Hexacarbonyls of Mo, W, and Sg: Metal–CO Bonding Revisited

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Hexacarbonyls of Mo, W, and Sg: Metal−CO Bonding Revisited Miroslav Iliaš†,‡,§ and Valeria Pershina*,‡ †

Helmholtz Institute Mainz, Johannes Gutenberg-Universität, 55099 Mainz, Germany GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany § Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 97401 Banská Bystrica, Slovakia ‡

S Supporting Information *

ABSTRACT: Calculations of the first bond dissociation energies (FBDEs) and other molecular properties of M(CO)6, where M = Mo, W, and Sg, have been performed using a variety of nonrelativistic and relativistic methods, such as ZORA-DFT, X2c+AMFI-CCSD(T), and Dirac−Coulomb density functional theory. The aim of the study is to assist experiments on the measurements of the FBDE of Sg(CO)6. We have found that, different from the results published earlier, the metal−CO bond in Sg(CO)6 should be weaker than that in W(CO)6. A comparison of the relativistic and nonrelativistic FBDE values, as well as molecular orbital and vibrational frequency analyses within both the nonrelativistic and relativistic approaches, have shown that this is a relativistic, predominantly scalar, effect causing weaker d(M) → π(CO) back-bonding in Sg(CO)6 than in the lighter homologues. Good agreement between the calculated FBDEs in this work and the experimental FBDEs for the Mo and W compounds gives credit to the present FBDE of Sg(CO)6, which should serve as guidance for ongoing experiments.

1. INTRODUCTION The study of transition-metal carbonyls is an exciting area of chemical research. It has both the fundamental aspect connected with an unusual bonding between the metal atom in a zeroth oxidation state and the CO molecule and that related to their various applications.1,2 This class of compounds has recently been enriched by a new species, hexacarbonyl of a superheavy element (SHE) with Z = 106, Sg(CO)6.3 This compound was produced in a chemical reaction of the Sg atom with a mixture of the He and CO gases. (The 265Sg isotope was synthesized in the nuclear fusion reaction of a 22Ne beam with a 248 Cm target. The half-lives of two α-decaying states of 265Sg +3.7 are 8.5+2.6 −1.6 and 14.4−2.5 s, respectively.) Moreover, chemical properties such as the volatility of Sg(CO)6, as an adsorption process on the surface of the chromatography column, have been studied using a gas−solid chromatography technique.3 It was shown that the volatility of Sg(CO)6 is very similar to that of its lighter homologues, Mo(CO)6 and W(CO)6. This means that the chemical species of Sg formed under these conditions is, indeed, Sg(CO)6 and that its electronic structure is similar to those of M(CO)6 (M = Mo and W). (The experimental study of the lighter homologues of Sg(CO)6 had been performed earlier.4) Chemical bonding in compounds of the heaviest elements has been of particular interest for chemical studies because of increasingly important relativistic effects. For elements of the 6d series, it is made by participation of the valence 7s and 6d atomic orbitals (AOs) of the metal atoms. Relativistic stabilization and contraction of the 7s AO and destabilization and expansion of the 6d AOs enormously influence bonding and other properties of the compounds of these elements. Mostly, they are responsible for the continuation of trends in © XXXX American Chemical Society

the stability of the oxidation states and complex formation in the groups.5,6 They are also responsible for an increase in covalence and bonding at the scalar relativistic (SR) level, even though large spin−orbit (SO) effects may result in some decrease in the bond strength of the 6d-element compounds, e.g., of (oxy)halides of Rf through Bh, with respect to that of the 5d elements (see Table 9 in ref 6). Thus, e.g., twocomponent (2c) relativistic effective core potential coupledcluster (RECP CC) calculations7 have shown that the SO splitting of the 6d(Sg) AOs of 1.0 eV diminishes the dissociation energy (De) of SgO2Cl2 by 1.5 eV with respect to the SR value, so that its De becomes 0.8 eV smaller than the De of WO2Cl2. (The SR calculations show an increase in De from WO2Cl2 of 22.2 eV to SgO2Cl2 of 22.5 eV.) Bonding in group 6 carbonyls is clearly different from that of the (oxy)halides of these elements; however, it should also be influenced by strong relativistic effects. Earlier discrete variational Xα calculations8 have shown that the electronic structure of Sg(CO)6 should be different from that of U(CO)6. Later on, RECP Møller−Plesset (MP2)/CC calculations9 of the same authors have shown that, contrary to the (oxy)halides, the first bond dissociation energy (FBDE) of M−CO should increase from W(CO)6 to Sg(CO)6 by 4 kJ/mol. The reason for that is claimed to be the relativistically increased d(M) → π(CO) back-donation in the Sg compound, even though the σ(CO) → d(M) forth-donation should be slightly smaller for Sg than for W. This result encouraged the production of Sg(CO)6, as was reported in ref 3. Received: November 15, 2016

A

DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 1. Calculated and Experimental Geometries of the M(CO)6 and M(CO)5 (M = Mo, W, and Sg) Molecules: Bond Distances, Re (in Å), and Angles (in deg) molecule

distance

SO ZORAa

SR ZORAb

4c DFTc

MP2d

CCDd

expte

Mo(CO)6

Mo−C C−O Mo−Cax Mo−Ceq C−Oax C−Oeq ∠Cax−Mo−Ceq ∠Mo−Ceq−Oeq W−C C−O W−Cax W−Ceq C−Oax C−Oeq ∠Cax−W−Ceq ∠W−Ceq−Oeq Sg−C C−O Sg−Cax Sg−Ceq C−Oax C−Oeq ∠Cax−Sg−Ceq ∠Sg−Ceq−Oeq

2.071 1.153 1.941 2.060 1.163 1.155 89.9 178.4 2.062 1.154 1.939 2.052 1.165 1.157 90.8 179.3 2.122 1.155 1.986 2.109 1.168 1.158 91.1 180.0

2.068 1.156 1.949 2.060 1.166 1.158 89.9 178.4 2.062 1.157 1.944 2.052 1.167 1.159 90.4 178.6

2.067 1.152

2.045 1.161 1.919 2.043 1.175 1.162 87.7 177.5 2.039 1.162 1.927 2.034 1.175 1.164 88.9 178.4 2.088 1.164 1.969 2.078 1.177 1.166 91.4 179.8

2.076 1.147 1.963 2.075 1.158 1.148 89.8 177.9 2.065 1.148 1.950 2.061 1.161 1.149 90.0 178.2 2.112 1.150 1.987 2.105 1.164 1.152 90.9 179.2

2.063 1.145

Mo(CO)5

W(CO)6 W(CO)5

Sg(CO)6 Sg(CO)5

a

2.062 1.153

2.123 1.154

2.058 1.148

The NR ADF M−CO bond lengths are Mo(CO)6 of 2.081 Å, W(CO)6 of 2.095 Å, and Sg(CO)6 of 2.174 Å. bReference 39. cReference 16. Reference 9. eReference 40.

d

of Sg(CO)6 with respect to that of Mo(CO)6 and W(CO)6 using the calculated molecular properties and a model of the molecule−slab dispersion interaction. We have shown that Sg(CO)6 should be almost equally volatile to W(CO)6 having adsorption enthalpies, −ΔHads, on quartz of 46.5 ± 2.5 and 46.2 ± 2.5 kJ/mol, respectively. This prediction was confirmed by the following experiments,3 giving −ΔHads of Sg(CO)6 of 50 ± 4 kJ/mol, in good agreement with the theoretical value. In view of the diverse predictions of trends in chemical bonding of various group 6 compounds on going over to Sg and the wish to have our own set of data for running experiments, in this work, we have newly calculated FBDEs of the M(CO)6 (M = Mo, W, and Sg) molecules using a variety of quantum-chemical methods. We have also predicted various related molecular properties and performed a detailed bond analysis. A decomposition reaction, as usual, was considered:

For macroamounts of Mo(CO)6 and W(CO)6, the FBDEs have been obtained by conventional methods. First, their FBDEs were estimated with the use of thermodynamic data.10 Later, laser pyrolysis allowed for direct measurements of this property.11 Because of the specific nature of SHEs, i.e., their short half-lives, FBDE measurements are to be performed with the use of a special gas−solid chromatography technique.12,13 According to this technique, decomposition of the carbonyls should occur on a metal surface of a decomposition column. Decomposition curves showing a relative yield of undecomposed species (i.e., survival probability, in percent) at the outlet of the column are obtained as a function of the column temperature. Those curves are then used for Monte Carlo simulations to deduce FBDEs with the help of an adsorption/ decomposition model containing various assumptions. The first measurements of the FBDEs of Mo(CO)6 and W(CO)6 have already been performed, showing that the bond is, indeed, stronger in W(CO)6 than in Mo(CO)6.13 Using the calculated FBDEs of ref 9, modeling of the decomposition process of Sg(CO)6 has been performed in ref 14. Because of the predicted9 larger FBDE of Sg(CO)6 than that of M(CO)6 (M = Mo and W), decomposition of the Sg carbonyl was expected to take place at higher temperatures than those of the lighter homologues. Experiments are in the works to measure this value.15 In our previous theoretical work on the group 6 hexacarbonyls with the use of the four-component (4c) density functional theory (DFT) method,16 we found that the electronic structure of Sg(CO)6 should be very similar to those of the Mo and W homologues. The structural data (geometries) obtained were in good agreement with those of Nash and Bursten.9 Moreover, we have predicted the volatility

M(CO)6 (Oh) → M(CO)5 (C4v) + CO

(1)

In the next section, a description of the methods used is given, while the results and their discussion are offered in section 3, followed by the conclusions in section 4.

2. METHODS OF CALCULATIONS Two groups of all-electron methods with relativistic Hamiltonians were employed here: the DFT and ab initio correlated ones, namely, MP2 and CC, with the iterative treatment of single and double excitation amplitudes and perturbative triples, CCSD(T).17 All of the studied systems of eq 1 are closed shells. Time-effective geometry optimizations of M(CO)6, M(CO)5 (M = Mo, W, and Sg), and CO molecules were performed using the Amsterdam Density Functional (ADF) suite.18,19 Within the ADF program package, we employed the zeroth-order regular approximation, ZORA, 2c Hamiltonian incorporating SO B

DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry effects (SO ZORA),20−22 the BP8623−25 functional, and the TZ2P basis sets.26 Likewise, for comparative purposes, we performed ADF calculations using scalar-relativistic (SR ZORA) and nonrelativistic (NR) Hamiltonians with all electrons included. The ADF-optimized geometries were utilized in the subsequent infinite-order 2c relativistic (X2c+AMFI27,28) CCSD(T)29 calculations with the DIRAC program30 and also in the 4c Dirac−Coulomb (DC) DFT-BP86 calculations with the ReSpect software.31 For our systems, we utilized uncontracted Dyall vdz32−35 basis sets in the DIRAC MP2 and CCSD(T) correlation methods. The number of correlated electrons was 54, 46, and 8 for M(CO)6, M(CO)5, and CO molecules, respectively. The virtual active space for electronic correlation was restricted by leaving spinors higher than 25 au, counting 584, 602, and 602 spinors for Mo(CO)6, W(CO)6, and Sg(CO)6, respectively, and 504, 522, and 522 spinors for Mo(CO)5, W(CO)5, and Sg(CO)5, respectively. The virtual active space for CO was composed of 80 spinors, neglecting those above 25 au. In the DC-DFT calculations with the ReSpect code, the uncontracted Dyall vtz32−35 basis sets were employed. In all of our calculations with the ADF, DIRAC, and ReSpect packages, the Gaussian nuclei model was used. To analyze the bonding, Hirshfeld effective charges36 were calculated using the ADF code, and Mulliken37 molecular orbital (MO) analysis based on the M and CO fragments (in the single-point group symmetry of the SR ZORA Hamiltonian) was performed. The DIRAC projection analysis38 was also employed to eliminate the basis set sensitivity of the Mulliken population analysis. (The X2c +AMFI27,28 2c Hamiltonian including SO effects in connection with the BP86 functional and Dyall vdz32−35 basis sets was used.) DIRAC projection analysis was possible, however, only in terms of atomic (M, C, and O) fragments.

Table 2. FBDEs of M−CO (in kJ/mol) Obtained at Various Levels of Theory method a

ADF (NR) ADF (SR)a

ADF (SO)a DC-DFTc X2c+AMFI-MP2d X2c+AMFICCSD(T)d RECP-MP2e RECP-CCDe RECP-CCSDe RECP-CCSD(T)e ZPT expt

Mo(CO)6

W(CO)6

Sg(CO)6

155.07 163.63 (165.69b) 163.49 163.20 188.28 158.19

218.47 191.19 (188.28b) 190.73 189.83 213.59 181.45

223.81 181.09

214.22 147.27 170.71 182.00 −5.17 167.4 ± 8f

243.93 174.89 197.90 207.94 −5.43 192.5 ± 8f

246.44 182.00 204.59 212.13 −5.59 in progressg

180.22 177.42 204.45 176.22

a

Optimized geometries for the corresponding NR, SR ZORA, and 2c SO ZORA Hamiltonians. bSR ZORA.39 cReSpect. dDIRAC. eReference 9 values calculated at the MP2 (for RECP-MP2) and CCD (for the rest) geometries. fReference 11. gReference 15.

3. RESULTS AND DISCUSSION The geometries of M(CO)6 and M(CO)5 (M = Mo, W, and Sg) calculated in this work at the NR, SR ZORA, and SO ZORA levels of theory along with those from earlier calculations9,16,39 and available experimental data40 are given in Table 1. The present ADF SO ZORA results for the M(CO)6 geometries are in very good agreement with the experimental data40 and with those from the earlier 4c DFT calculations,16 particularly for the W and Sg compounds. Also, our geometries of M(CO)6 and M(CO)5, where M = Mo and W, nicely match those of previous SR ZORA calculations.39 (The RECP MP2 Re values are further off, and the CCD ones9 are slightly overestimated for the Mo and W carbonyls.) An essential difference between the present ADF SO ZORA and DC-DFT calculations, on the one hand, and the RECP CCD ones,9 on the other hand, is a somewhat smaller Re(Sg−CO) in Sg(CO)6 of the latter: the CCD difference in Re(M−CO) between Sg and W is 0.047 Å, while the SO ZORA one is 0.060 Å. (The smaller RECP Re(Sg−CO) might be associated with the enhanced Sg−CO bonding obtained in those calculations, as discussed below.) For M(CO)5, the ADF and RECP CCD geometries are very similar; however, the present ADF values for W(CO)5 are somewhat smaller than the RECP CCD ones.9 The FBDEs of M(CO)6 (M = Mo, W, and Sg) calculated in this work according to reaction (1) using various methods, such as ADF ZORA, DC-DFT, and X2c+AMFI-MP2/CCSD(T), in comparison with the experimental data11 and RECP calculations,9 are shown in Table 2 and Figure 1. The zero-point and thermal (ZPT) contributions to FBDE obtained from the ADF vibrational frequency calculations are also given in Table 2. Nash and Bursten9 reported the ZPT value as ∼1.5−2 kcal/mol on average and Frenking and Frohlich1 as 2 kcal/mol for W(CO)6. One can see from Table 2 and Figure 1 that the best agreement between the calculated

Figure 1. FBDEs of M(CO)6, where M = Mo, W, and Sg, calculated using various methods (see Table 2) in comparison with the experimental data for the Mo and W carbonyls (open squares).

and experimental values (having significant error bars) for the Mo and W hexacarbonyls is reached by the present ADF SR/ SO and DC-DFT calculations. Our ADF SR results for the Mo and W systems also agree with the previous SR ZORA data.39 The X2c+AMFI-CCSD(T) results, obtained at the highest level of theory applied in this work, are slightly lower than the experimental values for the Mo and W compounds; however, they are also not far off. All of the RECP values, particularly the CCSD(T) ones,9 although presumably at a higher level of the CC theory, are significantly larger than the experimental values and our best ones (Figure 1). The main difference between the present relativistic ADF, ReSpect, and DIRAC calculations, on the one hand, and the RECP ones,9 on the other hand, is, however, an opposite trend in FBDE from W(CO)6 to Sg(CO)6: all of the former show a decrease in this direction, while the latter show an increase (Figure 1). (The reason for the opposite RECP trend in FBDE C

DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 3. Calculated ADF Energies, E (in eV), of Some Important HOMOs of M(CO)6 (M = Mo, W, and Sg)

from W(CO)6 to Sg(CO)6 and the shorter Sg−CO distance is unknown to us but might be connected with the basis sets used.) It is interesting that the decrease in the FBDE from the Wo to Sg compound is obtained by the present ADF calculations already at the SR level, while the SO effects only enhance this effect, particularly in Sg(CO)6. (The NR De values show a steady increase from the Mo to Sg compound.) As was mentioned in the Introduction, such a reversal of the trend in bonding from the 5d to 6d elements was found in other types of compounds of the 6d elements, e.g., in group 6 MO2Cl2, however, only at the SO level: The SR values show an increase in the group.7 Thus, SR effects are predominant in defining the trend in bonding of the group 6 carbonyls. The increase in FBDE from W(CO)6 to Sg(CO)6 was found in ref 9 “to be consistent with greater back-bonding in Sg(CO)6 than in W(CO)6” due to destabilization of the 6d AOs in Sg. To analyze the bonding in the group 6 carbonyls, Figure 9 of ref 1 showing the MO scheme with all of the main AOs involved in the bond formation is useful. Important orbitals involved in this process are those of T1u, Eg, and A1g symmetry, responsible for the σ(CO) → d(M) forth-donation, and of the T2g symmetry, responsible for the d(M) → π(CO) backdonation. A MO scheme with the Eg and T2g orbitals, mainly responsible for forth- and back-donations in M(CO)6, is also shown in Figure 2 in order to facilitate the discussion. The symmetries and their energies of some MOs of M(CO)6 (M = Mo, W, and Sg) are given in Table 3.

symmetry (Oh)

appr.a

E

HOMO

T2g

HOMO−1

T1u

HOMO−4

Eg

HOMO

T2g

HOMO−1

T1u

HOMO−5

Eg

HOMO

T2g

HOMO−1

T1u

HOMO−6

Eg

R NR R NR R NR R NR R NR R NR R NR R NR R NR

−6.609 −6.607 −10.329 −10.265 −11.880 −11.837 −6.657 −6.664 −10.483 −10.272 −12.088 −12.000 −6.534 −6.644 −10.402 −9.948 −12.142 −12.061

molecule

MO

Mo(CO)6

W(CO)6

Sg(CO)6

a

Molecules are in the R (SO ZORA) and NR ADF geometries, respectively.

The calculated ADF frequencies for the T1u, Eg, and A1g modes are close to the RECP MP2 ones,9 both being somewhat smaller than the experimental values. In agreement with the calculations of ref 9, our relativistic values show a slight decrease toward Sg(CO)6 (Figure 3a), evidencing the decreasing σ(CO) → d(M) forth-donation in the row Mo− W−Sg. The NR values show an opposite trend to an increase from the Mo to Sg compound. Thus, relativistic effects result in a decrease in the σ(CO) → d(M) forth-donation, indicating bond weakening along this mode in the row Mo−W−Sg. The main contribution to bonding, as indicated above, is, however, due to the T2g orbital, responsible for the d(M) → π(CO) back-donation. Our calculated relativistic M−CO frequencies for the T2g mode are in perfect agreement with the experiment data41−43 for the Mo and W compounds (Table 4). One can also see from Figure 3b that both the NR and R frequencies increase along this mode from Mo(CO)6 to W(CO)6, while strong relativistic effects in Sg result in its dramatic decrease in Sg(CO)6, implying a decrease in the backdonation and, hence, in the bonding along this mode. The NR value of the T2g frequency for Sg(CO)6 is, on the contrary, the largest among the homologues. Such a reversal of the trend and a Λ shape of the frequencies for the T2g mode, as the most important for bonding through the T2g MO [the d(M) → π(CO) back-donation], in the row Mo(CO)6−W(CO)6−Sg(CO)6 are nicely reflected by the Λ shape of the FBDEs, calculated in this work. Thus, we see that, because of the relativistic effects, the back-bonding in Sg(CO)6 is much weaker than that of W(CO)6, which explains a relativistic decrease in the FBDE. This conclusion differs from that of ref 9, where “the implicit increased Sg 6d → CO 2π back-bonding” in Sg(CO)6 with respect to the Mo and W compounds was claimed and attributed to “the greater relativistic destabilization of the Sg 6d orbitals relative to the W 5d orbitals”. The latter was judged by the “red shift”, i.e., decreasing frequencies of the T1u, Eg, and A1g modes in the row Mo−W−Sg that are, however, not responsible for the backdonation. Thus, as in many other 6d-element compounds,6

Figure 2. Principal MOs of group 6 M(CO)6 responsible for the σ(CO) → d(M) forth-donation and d(M) → π(CO) back-donation.

One can see that the σ-forth-donation occurs preferentially from the Φσ(Eg) of CO to the vacant d(Eg) AO of M, while the π-back-donation is from the d(T2g) AO of M to the vacant Φπ(T2g) of CO. As indicated in ref 1, the T2g orbital, responsible for the π-back-donation, contributes “much more to the bond energy (−204 kcal/mol)” in Cr(CO)6, for example, than the Eg orbital “(−68 kcal/mol), which gives the largest part of the OC → TM σ-donations”. To analyze the trend in FBDE, vibrational frequencies of the T1u, A1g, and Eg modes, responsible for the σ-forth-donations, were calculated in ref 9. The vibrations due to the T2g(π) MO, which is responsible for the d(M) → π(CO) back-bonding, have, however, not been considered there. Thus, in order to check the arguments of ref 9, we have calculated the M−CO vibrational frequencies of M(CO)6 (M = Mo, W, and Sg) for the T2g, T1u, Eg, and A1g modes. The results are shown in Table 4. They are also depicted in Figure 3. D

DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 4. Calculated Relativistic (R) and Nonrelativistic (NR), as Well as Experimental M−CO Stretching Frequencies (in cm−1) of the M(CO)6 (M = Mo, W, and Sg) Molecules T2g

Eg

A1g

molecule

method

NR

R

NR

R

NR

R

NR

R

Mo(CO)6

ADFa MP2b exptc ADFa MP2b exptc ADFa MP2b

471.3

475.7

1970.1

1992.5

477.7 480.2

1980.1

544.3

482.0 436.6

1989.9

1988.4 2002.7 2024.8 1987.0 1993.3 2021.1 1977.2 1967.1

2083.7

519.9

1965.9 1968.9 2003.0 1964.3 1969.9 1997.6 1953.3 1956.1

2081.4 2093.4 2120.7 2085.1 2093.7 2126.2 2078.7 2085.2

W(CO)6

Sg(CO)6 a

T1u

2003.3

2016.1

2095.8

2104.4

This work, NR/SO ZORA. bReference 9. cReferences 41−43.

Figure 3. Calculated relativistic (solid lines) and nonrelativistic (dashed lines) vibrational stretching frequencies of (a) the T1u, Eg, and A1g modes and (b) the T2g mode of M(CO)6 (M = Mo, W, and Sg).

relativistic, in this case both SR and SO, effects result in weaker bonding in Sg(CO)6 than in the lighter congeners. To find an explanation for such a reversal of the trend in FBDE from W(CO)6 to Sg(CO)6 in terms of the MO composition, we have performed MO and bond analyses along the ADF Hirshfeld36 and DIRAC population analysis38 schemes. Accordingly, Table 5 and Figure 4 contain Hirshfeld net metal atom charges, qM, calculated using the ADF package, as well as projection analysis gross Mulliken metal atom charges, QM, together with the total M−C overlap populations, OP(M−C) calculated using the DIRAC code. Table 5. Hirshfeld Effective Metal Charges, qM, DIRAC Projection Analysis Net Mulliken Charges, QM, and M−C Overlap Populations, OP(M−C) molecule

appr.a

qMb

QM c

OP(M−C)c

Mo(CO)6

R NR R NR R NR

0.71 0.72 0.84 0.94 0.77 0.96

0.56

0.41

0.75

0.54

0.70

0.52

W(CO)6 Sg(CO)6

Figure 4. Hirshfeld effective metal charges, qM, DIRAC projection analysis net Mulliken charges, QM, and M−C overlap populations, OP(M−C).

Both qM and QM show that metals are positively charged in these molecules, while COs are negatively charged, which means that the electron density is, indeed, shifted toward the

a

Molecules are in the R (SO ZORA) and NR ADF geometries, respectively. bADF code. cDIRAC code. E

DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX

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Sg(CO)6, so that it is now up to the experimentalists to confirm or correct this prediction. According to our results, decomposition of Sg(CO)6 should occur at slightly lower temperatures than those of W(CO)6.

CO fragment, supporting the conclusion about a stronger d(M) → π(CO) than the forth CO → d(M) σ-donation. The relativistic qM (and also QM) shows the following trend qMo < qW > qSg, as does that in the T2g frequencies and in the FBDEs, while the NR qM shows a steady increase in the row, Mo ≪ W < Sg, as does that in the NR FBDEs. The breakdown of the energy contributions in group 6 carbonyls on the example of Cr(CO)6 described in ref 1 shows that the electrostatic attraction between M and CO is very large and the main source of chemical bonding. This comes “mainly from the penetration of the occupied 5σ orbitals of (CO)6 into the metal 3spd shell, leading to less shielding and thus a stronger attraction by the highly charged metal nucleus.”1 Thus, the smaller relativistic qM or QM in Sg(CO)6 means that the electron density is not shifted so much in this compound from Sg to CO as in W(CO)6, so that the Sg−CO electrostatic interaction is smaller than the W−CO one. Nonrelativistically, it is just the other way around: the largest qM on Sg is the source of its largest ionic bonding with CO in the row of homologues. Again, a Λ shape in QM or qM is in harmony with such a shape in the FBDEs and in the T2g frequencies of the M−CO bond in the group. Finally, DIRAC relativistic M−C overlap population data (Table 5) also confirm the largest overlap for the W−C bond, pointing to it as to the strongest one. Concerning the gross population analysis, both using the ADF Mulliken and DIRAC projection analysis schemes, we have found out that they are not suitable for interpreting the Λshaped trend of the relativistic FBDEs. They show decreasing portions of the metal AO contributions in all of the MOs for both the relativistic and nonrelativistic Hamiltonians. Because of the extended basis sets, these values are not suitable for the comparative study performed in this work. In summary, the results of the present bond and charge distribution analyses confirm a decrease in the Sg−CO bonding in comparison with the W−CO one and show that this is a relativistic, predominantly scalar, effect. Good agreement between the calculated and experimental FBDEs for Mo(CO)6 and W(CO)6 gives credit to the present result for Sg(CO)6, so that it is now time for experimentalists15 to confirm or correct this prediction. According to our results, decomposition of Sg(CO)6 should occur at lower temperatures than those of W(CO)6 corresponding to a decrease of about 5−10 kJ/mol in the binding energy.

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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.6b02759. Packed input files for ADF, DIRAC, and ReSpect program suites, coordinates of optimized molecular geometries, text files with excerpts of raw outputs, and launching scripts (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Miroslav Iliaš: 0000-0002-8038-6489 Valeria Pershina: 0000-0002-7478-857X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.I. thanks the HIM for financial support through the Visiting Scholar Agreement and is thankful for financial support of the Slovak Research and Development Agency (Project APVV-150105). Part of the calculations was performed in the Computing Centre of the Slovak Academy of Sciences using the supercomputing infrastructure acquired in Projects ITMS 26230120002 and 26210120002 (Slovak infrastructure for high-performance computing) supported by the Research & Development Operational Programme funded by the ERDF. The authors also acknowledge the feedback and useful discussions of the details of the experiments with A. Yakushev (GSI, Germany) and R. Eichler (PSI, Switzerland).

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4. CONCLUSIONS Calculations of the FBDEs and other molecular properties of M(CO)6, where M = Mo, W, and Sg, have been performed with the use of a variety of both relativistic and nonrelativistic methods implemented in program packages such as ADF ZORA, ReSpect, and DIRAC. The aim of the study was to assist the running experiments on online measurements of the FBDE of Sg(CO)6. We have found out that, in difference from the previous results,9 the FBDE of Sg(CO)6 should be smaller than that of W(CO)6. This was obtained at both the SR and SO levels of theory, which is partially different from other compounds of Sg, where only SO effects are responsible for weakening of the bond. Charge distribution and vibrational frequency analyses have shown that this is a relativistic effect resulting in a weaker d(M) → π(CO) back-donation in Sg(CO)6 in comparison with that of W(CO)6. Good agreement between the calculated FBDEs of the Mo and W compounds and the experimental values gives credit to the present result for F

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Inorganic Chemistry

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DOI: 10.1021/acs.inorgchem.6b02759 Inorg. Chem. XXXX, XXX, XXX−XXX