Supporting Information
Wiley-VCH 2015
69451 Weinheim, Germany
Assessing the Viability of Extended Nonmetal Atom Chains in MnF4n+2
(M = S and Se)**
Ivan A. Popov, Boris B. Averkiev, Alyona A. Starikova, Alexander I. Boldyrev,*
Ruslan M. Minyaev,* and Vladimir I. Minkin*
anie_201409418_sm_miscellaneous_information.pdf
Supporting Information
Figure S1. Representative isomers of S2F10 and their relative energies (corrected for zero-point energies) at the M06-2X/6-311+G(2df) level
of theory.
S1
Figure S2. AdNDP results of chemical bonding in a) S2H2 , b) S2F2 and c) S2F10 at the M06-2X/6-311+G(2df) level of theory (six lone pairs
(six 1c-2e bonds) with ON=1.97-2.00 |e| on two fluorine atoms in S2F2 and thirty lone pairs with ON=1.97-1.99 |e| on ten fluorine atoms in
S2F10 are not shown for clarity). d) Multicenter representation of eight 2c-2e S-Feq σ bonds via four 3c-4e Feq-S-Feq bonds and 2c-2e S-S σ
bond via the 12c-2e bond.
S2
Figure S3. Dissociation products of the S2F10 molecule: SF6 (left) and SF4 (right).
Figure S4. SF6-SF4 transition state TS2 corresponding to the saddle point on the PES.
S3
Figure S5. SnF4n+2 molecules (n=2-9) in D4d (even n) and D4h (odd n) conformations corresponding to local minima on the PES and their
optimized bond lengths (Å) at the M06-2X/6-311+G(2df) level of theory.
S4
Table S1. Calculated properties of SnF4n+2 molecules at the M06-2X/6-311+G(2df) level of theory.
1
Molecule
R(S-S), Å ΔE1,
HOMO-LUMO gap, eV
kcal/mol
S2F10, 1A1 (D4d)
2.26
-23.3
10.34
S3F14, 1A1g (D4h)
2.26
-21.9
9.54
S4F18, 1A1 (D4d)
2.26
-22.1
9.28
S5F22, 1A1g (D4h)
2.26
-22.1
9.19
S6F26, 1A1 (D4d)
2.26
-22.0
9.15
S7F30, 1A1g (D4h)
2.26
-22.0
9.13
S8F34, 1A1 (D4d)
2.26
-22.1
9.12
S9F38, 1A1g (D4h)
2.26
-22.0
9.10
Dissociation energy for the SnF4n+2 Sn-1F4(n-1)+2 + SF4 channel.
Figure S6. Phonon dispersion of the infinite –(SF4–SF4)∞– chain. The structure is stable to distortions hence a local minimum.
Detailed SSAdNDP results
–(SF4–SF4)∞–
Initial general SSAdNDP analysis revealed three lone pairs on each fluorine atom with ON=1.94-1.98 |e| accounting for a total twenty-four 1c2e bonds. Remaining 10 electron pairs within one unit cell were found to participate in the formation of ten 2c-2e bonds: two 2c-2e S-S σ
bonds and eight 2c-2e S-F σ bonds with ON=1.99 |e| (not shown) and ON=2.00 |e|, respectively. Counterintuitive high ON value of the S-S σ
bonds obtained via the general SSAdNDP search should be treated with caution. It is important to note that unlike NBO hybrids, SSAdNDP
bonds are not rigorously orthogonal.[33] Relaxing orthogonality ensures that for a given n, the results of general search are independent of the
order in which the atom combinations are searched yielding symmetry-consistent set of bonds, but it may lead to overestimation of bond ONs
due to partial double use of some NAOs by neighboring bonds. Unlike general SSAdNDP search (where the density is depleted after all
bonds for a given n are revealed), in the user-directed form, the density matrix is updated after every single bond’s ON is found. Thus, for two
S5
adjacent symmetrically equivalent bonds, the resulting ONs will be different, if some bond overlap is present. In such case, the averaged
occupation may be accepted as the bonds’ ONs. Therefore, a user-directed form of the SSAdNDP analysis was further applied to examine
the result obtained by the general search. We have evaluated the degree of overlap (and ON overestimation) by comparing the ONs of two
symmetrically equivalent S-S σ bonds in consecutive user-directed SSAdNDP analysis. After eight 2c-2e S-F σ bonds (ON=1.96 |e|) were
revealed by the user-directed search and the density was depleted, it found two S-S σ bonds: with ONs of 1.78 |e| and 1.43 |e| as we
expected. Thus, the averaged ON of 1.61 |e| was accepted as the correct ON of the S-S σ bond in the –(SF4–SF4)∞– periodic system.
However, according to the NEC analysis for the S atom, it has the following occupation of orbitals: 3s 1.443p2.484s0.013d0.17, which is very similar
to that one of S2F10. Therefore, we believe that the initially found eight 2c-2e S-F bonds should be described as four 3c-4e on the Feq-S-Feq
fragments shown in Figure 2b as the combination of bonding and nonbonding orbitals. User-directed SSAdNDP analysis also allows us to
find 10c-2e bond (with 8 fluorine atoms inclusively within one unit cell) instead of 2c-2e S-S σ bond. This approach gives us the ON(10c-2e
bond)=1.98 |e|, which shows ~0.4 |e| is distributed among fluorine atoms with anti-bonding character, similar to S2F10.
–(SeF4–SeF4)∞–
It turned out that the overall chemical bonding picture is similar to that of –(SF4–SF4)∞–: ON(10c-2e bond)=1.99 |e| and ON(3c2e(bonding))=2.00 |e|, ON(3c-2e(nonbonding))=1.91 |e|.
Figure S7. Molecular structures of the staggered (I) and eclipsed (TS3) structures of Se 2F10 at 0 K and their relative energies at M06-2X/6311+G(2df) corrected for zero-point energies (in kcal/mol).
Figure S8. Dissociation products of the Se2F10 molecule: SeF6 (left) and SeF4 (right).
Figure S9. SeF6-SeF4 transition state TS4 corresponding to the saddle point on the PES.
S6
Figure S10. SenF4n+2 molecules (n=2-6) in D4d (even n) and D4h (odd n) conformations and lower symmetry SenF4n+2 molecules (n=7-9)
corresponding to local minima on the PES (two projections showing the lowering of high symmetry) with their optimized bond lengths (Å) at
the M06-2X/6-311+G(2df) level of theory.
S7
Table S2. Calculated properties of SenF4n+2 molecules at the M06-2X/6-311+G(2df) level of theory.
1
Molecule
R(Se-Se), Å ΔE1,
HOMO-LUMO gap, eV
kcal/mol
Se2F10, 1A1 (D4d)
2.47
-31.4
8.79
Se3F14, 1A1g (D4h) 2.46
-30.1
8.05
Se4F18, 1A1 (D4d)
2.46
-29.7
7.80
Se5F22, 1A1g (D4h) 2.46
-30.5
7.69
Se6F26, 1A1 (D4d)
2.46
-29.6
7.62
Se7F30, 1A1g (D4h) 2.46
-30.7
7.60
Se8F34, 1A1 (D4d)
2.46
-30.9
7.59
Se9F38, 1A1g (D4h) 2.46
-30.2
7.57
Dissociation energy for the SenF4n+2 Sen-1F4(n-1)+2 + SeF4 channel.
Table S3. Direct coordinates (VASP calculations) at the DFT-PBE level of theory for the optimized infinite-length –(SF4–SF4)∞ linear chain
exhibiting direct S-S σ bond.
A = (11.3545811310704323 0.0000000000000000 0.0000000000000000)
B = (0.0000000000000000 11.3545811310704323 0.0000000000000000)
C = (0.0000000000000000 0.0000000000000000
4.7592505241252177)
S
S
F
F
F
F
F
F
F
F
0.5000000000000000
0.5000000000000000
0.4452086399967925
0.6327415482338097
0.3672584517661903
0.5547913600032075
0.6327415482338097
0.3672584517661903
0.4452086399967925
0.5547913600032075
0.5000000000000000
0.5000000000000000
0.6327415482338097
0.5547913600032075
0.4452086399967925
0.3672584517661903
0.4452086399967925
0.5547913600032075
0.3672584517661903
0.6327415482338097
0.2500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.2500000000000000
0.2500000000000000
0.2500000000000000
0.2500000000000000
Table S4. Direct coordinates (VASP calculations) at the DFT-PBE level of theory for the optimized infinite-length –(SeF4–SeF4)∞ linear chain
exhibiting direct Se-Se σ bond.
A = (11.8782682265113522 0.0000000000000000 0.0000000000000000)
B = (0.0000000000000000 11.8782682265113522 0.0000000000000000)
C = (0.0000000000000000 0.0000000000000000
5.2889251499790433)
Se
Se
F
F
F
F
F
F
F
F
0.5000000000000000
0.5000000000000000
0.4424566893262138
0.6388189741655950
0.3611810258344050
0.5575433106737862
0.6388189741655950
0.3611810258344050
0.4424566893262138
0.5575433106737862
0.5000000000000000
0.5000000000000000
0.6388189741655950
0.5575433106737862
0.4424566893262138
0.3611810258344050
0.4424566893262138
0.5575433106737862
0.3611810258344050
0.6388189741655950
0.2500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.7500000000000000
0.2500000000000000
0.2500000000000000
0.2500000000000000
0.2500000000000000
S8
Experimental Section
Calculations: Initially we tested the following exchange-correlation potentials: B3LYP,[37] PBE0,[38] and M06-2X[39] with 6-311+G(d), 6311+G(2df), 6-311+(3df),[40] and aug-cc-pVTZ[41] basis sets for the optimization of the S2F10 molecule. We found that the M06-2X/6311+G(2df) combination yields a good agreement with the experimental data: calculated R(S-S) = 2.26 Å, R(S-Fax) = 1.56 Å, R(S-Feq) = 1.58
Å, and <FaxSFeq= 89.8o vs. experimental R(S-S) = 2.274(5) Å, R(S-Fax) = 1.574(3) Å, R(S-Feq) = 1.547(6) Å, and <FaxSFeq = 89.8(1)o.[25b]
Therefore, all the calculations of other MnF4n+2 molecules reported in this study are done at this level of theory using Gaussian 09 program. [42]
Geometry optimizations of –(MF4–MF4)∞– infinite chains were performed using two programs for credibility of obtained results: Vienna ab
initio simulations package (VASP, version 4.6) program[43] with PAW pseudopotentials from the VASP database[44,45] and CASTEP
program,[46] both with the PBE density functional.[37] In VASP, the plane-wave cutoff energy of 1000 eV of the associated pseudopotential was
used. The Brillouin zone was sampled by 4x4x10 and 4x4x9 k points Monkhorst-Pack grid[47] for the –(SF4–SF4)∞– and –(SeF4–SeF4)∞–
systems, respectively. In CASTEP, all the calculations were done using plane-wave basis set with norm-conserving pseudopotential and
energy cutoff 940 eV. The Brillouin zone of the reciprocal space of periodic structures was sampled by 1x1x3 k points Monkhorst-Pack grid.
Such grids provide the minimum k-point separation of 0.07 Å-1. Calculations of the phonon density of states were performed within the linear
response theory[48] via CASTEP to determine the stability of the periodic structures.
Chemical bonding analysis of the MnF4n+2 molecules was performed at the M06-2X/6-311+G(2df) level of theory using the adaptive natural
density partitioning (AdNDP) method,[33] which has been used successfully to analyze the chemical bonding of bare and doped boron
clusters,[49] as well as 2D nanostructures of boron and carbon. [50] Chemical bonding analyses of the –(MF4–MF4)∞– infinite chains were
performed using the solid state adaptive natural density partitioning (SSAdNDP) method, developed by Galeev et al. [36] Both methods are
extension of the natural bonding orbital (NBO) method developed for molecules by Foster and Weinhold [32] and for extended systems by
Dunnington and Schmidt.[51] The AdNDP method analyzes the first-order reduced density matrix in order to obtain its local block
eigenfunctions with optimal convergence properties for an electron density description. The obtained local blocks correspond to the sets of n
atoms (n ranging from one to the total number of atoms in the molecule) that are tested for the presence of two-electron objects (n-center two
electron (nc-2e) bonds, including core electrons and lone pairs as a special case of n = 1) associated with this particular set of n atoms.
AdNDP initially searches for core electron pairs and lone pairs (1c-2e), then 2c-2e, 3c-2e,..., and finally nc-2e bonds. At every step the
density matrix is depleted of the density corresponding to the appropriate bonding elements. A user-directed form of the AdNDP analysis can
be applied to specified molecular fragments and is analogous to the directed search option of the standard NBO code. [31,32] AdNDP accepts
only those bonding elements whose occupation numbers (ONs) exceed the specified threshold values, which are usually chosen to be close
to 2.00 |e|. However, the criterion for ONs might be adjustable for a particular case in the AdNDP procedure. When all the recovered nc-2e
bonding elements are superimposed onto the molecular frame the overall pattern always corresponds to the point group symmetry of the
system. Thus, the AdNDP method recovers both Lewis bonding elements (1c-2e and 2c-2e objects, corresponding to the core electrons and
lone pairs, and two-center two-electron bonds) and delocalized bonding elements, which are associated with the concepts of aromaticity and
antiaromaticity. From this point of view, AdNDP achieves seamless description of systems featuring both localized and delocal ized bonding
without invoking the concept of resonance. Essentially, AdNDP is a very efficient and visual approach to interpretation of the molecular
orbital-based wave functions.
In SSAdNDP a projection algorithm is used to obtain a representation of the delocalized PW DFT results in a localized AO basis. As long as
an appropriate AO basis set is chosen (it is usually trimmed of any functions with angular momentum l≥ 4 as well as diffuse f unctions with
exponents <0.1), projection is found to result in an accurate density matrix.[51] In this study cc-pCVDZ basis set was used to represent the
projected PW density using a 3x3x7 k-point grid. This basis set was selected so that on average less than 1% of the density of each
occupied plane wave band was lost in projecting into the AO basis to guarantee that the density matrix used in the SSAdNDP procedure
accurately represents the original plane wave results. The Visualization for Electronic and Structural Analysis software (VESTA, series 3)[52]
and Molekel 5.4.0.8[53] were used for all visualizations.
S9