expt

G-J

1.35 1.07 1.75 2.78

2.12 1.67 2.29 3.86

1.97 1.62 2.15 4.39c

2.0771 1.6672 2.2973

1.02 1.01 1.03 1.04

b

Table 6. Comparison of SO and SR Effects on Nuclear Shieldings (in ppm) of the M Atom in M2 Molecules at the ZORA-PBE/TZ2P Levela

Wiberg

b

NR Δ(SR‑NR)b Δ(SO‑NR)b Δ(SO‑SR)b

1.06 1.02 1.04 1.13

a b

c

Gopinathan-Jug bond orders. Wiberg bond orders. Rg (6d107s1) configuration was applied for the IBDE calculation. The bond dissociation energy (BDE) for Rg2 is 1.291 eV at the CCSD(T)/ QZVP level with Rg (6d97s2) electron configuration.45 SO coupling is not included in these calculations.

Cu

Ag

Au

Rg

2184 −45 77 121

4489 32 472 440

9129 2901 3976 3685

14 488 5102 35 184 30 082

Here no frozen-core approximation was used to ensure the accuracy. NR SO NR SO SR Δ(SR‑NR) = σSR iso − σiso , Δ(SO‑NR) = σiso − σiso , Δ(SO‑SR) = σiso − σiso.

the shielding constants for many heavy-element molecules.74−77 Both SR and SO coupling effects are evaluated herein to investigate the relativity-induced changes of the NMR shielding. Obviously, the chemical shifts resulting from the SR and SO coupling effects of Rg2 are dramatically larger than those of the other lighter congener dimers. More s-type orbital contributions will give rise to significant chemical shift caused by SO in NMR,78,79 compared with the nonrelativistic result, which is consistent with the fact that s-type orbitals will be stabilized by the direct relativistic ef fect. To explore the relativistic effects on the bonding character and covalency, electron localization function (ELF) analyses are further done for the coinage metal dimers. The ELF patterns in the bonding region on the basis of the SR level are depicted in Figure 4, also compared with the NR and SO coupled levels. It displays an apparent change in the Rg2 molecule from the NR to the SR level, where more electron density is situated in the bonding region between the two atoms. On account of the relativistic effects, Au2 also has a modest increase in electron density but with almost no change for Ag2 and Cu2. Moreover, SO coupling somewhat changes the ELF distribution of the covalent bond formation in Rg2, as an electron density reduction showing in the central yellow part and an increase showing in blue part slightly deviate from the central part of Figure 4, which is not found in the other congeners. 3. Determining the Ground State of Rg2. As the LUMO is energetically rather close to the HOMO in Rg2 (Figure 2), it is less straightforward to determine the electronic ground state. The actual difference of bonding character of 1 Σ g + ([1σ g 2 1π u 4 2σ g 2 1σ u 2 1δ g 4 ]1π g 4 1δ u 4 2σ u 0 ) and 3 Π u ([···] 1πg31δu42σu1) states is trivial, as the latter involves an electron transfer from d-π* to d-σ* orbitals, both of which are antibonding. The Mayer bond order index is calculated to be 1.07 and 0.90 for 1Σg+ and 3Πu, respectively, with the small decrease likely due to stronger bonding of σ-type than π-type. At the SR level, the 1Σg+ and 3Πu states are nearly degenerate, while the 3Δg ([···]1πg41δu32σu1) state originating from transferring one electron from HOMO to LUMO has much higher excitation energy (1.279 eV) than 1Σg+ (see Figure 5 and Table S2 for details).

force constants at first decline from Cu2 (1.35 N/cm) to Ag2 (1.07 N/cm) due to the increased Pauli repulsion in Ag(d10)− Ag(d10) between the less-contracted 4d semicore orbitals; the σ(s−s) bond of Cu2 is stronger than that of Ag2 as a result of significantly smaller Cu 3d orbitals due to the quantum primogenic effect.61−63 The force constants then increase markedly to 1.75 N/cm for Au2 and 2.78 N/cm for Rg2 as a result of increased s-d hybridization caused by relativistic effects. The various bond orders also present the same trend as the ke values. Specifically, Intrinsic Bond Dissociation Energies (IBDEs)64,65 are calculated in these coinage metal dimer cases with the same atomic electron configurations. IBDE of Rg2 reaches up to 4.391 eV, which is much higher than for the other molecules, partly because d10s1 is not its atomic ground-state configuration, which lies 3.1 eV above the d9s2 ground state at the CCSD(T) level. The bonding strength indicators mentioned above were calculated based on scalar relativistic calculations. While they seem to suggest that there is stronger bonding in Rg2 in comparison with the other dimers, the SO coupling effect to bonding strength is yet to be determined. The difference of bond energies and force constants were also predicted in M2−Ng (M = Cu−Au and Ng = Kr−Rn) systems,66 which can be explained by strong relativity as well as the lanthanide contraction in the case of Au that tends to destabilize the d and f shells and stabilize the s and p shells.12,18,30,32,67−69 Similar trends were evident in the previous calculations on the diatomic compound RgH, which shows that the strength of the roentgenium−hydrogen bond is doubled due to the relativistic effects.46,70 The bonding picture change from σ(s−s) bonding in Cu2, Ag2, and Au2 to σ(d−d) bonding in Rg2 implies that the nuclear shielding of the external magnetic field should be rather different for these two groups of molecules. We therefore calculated the coinage atom shielding constants for M2 using the ADF software with zeroth order regular approximation (ZORA), and the results are listed in Table 6. The SR- and SOZORA methods have been verified to be effective in simulating E


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Inorganic Chemistry

Figure 4. ELFs for Cu2, Ag2, Au2, and Rg2 calculated using the NR-, SR-, and SO-ZORA methods. The corresponding scale to each item is shown in the right panel.

the Ω state of 2u after SO splitting from 3Πu is competitive with 0g+ (from 1Σg+) as the ground state. In our CASSCF/CASPT2/ SO calculations, the energy difference between 2u and 0g+ is only ∼0.04 eV, which casts doubt on the true ground state of Rg2 due to methodology inaccuracy. Moreover, upon including the SO splitting, 3Δg will split into 3g, 2g, 1g states in energetic ascending order, where the lowest SO state 3g is 0.695 eV higher than 0g+. Since this calculation uses an approximation method to evaluate the energies of the SO states, more accurate methods are needed to deal with the dynamic and static electron correlation as well as the SO coupling effects to determine the true ground state for Rg2 in the future.

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CONCLUSIONS

We have studied a series of coinage metal dimers M2 (M = Cu, Ag, Au, Rg) through quantum-chemical calculations to explore the relativistic effects on chemical bonding. This kind of metal dimer represents the simplest yet cogent case to explain the influence of relativistic effects on the change of bonding pattern. The relativistic effects are so important for the group11 superheavy element Rg that the 6d orbitals (with decreasing 7s contribution) play the prominent role in forming chemical bonding in the Rg2 molecule, which differs from the other lighter dimer species with ns−ns bonding. Such strong relativity-enhanced 6d7s hybridization seems to strengthen the Rg−Rg chemical bonding, as shown by the higher adiabatic force constants, intrinsic bond energies, and bond orders calculated at the scalar relativistic level. The calculated nuclear shieldings become much larger when SR and SO coupling effects are taken into account. The electron distribution in the superheavy Rg2 molecule is influenced by both SR and SO coupling relativistic effects. The small energy gap between the 1 + Σg and 3Πu states may result in a triplet-dominanted 0g+ ground state after SO coupling. The coinage metal dimers provide a simple and clear textbook example, where relativistic effects change the chemical bonding pattern and the periodic trends of elements in the same group of the periodic table.

Figure 5. Energy correlation diagram for Rg2: (a) SR state-averageCASPT2 energy levels (left) and (b) SO states from CASSCF/ CASPT2/SO (right).

The first SR-excited state 3Πu will split into 1u, 2u twofold degenerate states and 0u+, 0u− nondegenerate states upon firstorder SO splitting, whereas 1Σg+ turns out to be a 0g+ state being energetically modified only with the second-order SO splitting. The energy of the 3Πu state is much higher than 1Σg+ for Cu2, Ag2, and Au2; thus, the small SO coupling effect is not able to split the state enough so that the ground state is still singlet dominant beyond doubt. But in case of Rg2, 1Σg+ is only 0.42 eV more stable than 3Πu from SR CASPT2/CASSCF calculations (Table S2). For more accurate results, geometry optimization based on CCSD(T)/ QZVP calculations for these two electronic states was also performed; the complete basis set (CBS) extrapolated energies were then obtained by X−3 extrapolation, which serves as reference energy [CCSD(T)/CBS] for CCSDT(Q) calculations with δT+(Q) parameters at the QZVP level. The CCSDT(Q) results show that the energy difference between the SR 1Σg+ and 3Πu states is only 0.31 eV; as a consequence, F


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Inorganic Chemistry

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00438. Computational method and its corresponding references; tables of the MO compositions in percentage of M2 molecules; relative energies of spin−orbit states of Rg2 dimer; NR and SR MO correlation diagrams of Rg2; NO contours of Cu2, Ag2, and Au2 from DMRG-CI (22e, 28o) calculations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (H.S.H.) *E-mail: [email protected]. (J.L.) ORCID

Jun Li: 0000-0002-8456-3980 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Prof. Dr. W. H. E. Schwarz and Prof. Dr. P. Schwerdtfeger for fruitful discussion. This work was supported by the National Natural Science Foundation of China (Grant Nos. 21590792, 21433005, and 91426302). The calculations were partially performed by using supercomputers at the Computer Network Information Center, Chinese Academy of Sciences and Tsinghua National Laboratory for Information Science and Technology.

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REFERENCES

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