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Fig. 18 Computed DDEC6 SBOs and bond orders for seven simple solids.

Figure 18 Computed DDEC6 SBOs and bond orders for seven simple solids.

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Table1 Failure modes for different methods of computing bond indices of stretched Oz. The method categories and error types are explained in the main text. For each error type, the numerator gives the number of fails observed, and the denominator gives the number of samples for which a fail or no fail decision could be determined. DDEC6 bond indices did not fail, while the others did. All methods in category 2B exhibited type 1 failures. Abbreviations: bond index (BI), bond order (BO), contact exchange (CE), first-order delocalization index (FODI), Mayer bond index (MBI), and overlap population (OP)
Table1 Failure modes for different methods of computing bond indices of stretched Oz. The method categories and error types are explained in the main text. For each error type, the numerator gives the number of fails observed, and the denominator gives the number of samples for which a fail or no fail decision could be determined. DDEC6 bond indices did not fail, while the others did. All methods in category 2B exhibited type 1 failures. Abbreviations: bond index (BI), bond order (BO), contact exchange (CE), first-order delocalization index (FODI), Mayer bond index (MBI), and overlap population (OP)
Fig. 2 DDEC6 bond order versus bond length for the O2 molecule singlet (circles), triplet (triangles), and quintet (squares) spin states. The lines show the fitted model functions listed in Table 2.
Fig. 2 DDEC6 bond order versus bond length for the O2 molecule singlet (circles), triplet (triangles), and quintet (squares) spin states. The lines show the fitted model functions listed in Table 2.
Fig. 3 Diagram showing key relationships between equations for computing DDEC6 bond orders. Red boxes enclose the main equation anc high level concepts. Arrows indicate the sources of selected inputs or concepts used in each equation. Each variable reappearing in severa different equations is marked with a specific color of squiggly underline (note: sometimes a variable reappears inside a summation). Blue text annotations explain key terms.
Fig. 3 Diagram showing key relationships between equations for computing DDEC6 bond orders. Red boxes enclose the main equation anc high level concepts. Arrows indicate the sources of selected inputs or concepts used in each equation. Each variable reappearing in severa different equations is marked with a specific color of squiggly underline (note: sometimes a variable reappears inside a summation). Blue text annotations explain key terms.
Table 2. Fitted model parameters for eqn (8) describing In(DDEC6 bond order) versus (non-equilibrium) bond length for the [Ha]*, Hz, and O2 molecules. p; was fixed to its theoretical value. p2 and pz were fit in Microsoft Excel using the Generalized Reduced Gradient solver. The squared correlation coefficients >0.99 indicate the model described the data well
Table 2. Fitted model parameters for eqn (8) describing In(DDEC6 bond order) versus (non-equilibrium) bond length for the [Ha]*, Hz, and O2 molecules. p; was fixed to its theoretical value. p2 and pz were fit in Microsoft Excel using the Generalized Reduced Gradient solver. The squared correlation coefficients >0.99 indicate the model described the data well
Fig. 4 DDEC6 bond order versus stretched bond length for the Hz singlet, Hz triplet, and [H2]* doublet spin states. The lines show the fitted model functions listed in Table 2.
Fig. 4 DDEC6 bond order versus stretched bond length for the Hz singlet, Hz triplet, and [H2]* doublet spin states. The lines show the fitted model functions listed in Table 2.
Fig. 5 Graphic explaining why the confluence of atomic exchange propensities is important and its relationship to DDEC6 charge and spin partitioning.
Fig. 5 Graphic explaining why the confluence of atomic exchange propensities is important and its relationship to DDEC6 charge and spin partitioning.
Table 3 Computational details for each system studied “ MUGBS on Db and aug-ce-pvqz on F atoms. ” Geometry optimized but constrained to octahedral symmetry. © Since the experimental hexagonal ice crystal contains many fractionally occ upied I H atom sites,” the geometry for electron density generation had to choose an appropriate fraction of these to populate with actual H atoms. “ The ice surface geometry is a slab with several ice layers (extracted from the ice crystal structure) followed by >10 A vacuum space. ° AE for CCSD and FC for SAC-CL/ The CISD method for a two-electron system (e.g., stretched Hz.) is an exact full configuration interaction calculation. * AE except RECP on Rb, Te, I, and Cs. ” The HF calculation for a one-electron (e.g., stretched [H,]') system is an exact exchange-correlation calculation. ' AE except RECP on Te.
Table 3 Computational details for each system studied “ MUGBS on Db and aug-ce-pvqz on F atoms. ” Geometry optimized but constrained to octahedral symmetry. © Since the experimental hexagonal ice crystal contains many fractionally occ upied I H atom sites,” the geometry for electron density generation had to choose an appropriate fraction of these to populate with actual H atoms. “ The ice surface geometry is a slab with several ice layers (extracted from the ice crystal structure) followed by >10 A vacuum space. ° AE for CCSD and FC for SAC-CL/ The CISD method for a two-electron system (e.g., stretched Hz.) is an exact full configuration interaction calculation. * AE except RECP on Rb, Te, I, and Cs. ” The HF calculation for a one-electron (e.g., stretched [H,]') system is an exact exchange-correlation calculation. ' AE except RECP on Te.
Fig. 6 The computational time and memory requirements scale linearly with increasing number of atoms in the unit cell. This plot contains data for periodic ice crystal supercells. The blue line is the total DDEC6 analysis computational time. The orange line is the computational time for bond order computation. The red line is the total amount of random access memory (RAM) required to perform the entire DDEC6 analysis.
Fig. 6 The computational time and memory requirements scale linearly with increasing number of atoms in the unit cell. This plot contains data for periodic ice crystal supercells. The blue line is the total DDEC6 analysis computational time. The orange line is the computational time for bond order computation. The red line is the total amount of random access memory (RAM) required to perform the entire DDEC6 analysis.
Table 4 Bonding analysis of 26 diatomic molecules. 2S + 1 is the ground state spin multiplicity: 1 for singlet, 2 for doublet, 3 for triplet, etc. Experimental bond dissociation energy (B.D.E.) and computed bond length error (B.L.E.) for coupled-cluster (C.C.) and DFT (PBE functional) methods are listed. The DDEC6 bond order (B.O.) for C.C. and PBE are similar and performed well for all diatomics. For C.C., the DDEC6 bond- order-to-contact-exchange ratio and bond-order-to-overlap-population ratio are also listed. The heuristic B.O. is listed for comparison
Table 4 Bonding analysis of 26 diatomic molecules. 2S + 1 is the ground state spin multiplicity: 1 for singlet, 2 for doublet, 3 for triplet, etc. Experimental bond dissociation energy (B.D.E.) and computed bond length error (B.L.E.) for coupled-cluster (C.C.) and DFT (PBE functional) methods are listed. The DDEC6 bond order (B.O.) for C.C. and PBE are similar and performed well for all diatomics. For C.C., the DDEC6 bond- order-to-contact-exchange ratio and bond-order-to-overlap-population ratio are also listed. The heuristic B.O. is listed for comparison
“ From ref. 125. From ref. 124. A range of values is reported, because the different Mn atoms are not equivalent; the ASM magnitudes of individual Mn atoms in the structure fall at various points within this range. ° From ref. 126. Table 5 Comparison of experimental and calculated magnetic properties of the 3d and 5d transition metal solids. The elements Sc and Mn are denoted as incipient magnetism, because they reside close to the border between non-magnetic and magnetic ordering. My DFT calculations showed non-magnetic and weakly ferromagnetic ordering of Sc have equivalent energies. Except for Mn, the calculated and experimental properties are in generally good agreement. The non-collinear magnetic structure of Mn is extremely delicate and beyond the accuracy of existing DFT functionals*4
“ From ref. 125. From ref. 124. A range of values is reported, because the different Mn atoms are not equivalent; the ASM magnitudes of individual Mn atoms in the structure fall at various points within this range. ° From ref. 126. Table 5 Comparison of experimental and calculated magnetic properties of the 3d and 5d transition metal solids. The elements Sc and Mn are denoted as incipient magnetism, because they reside close to the border between non-magnetic and magnetic ordering. My DFT calculations showed non-magnetic and weakly ferromagnetic ordering of Sc have equivalent energies. Except for Mn, the calculated and experimental properties are in generally good agreement. The non-collinear magnetic structure of Mn is extremely delicate and beyond the accuracy of existing DFT functionals*4
Table 6 Bonding analysis of the 3d and 5d transition metal solids. For each element, the chemical group, low energy crystal structure, experimental and DFT molar density (mol L~4), experimental mass density (g cm73), and computed bonding properties are listed. There is reasonable agreement between the heuristic and DDEC6 SBOs. The SBO/SCE and SBO/SOP ratios varied from 1.08-1.24. The largest DDEC6 bond order for each material is also listed. These results show DDEC6 bonding analysis works for highly delocalized electrons in metallic solids
Table 6 Bonding analysis of the 3d and 5d transition metal solids. For each element, the chemical group, low energy crystal structure, experimental and DFT molar density (mol L~4), experimental mass density (g cm73), and computed bonding properties are listed. There is reasonable agreement between the heuristic and DDEC6 SBOs. The SBO/SCE and SBO/SOP ratios varied from 1.08-1.24. The largest DDEC6 bond order for each material is also listed. These results show DDEC6 bonding analysis works for highly delocalized electrons in metallic solids
Fig. 7 DDEC6 bond orders are reasonably consistent across the various Sz values comprising a spin multiplet. The CCSD results correspond to Sz = S, while the SAC-ClI results correspond to Sz = 0. Table 7 Asummary of key properties showing the electron density distributions of different Sz states of a spin multiplet are similar. The dipole moment magnitude, electronic spatial extent ((r?)), and traceless quadrupole eigenvalues are given in atomic units
Fig. 7 DDEC6 bond orders are reasonably consistent across the various Sz values comprising a spin multiplet. The CCSD results correspond to Sz = S, while the SAC-ClI results correspond to Sz = 0. Table 7 Asummary of key properties showing the electron density distributions of different Sz states of a spin multiplet are similar. The dipole moment magnitude, electronic spatial extent ((r?)), and traceless quadrupole eigenvalues are given in atomic units
comprises about 20% of air. This molecular oxygen is primarily in the triplet spin state comprised of Sz = —1, 0, and +1 values. When burning an object such as wood in air, the different Sz values of the O, triplet state react with essentially the same rates. In contrast, spin triplet and spin singlet O, molecules have vastly different reactivities.
comprises about 20% of air. This molecular oxygen is primarily in the triplet spin state comprised of Sz = —1, 0, and +1 values. When burning an object such as wood in air, the different Sz values of the O, triplet state react with essentially the same rates. In contrast, spin triplet and spin singlet O, molecules have vastly different reactivities.
Table 8 DDEC6 SBOs computed with the comprehensive bond orde! equation are chemically accurate. At least five different materials were included for each element's SBO statistics. The resulting avg., st dev., min., and max. are listed. These SBOs are consistent with ~1 (H) ~3 (B), ~4 (C), ~3-4 (N), ~2-3 (O), ~1 (F), and <1 (Na) bondinc electrons per atom
Table 8 DDEC6 SBOs computed with the comprehensive bond orde! equation are chemically accurate. At least five different materials were included for each element's SBO statistics. The resulting avg., st dev., min., and max. are listed. These SBOs are consistent with ~1 (H) ~3 (B), ~4 (C), ~3-4 (N), ~2-3 (O), ~1 (F), and <1 (Na) bondinc electrons per atom
Fig. 10 DDEC6 bonding analysis for three nanostructured materials with a high content of aromatic carbon atoms: graphene, graphite, and [Eu@Ceol*. bonds: H3N:BF3, B,Na, BN nanotube, BN sheet, and h-BN solid. Fig. 12 reports polyfluoroprene. Fig. 13 details diborane. Fig. 14 expresses results for three triatomics: [H-H-F] transition state, Na; cluster, and ozone singlet. Fig. 15 displays the SF, and [DbF,] octahedral structures. Fig. 16 illustrates a synthetic analog of an enterotoxin produced by Escherichia coli bacterium. Fig. 17 depicts three hydrogen bonding structures: natrolite (a
Fig. 10 DDEC6 bonding analysis for three nanostructured materials with a high content of aromatic carbon atoms: graphene, graphite, and [Eu@Ceol*. bonds: H3N:BF3, B,Na, BN nanotube, BN sheet, and h-BN solid. Fig. 12 reports polyfluoroprene. Fig. 13 details diborane. Fig. 14 expresses results for three triatomics: [H-H-F] transition state, Na; cluster, and ozone singlet. Fig. 15 displays the SF, and [DbF,] octahedral structures. Fig. 16 illustrates a synthetic analog of an enterotoxin produced by Escherichia coli bacterium. Fig. 17 depicts three hydrogen bonding structures: natrolite (a
Fig. 9 The range and average of DDEC6 bond orders for thirteen different bond types. The directly connected (red) and adjacent con- nected (black) atoms defined each bond type. A tilde (~) indicates further bond connections to the remaining structure, but the specific form of these did not affect the bond type. Dashed lines indicate delocalized 7t-electrons. Each bond type displayed here occurred in at least five bonds distributed over at least two materials. DDEC6 bond orders for each bond type showed excellent transferability between different materials.
Fig. 9 The range and average of DDEC6 bond orders for thirteen different bond types. The directly connected (red) and adjacent con- nected (black) atoms defined each bond type. A tilde (~) indicates further bond connections to the remaining structure, but the specific form of these did not affect the bond type. Dashed lines indicate delocalized 7t-electrons. Each bond type displayed here occurred in at least five bonds distributed over at least two materials. DDEC6 bond orders for each bond type showed excellent transferability between different materials.
Fig. 11 DDEC6 bonding analysis for five structures containing B—N bonds: HzN-BFz, B4N4 molecule, BN nanotube, BN sheet, and h-BN solid.
Fig. 11 DDEC6 bonding analysis for five structures containing B—N bonds: HzN-BFz, B4N4 molecule, BN nanotube, BN sheet, and h-BN solid.
Fig. 12 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for polyfluoroprene. This is an example of an organic polymer with one-dimensional periodic boundary conditions. The periodic lattice vector is illustrated by the red arrow. Fig. 14 summarizes DDEC6 analysis results for three triatomic systems: [H-H-F] transition state, Na; cluster, and the ozone spin singlet. On the left is the transition state structure
Fig. 12 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for polyfluoroprene. This is an example of an organic polymer with one-dimensional periodic boundary conditions. The periodic lattice vector is illustrated by the red arrow. Fig. 14 summarizes DDEC6 analysis results for three triatomic systems: [H-H-F] transition state, Na; cluster, and the ozone spin singlet. On the left is the transition state structure
Fig. 14 Computed DDEC6 bond orders (red), SBOs (blue), NACs (black), and ASMs (green) for three triatomic species. For the ozone singlet, the ASMs (not shown) are zero. for the chemical reaction H, + F < H + HF. The computed results show the unpaired electron resides mainly on the F atom and the H-H bond is of higher order than the H-F bond in this transition state. The SBO of the middle H atom is 1.11. Because the SBO of the middle H atom is also approximately one in the reactant (ie., H, molecule) and product (ie., HF molecule) states, this demonstrates an approximate (but not exact) conservation of total bond order along the reaction path. In the middle is shown the Na; cluster. Because of the Jahn-Teller effect,'*? this molecule forms an isosceles rather than an equi- lateral triangle. This triangle has two longer sides of bond order 0.22 and one shorter side of bond order 0.56. The computed results show the unpaired electron resides mainly on the Na atom that is farther from the other two Na atoms. On the right is shown the ozone singlet, which has significant multi-reference character. The bond order between the inner and outer oxygen atoms is 1.44. The bond order between the two outer oxygen atoms is 0.09. These three triatomic systems demonstrate the diversity of exchange-correlation methods that can be used to generate electron and spin density information used in DDEC6 analysis. The HF transition state was computed using a coupled-cluster method (ie., CCSD). The Na; cluster was computed using a dispersion-corrected density functional approximation (i.e., PBE+D3). The ozone singlet was computed using the complete active space self-consistent field (CAS-SCF) method, which is appropriate for studying multi-reference systems.
Fig. 14 Computed DDEC6 bond orders (red), SBOs (blue), NACs (black), and ASMs (green) for three triatomic species. For the ozone singlet, the ASMs (not shown) are zero. for the chemical reaction H, + F < H + HF. The computed results show the unpaired electron resides mainly on the F atom and the H-H bond is of higher order than the H-F bond in this transition state. The SBO of the middle H atom is 1.11. Because the SBO of the middle H atom is also approximately one in the reactant (ie., H, molecule) and product (ie., HF molecule) states, this demonstrates an approximate (but not exact) conservation of total bond order along the reaction path. In the middle is shown the Na; cluster. Because of the Jahn-Teller effect,'*? this molecule forms an isosceles rather than an equi- lateral triangle. This triangle has two longer sides of bond order 0.22 and one shorter side of bond order 0.56. The computed results show the unpaired electron resides mainly on the Na atom that is farther from the other two Na atoms. On the right is shown the ozone singlet, which has significant multi-reference character. The bond order between the inner and outer oxygen atoms is 1.44. The bond order between the two outer oxygen atoms is 0.09. These three triatomic systems demonstrate the diversity of exchange-correlation methods that can be used to generate electron and spin density information used in DDEC6 analysis. The HF transition state was computed using a coupled-cluster method (ie., CCSD). The Na; cluster was computed using a dispersion-corrected density functional approximation (i.e., PBE+D3). The ozone singlet was computed using the complete active space self-consistent field (CAS-SCF) method, which is appropriate for studying multi-reference systems.
Fig. 13 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for diborane.
Fig. 13 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for diborane.
Fig. 16 The 1ETM (Protein Data Bank identifier) biomolecule is a synthetic analog of an enterotoxin produced by Escherichia coli bacterium. Atoms are colored by element: H (white), C (gray), N (blue), O (red), S (yellow). This biomolecule is comprised of residues of the amino acids alanine, asparagine, cysteine, glutamic acid, glycine, leucine, proline, and a special modified protein residue. This structure contains three disulfide linkages. Fig. 15 summarizes DDEC6 analysis for two hexafluorides: SF, and [DbF,] . SFg is remarkably inert, has an estimated atmospheric lifetime of approximately 800-3200 years, and is one of the most potent greenhouse gases.’**"*4 It is used as an insulating dielectric in high voltage equipment,**'** as a gas tracer,'***97*8 and in various specialized medical applica- tions.°4° The hypercoordinate nature of SF, has been intensely debated.**’”2"*** The computed DDEC6 NACs, S-FE bond order of 0.95, and S SBO of 5.72 show SF, contains six single-order S-F bonds rather than four multi-centered bonds. This result confirms that SF, transcends the heuristic Lewis octet rule that predicts four rather than six shared electron pairs around the central sulfur atom. Dubnium is an artificially produced transactinide element with atomic number 105. The most stable dubnium isotope known to date has a half-life of approximately one day.’”° Because of this short half-life, the chemistry of dubnium is not yet adequately explored.**° Shown here is a computed dubnium hexafluoride anion constrained to octahedral symmetry, but it is not yet known whether such a species actually exists in aqueous solutions.** The Db-F bond ength (2.00 A) is longer than the S-F bond length (1.58 A). The Db-F bond order (0.75) is also lower than the S-F bond order 0.95). Because Db is less electronegative than S, the F atoms have a more negative NAC in [DbF,] than in SF..
Fig. 16 The 1ETM (Protein Data Bank identifier) biomolecule is a synthetic analog of an enterotoxin produced by Escherichia coli bacterium. Atoms are colored by element: H (white), C (gray), N (blue), O (red), S (yellow). This biomolecule is comprised of residues of the amino acids alanine, asparagine, cysteine, glutamic acid, glycine, leucine, proline, and a special modified protein residue. This structure contains three disulfide linkages. Fig. 15 summarizes DDEC6 analysis for two hexafluorides: SF, and [DbF,] . SFg is remarkably inert, has an estimated atmospheric lifetime of approximately 800-3200 years, and is one of the most potent greenhouse gases.’**"*4 It is used as an insulating dielectric in high voltage equipment,**'** as a gas tracer,'***97*8 and in various specialized medical applica- tions.°4° The hypercoordinate nature of SF, has been intensely debated.**’”2"*** The computed DDEC6 NACs, S-FE bond order of 0.95, and S SBO of 5.72 show SF, contains six single-order S-F bonds rather than four multi-centered bonds. This result confirms that SF, transcends the heuristic Lewis octet rule that predicts four rather than six shared electron pairs around the central sulfur atom. Dubnium is an artificially produced transactinide element with atomic number 105. The most stable dubnium isotope known to date has a half-life of approximately one day.’”° Because of this short half-life, the chemistry of dubnium is not yet adequately explored.**° Shown here is a computed dubnium hexafluoride anion constrained to octahedral symmetry, but it is not yet known whether such a species actually exists in aqueous solutions.** The Db-F bond ength (2.00 A) is longer than the S-F bond length (1.58 A). The Db-F bond order (0.75) is also lower than the S-F bond order 0.95). Because Db is less electronegative than S, the F atoms have a more negative NAC in [DbF,] than in SF..
Fig. 15 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for two hexafluorides.
Fig. 15 Computed DDEC6 bond orders (red), SBOs (blue), and NACs (black) for two hexafluorides.
Fig. 17 Three materials containing hydrogen bonds. In the structures shown above, the yellow lines mark the unit cell boundaries. Atoms are colored by element: H (white), O (red), Na (medium purple), Al (dark olive green), Si (desert sand). As shown in the top left, natrolite is a zeolite containing four water molecules per unit cell. As illustrated by the green lines, the hydrogen atoms from each water molecule hydrogen bond to the neighboring oxygen atoms bound to silicon. An ice slab is shown on the top right. Slabs are important test systems, because they contain both surface and buried atoms. The bottom left shows a large supercell of ice crystal hexagonal phase containing 8748 atoms. The bottom right shows an end view of the same structure with a hexagonal channel outlined in white. This hexagonal ice phase is the most common and makes up snowflakes and ice cubes. The DDEC6 method is well-suited for studying materials containing hydrogen bonds. Fig. 17 illustrates three materials containing hydrogen bonds: natrolite, ice crystal, and an ice solid surface. According to the IUPAC, “The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H in which X is more electronegative than H, and an atom or a group of atoms in the
Fig. 17 Three materials containing hydrogen bonds. In the structures shown above, the yellow lines mark the unit cell boundaries. Atoms are colored by element: H (white), O (red), Na (medium purple), Al (dark olive green), Si (desert sand). As shown in the top left, natrolite is a zeolite containing four water molecules per unit cell. As illustrated by the green lines, the hydrogen atoms from each water molecule hydrogen bond to the neighboring oxygen atoms bound to silicon. An ice slab is shown on the top right. Slabs are important test systems, because they contain both surface and buried atoms. The bottom left shows a large supercell of ice crystal hexagonal phase containing 8748 atoms. The bottom right shows an end view of the same structure with a hexagonal channel outlined in white. This hexagonal ice phase is the most common and makes up snowflakes and ice cubes. The DDEC6 method is well-suited for studying materials containing hydrogen bonds. Fig. 17 illustrates three materials containing hydrogen bonds: natrolite, ice crystal, and an ice solid surface. According to the IUPAC, “The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H in which X is more electronegative than H, and an atom or a group of atoms in the
Fig. 20 Computed DDEC6 SBOs and bond orders for two half- sandwich Ti organometallic complexes. Fig. 20 shows computed DDEC6 SBOs and bond orders (BO) for two half-sandwich Ti organometallic complexes. The top panel shows an ethylene polymerization backside chain initia- tion transition state having the structure [(C;Me;)Ti(OC,H>-2,6- Me,-4-Br)(CH3)(C,H,)]° [MeB(C,Fs)3] . In this transition state, the ethylene C=C bond is partially weakened (BO = 1.59) and bonds start to form between the incoming ethylene monomer and the Me initiating group (BO = 0.22) and Ti (BO = 0.31). There is also an agostic Ti-H(a#-C) bond order = 0.07. The
Fig. 20 Computed DDEC6 SBOs and bond orders for two half- sandwich Ti organometallic complexes. Fig. 20 shows computed DDEC6 SBOs and bond orders (BO) for two half-sandwich Ti organometallic complexes. The top panel shows an ethylene polymerization backside chain initia- tion transition state having the structure [(C;Me;)Ti(OC,H>-2,6- Me,-4-Br)(CH3)(C,H,)]° [MeB(C,Fs)3] . In this transition state, the ethylene C=C bond is partially weakened (BO = 1.59) and bonds start to form between the incoming ethylene monomer and the Me initiating group (BO = 0.22) and Ti (BO = 0.31). There is also an agostic Ti-H(a#-C) bond order = 0.07. The
Fig. 19 Computed DDEC6 SBOs, bond orders, NACs, and ASMs for the CuzBTCz metal-organic framework. Yellow lines mark the unit cell boundaries. Atoms are colored by element: H (white), C (gray), O (red), and Cu (copper). The illustrated SBOs, BOs, NACs, and ASMs are for the fully periodic crystal structure.
Fig. 19 Computed DDEC6 SBOs, bond orders, NACs, and ASMs for the CuzBTCz metal-organic framework. Yellow lines mark the unit cell boundaries. Atoms are colored by element: H (white), C (gray), O (red), and Cu (copper). The illustrated SBOs, BOs, NACs, and ASMs are for the fully periodic crystal structure.
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