537

Index

a – adatom adsorption energy as function of α-rhombohedral boron 139–140 metal position in periodic system β-effect 371–372 284–286 β-rhombohedral boron 140–142 – adsorbate coordination in relation to π-bonding. See heavy main-group atoms adsorbate valence 301–303 multiple bonding – molecular adsorption and CO adsorption π helix. See 310 helix 286–296 π-conjugation in donor-substituted – surface group orbitals 296–301 cyanoethynylethenes 365–366 adsorbate bond activation and formation π-conjugation in tunable – different metal surfaces reactivity 317, bis(gem-diethynylethene) fluorophores 318–321 366, 368, 369 – quantum-chemical view of bond activation σ-hole 525, 526, 528, 531 321–328 2p shell accounts radial nodes lack 2–4 adsorbate coordination in relation to adsorbate – high electronegativity and small size of valence 301–303 2p-elements 4–7 alkali metal clusters 172 – hybridization defects influence on magnetic alkali metal-indium clusters 142–143 resonance parameters 14–15 alloying 303–305 anisotropy of current (induced) density – inert-pair effect and dependence on partial (ACID) 396–403, 404 charge of central atom 7–10 anisotropy of magnetic susceptibility and – multiple-bond paradigm and bond strengths exaltation 387–391 13–14 annulene 390, 395, 401, 402, 409 – stereo-chemically active versus inactive lone aromatic compounds and transition states pairs 10–12 magnetic properties 383–384 310 helix 506 – examples 4n+2 interstitial electron rule and ring-cap – – aromatic transition states 406, 407–411 orbital overlap compatibility 122–125 – – benzene and borazine 397–398 ab initio and density functional theory – – coarctate transition states 411, 413–415 calculations of water dimer 510 – – fullerenes 400–401 actinocene 351 – – homoaromatic molecules 403–405 actinyls 349–350 ––Huckel¨ and Mobius¨ structures 401–403 active spaces 253–255, 265 – – organometallic compounds 404, 406 adaptive natural density partitioning (AdNDP) – – pyridine, phosphabenzene, and 425–426, 429, 433, 438, 439 silabenzene 398–399 adatom adsorption energy dependence on – molecules magnetic properties 386–387 coordinative unsaturation of surface atoms – – anisotropy of magnetic susceptibility and 276–283 exaltation 387–391

The Chemical Bond: Chemical Bonding Across the Periodic Table, First Edition. Edited by Gernot Frenking, Sason Shaik. c 2014 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2014 by Wiley-VCH Verlag GmbH & Co. KGaA. 538 Index

aromatic compounds and transition states condensed polyhedral clusters stability magnetic properties (contd.) affecting factors – – chemical shifts in NMR 391–392 – exo-polyhedral interactions 134–135 – – quantum theoretical treatment 392–397 – orbital compatibility 135–136 aromaticity 372–784. See also inorganic configuration interaction ansatz 222 aromatic compounds – density matrices 222–223 – historical review 384–386 – truncation procedure 222 – in group 14 cyclopropenylium cation conjugation homologs 375–376 – correlation with experimental data – in metallabenzenes 376–378 – in 1,3-butadienes, 12.1,3-butadiyne, – in neutral exocyclic substituted polyenes, and enones 361–363 ––π-conjugation in donor-substituted cyclopropenes (HC)2 C=X 374–375 Aromatic Ring-Current Sheildings method cyanoethynylethenes 365–366 (ARCS) 424 ––π-conjugation in tunable aromatic stabilization energies (ASEs) 358, bis(gem-diethynylethene) fluorophores 359 366, 368, 369 atoms in molecules (AIM) 237–238 – – Hammett and Hammett–Brown substituent constants 363–365 Coulomb interaction 523, 524, 526, b 528–530, 533 Ba Ga Sb 470–473 7 4 9 Coulomb repulsion overcoming in transition band structures 449 metal complex 494–495 Becke–Johnson (BJ) damping 489 covalency and actinides 342–347 benzene and borazine 397–398 covalent bonds in polar metallic solids Bloch orbitals 447–449 459–462 block-localized wavefunction (BLW) 515 Cr, Mo, and W containing complexes blueshifting hydrogen bonds 516 2 259–263 bond activation quantum-chemical view crystal orbital Hamilton population (COHP) – (100) surface uniqueness 323–325 455, 468, 470 – molecular π bond activation (particle shape crystal orbital overlap population (COOP) dependence) 321–323 curves 455, 468 – molecular π bond activation 325–328 crystal orbitals 449 bond order overlap population (BOOP) 275 crystal versus electronic structure 466–470 bond orders analysis 235–237 Born–Oppenheimer approximation 524 d Born–von Karman periodic boundary democracy principle 67 conditions 447 density functional theory (DFT) 229–230, Brillouin zone 449 276, 277, 284, 286, 288–289, 302, 306, 307, broken spin symmetry 233–235 322, 326, 446, 447, 455, 461, 463, 464–465, Brønsted–Evans–Polanyi relation 317, 320, 482, 510–511 321, 325, 330, 333 density-matrix renormalization group (DMRG) algorithm 227–228, 240, 241, c 242, 245, 246 capping principle 125–126 density of states (DOS) 461, 463, 471, 472 carbones 73–81 – analysis 453–456 carbonyl complexes 181–187 Dewar–Chatt–Duncanson (DCD) model 176 coarctate transition states 411, 413–415 diabatic states model 66–67 complete-active-space diamagnetism 387 configuration-interaction (CASCI) 227 diatomic molecules bonding analysis 27–29 complete-active-space self-consistent-field Diels–Alder reaction 406, 408, 409 (CASSCF) approach 225–227, 245, 348, difference-density techniques 531–533 349, 351, 352 different metal surfaces reactivity 317, complete-graph tensor-network (CGTN) 318–321 228–229 directional electrostatic bonding 523–524 Index 539

– anisotropic molecular electrostatic potential E2L2 two-center complexes 94–95 distribution around atoms 524–528 –Si2L2 –Pb2L2 (L=NHC) 95–101 – difference-density techniques 531–533 – two-center group 13 and group 15 – directional noncovalent interactions 533 complexes B L and N L 101–110 – electrostatic anisotropy, donor–acceptor 2 2 2 2 electron correlation 254, 266, 480, 482, 486, interactions and polarization 528–530 – purely electrostatic models 530–531 495, 496 directional noncovalent interactions 533 – – effects 224, 225, 227, 239, 240, 242, 245 dispersion correction 486, 488–490, electron-counting rules in cluster bonding 492–493, 495 113–114 dispersion interaction 477–480 –4n+2 interstitial electron rule and ring-cap – examples orbital overlap compatibility 122–125 – – Coulomb repulsion overcoming in – capping principle 125–126 transition metal complex 494–495 – electronic requirement of condensed – – hexamethylethane derivatives 493–494 – – substituted ethenes 492–493 polyhedral boranes and mno rule – London dispersion energy theory 480–485 126–134 – theoretical methods to compute dispersion – electronic structure of elemental boron and energy 485 boron-rich metal borides 139 – – general 486 ––α-rhombohedral boron 139–140 – – supermolecular density functional theory ––β-rhombohedral boron 140–142 488–490 – – alkali metal-indium clusters 142–143 – – supermolecular wave function theory ––Mg B electronic structure 143–144 (WFT) 486–488 ∼5 44 – – symmetry-adapted perturbation theory – factors affecting stability of condensed (SAPT) 490, 491 polyhedral clusters donor–acceptor bonding 175, 176, 188, 190, – – exo-polyhedral interactions 134–135 192, 193, 195, 196, 203, 207, 211 – – orbital compatibility 135–136 donor–acceptor complexes of main-group – hypoelectronic metalloboranes 136–138 elements 71–73 – localized bonding schemes for bonding in –EL single-center 73 2 polyhedral boranes 119–122 ––CL carbones 73–81 2 – Wade’s rules 114–119 – – donor–acceptor bonding in heavier electron density distribution analysis tetrylenes ER2 and tetrylones EL2 (E=Si–Pb) 88–94 513–514 – – isoelectronic group 15 and group 13 electronic localization 456–458, 462–466 + homologues (N )L2 and (BH)L2 electron localization function (ELF) 82–88 456, 514 –E2L2 two-center complexes 94–95 – f block applications 341–342 ––SiL –Pb L (L=NHC) 95–101 2 2 2 2 – magnetic versus metallic behavior in K P – – two-center group 13 and group 15 4 3 462–466 complexes B2L2 and N2L2 101–110 donor-acceptor interactions 28, 36, 37, 38, electrostatic and orbital interactions 40, 41, 44–46. See also dispersion interaction 509–510 double bonding 13, 15, 16 electrostatic anisotropy, donor–acceptor interactions and polarization e 528–530 EL2 single-center 73 elemental boron and boron-rich metal borides –CL carbones 73–81 2 electronic structure 139 – donor–acceptor bonding in heavier – α-rhombohedral boron 139–140 tetrylenes ER2 and tetrylones EL2 (E=Si–Pb) 88–94 – β-rhombohedral boron 140–142 – isoelectronic group 15 and group 13 – alkali metal-indium clusters 142–143 + homologues (N )L2 and (BH)L2 82–88 –Mg∼5B44 electronic structure 143–144 540 Index

energy decomposition analysis (EDA) 181, homonuclear diatomic molecules 255–258 182, 185, 188, 191, 193, 194, 197, 202, 207, honorary d-elements 19–20 359–360, 373, 374, 376, 378, 482, 483, 491, Huckel¨ and Mobius¨ structures 401–403 511–512. See also transition metal hybridization defects influence on magnetic compounds chemical bonding resonance parameters 14–15 energy decomposition approach to bonding in hydrogen bonding 501–502 f block compounds 338–339 – fundamental properties 502–504 – towards 32-electron rule 340–341 – in biological molecules 506–507 – U–N and U–O bonding in uranyl(VI) – theoretical descriptions complexes 339–340 ––ab initio and density functional theory entanglement measures for single-and calculations of water dimer 510–511 multireference correlation effects – – electron density distribution analysis 239–242 513–514 ethylene and acetylene complexes 190, – – electrostatic and orbital interactions 192–195 509–510 exchange repulsion (EXR) 479, 481, 482 – – energy decomposition analysis 511–512 – – improper, blueshifting hydrogen bonds f 516 Fe2 complexes 264–265 – – resonance-assisted hydrogen bonding Fermi’s golden rule expression 272 515 Fermi level and electron counting 449–451 – – topological analysis of electron density and ferrocene and bis(benzene)chromium electron localization function 514 199–203 – – valence bond 508–509 frustrated Lewis pairs (FLP) 482, 483 – with varying strengths 504–506 frustrated recoupled pair bond 57 hydrogen bonding 524, 529, 530, 531, 533 fullerenes 400–401 hydrogen bridge 503 g hyperconjugation 370 – β-effect 371–372 gauge-including magnetically induced current – in ethane and ethane-like compounds (GIMIC) 424 generalized valence bond (GVB) 226 370–371 group-13 diyl complexes 195–199 hypervalency 15, 16, 17, 21 group orbital density of states (GODOS) 299, hypoelectronic metalloboranes 136–138 300

h i halogen bonding 526, 529, 531, 532 inert-pair effect and dependence on partial Hammett and Hammett–Brown substituent charge of central atom 7–10 constants 363–365 inorganic aromatic compounds 421–422 heavy main-group atoms multiple bonding – aromaticity and antiaromaticity 422–426 25–27 – conventional aromatic and anti-aromatic inorganic molecules 426 – comparative bonding analysis of N2 and P2 – – aromatic P2−,P−,P and analogs with N4 and P4 29–32 4 5 6 – diatomic molecules bonding analysis 428–430 27–29 – – inorganic B3N3H6 borazine and – tetrylynes HEEH (E=C–Pb) 1,3,2,4-diazadiboretiidine B2N2H4 – – bonding analysis 32–34 427–428 – – different structures 34–41 – unconventional aromatic and antiaromatic – – energy decomposition analysis 41–45 inorganic molecules 430–431 hexamethylethane derivatives 493–494 ––σ-aromatic and σ-antiaromatic species high electronegativity and small size of 431–432 2p-elements 4 ––σ-/π-aromatic, σ-/π-antiaromatic, and – hybridization defects 4–7 species with σ-/π-conflicting aromaticity homoaromatic molecules 403–405 432–436 Index 541

––σ-/π-/ δ-aromatic, σ-/π-/δ-antiaromatic, – – inert-pair effect and dependence on partial and species with σ-/π-/ δ-conflicting charge of central atom 7–10 aromaticity 436–440 – – multiple-bond paradigm and bond insulators 450, 456–459 strengths 13–14 intermolecular H bond 503 – – stereo-chemically active versus inactive intermolecular perturbation theory (IMPT) lone pairs 10–12 532 – honorary d-elements 19–20 k – outer d-orbitals in bonding 15–17 Kitaura–Morokuma (KM) energy – secondary periodicities 17–19 decomposition analysis 511–512 matrix product states (MPS) 227, 228 Kohn–Sham density functional theory metallabenzenes 376–378 (KSDFT) 338, 340, 342, 353 metal–metal multiple bonding 211–213 – with multireference quantum chemical l bonds modeling 253 lanthanides and actinides 337 ––Cr,Mo ,andW containing complexes – covalency and actinides 342–347 2 2 2 259–263 – electron localization function f block – – effective bond orders 253–254 applications 341–342 ––Fe complexes 264–265 – energy decomposition approach to bonding 2 in f block compounds – – homonuclear diatomic molecules 338–339 255–258 2− – – towards 32-electron rule 340–341 – – multiple bond in Re2Cl8 254–255 – – U–N and U–O bonding in uranyl(VI) metal particle composition and size complexes 339–340 dependence – multi-configurational descriptions of – alloying 303–305 bonding in f element complexes 347 – particle size dependence 305–310

– – bonding in actinyls 349–350 Mg∼5B44electronic structure 143–144 – – oxidation state ambiguity in f block mno rule 126–134 metallocenes 350–353 molecular electrostatic potential (MEP) – – quintuply bonded actinide dimer 523–528, 533 347–349 molecular Wankel motor 436 – technical issues 338 monovalent metal clusters highest spin states Larmor–Langevin equation 388, 391–393 bound triplet pairs 149–150 local density of states (LDOS) 272, 277, 284, – calculation methods and details 170 297–299, 305, 306, 310 localized bonding schemes for bonding in –NPFMbonding polyhedral boranes 119–122 – – in coinage metal clusters 161–167 n+1 localized molecular orbitals 487 – – generalization in Lin clusters local spin 230–233 156–161 n+1 London dispersion 477. See also dispersion –– Lin clusters 152–154 n+1 interaction –– Lin(n = 2–10) series 152 – energy theory 480–485 – – orbital cartoons 154–156 lone-pair bond weakening effect (LPBW) – – resonating bound triplet pairs 13 167–168 – prototypical bound triplet pair in 3Li 150, m 2 151 main-group elements chemical bonding – VB configuration count ad expressions for 1–2 – 2p shell accounts radial nodes lack 2–4 de for NPFM clusters 171–172 – – high electronegativity and small size of – VB wave function symmetry assignment 2p-elements 4–7 170–171 – – hybridization defects influence on Mott–Hubbard localized states 456–457 magnetic resonance parameters Mott transition 458 14–15 multicenter indices (MCI) 424 542 Index

multi-configurational descriptions of bonding ––ab initio single-reference approaches in f element complexes 347 223–224 – bonding in actinyls 349–350 – – configuration interaction ansatz – oxidation state ambiguity in f block 222–223 metallocenes 350–353 – – density functional theory for open-shell – quintuply bonded actinide dimer 347–349 molecules 229–230 multiple-bond paradigm and bond strengths – – electronicstructures definition 221–222 13–14 orbital interactions 75–78, 81, 82, 85, 86, 87, 88, 96, 98, 101, 103 104, 106, 179, 180, 183, n 186, 189, 193, 195, 198–200, 208, 210, 212, natural bond orbital (NBO) 425, 525, 530 213 natural energy decomposition analysis organometallic compounds 404, 405–406 (NEDA) 512 outer d-orbitals in bonding 15–17 natural-orbital occupation numbers 223 overlap population density of states (OPDOS) natural orbitals 348–352, 353 274, 275, 291, 293, 296–298 Newns–Anderson model 272, 282, 283 p NMR chemical shifts 391–392 partial density of states (PDOS) 278, noncovalent interactions (NCIs) 477, 485, 280–281–283, 294, 295, 297, 300 486, 489–491, 533 particle size dependence 305–310 no-pair ferromagnetic (NPFM) bonding Pauli repulsion 330–331 171–172 Peierls distortions 451–452 – in coinage metal clusters 161 pericyclic reactions 406, 409, 411, 413 – – structures and bonding 161–163 phosphane complexes and n-heterocyclic – – valence bond modeling 163–167 carbine complexes 187–190 – generalization in n+1Li clusters 156 n point-charge models 531 ––n+1Li patterns VB modeling 158–161 n polar flattening 525 – – VB mixing diagram representation of polar metallic solids 459–462 bonding in 3Li 156, 157 2 purely electrostatic models 530–531 – n+1Li clusters 152–154 n pyridine, phosphabenzene, and silabenzene – n+1Li (n = 2–10) series 152 n 398–399 – orbital cartoons 154–156 – resonating bound triplet pairs 167–168 q nucleus-independent chemical shift (NICS) quantum theoretical treatment 392–397 396, 423–424 quantum theory of atoms-in-molecules (QTAIM) 345–347, 514–516 o occupation numbers (ONs) 425 r open-shell transition-metal complexes 2− Re2Cl8 multiple bond 254–255 219–220 recoupled pair bond dyad 59 – qualitative interpretation recoupled pair bonding in hypervalent – – atoms in molecules 237–238 molecules 49–50 – – bond orders analysis 235–237 – comparison with other models 64 – – broken spin symmetry 233–235 – – democracy principle 67 – – entanglement measures for single-and – – diabatic states model 66–67 multireference correlation effects – – Rundle–Pimentel 3c-4e model 64–65 239–242 – multireference wavefunction treatment of – – local spin 230–233 bonding 50–53 – spin density distributions 243 – SF and OF low-lying states 53–57 – – multiconfigurational study 245–246 –SF2 and OF2 (and beyond) low-lying states – – one-determinant picture 243–245 58 – theoretical foundations 220–221 ––OF2 triplet states 62–63 1 ––ab initio multireference approaches ––OF2(X A1) 62 3 224–229 ––SF2(a B1) 59, 61 Index 543

3 ––SF2(b A2) 61–62 supermolecular wave function theory (WFT) 1 ––SF2(X A1) 58–59 486–488 ––SF3 and SF4 63–64 surface molecule limit 274 ––SF5 and SF6 64 surface reactivity 269 relativistic effects 2, 8, 11, 17–19 symmetry-adapted perturbation theory (SAPT) resonance-assisted hydrogen bonding 515 490, 491, 530, 531 ring current. See aromatic compounds and transition states magnetic properties t Rundle–Pimentel 3c-4e model 64–65 tensor network states (TNSs) 228 tetrylynes HEEH (E=C–Pb) – bonding analysis 32–34 s – different structures 34–41 scandide contraction 18, 21 – energy decomposition analysis 41–45 secondary periodicities 17–19 thermochemistry. See dispersion interaction semiconductor 450, 451, 459 three center, four electron model. See semimetals 451 Rundle–Pimentel 3c-4e model SF and OF low-lying states 53–57 through resonance 364 SF2 and OF2 (and beyond) low-lying states time-dependent density functional theory 58 (TDDFT) 484, 485 –OF2 triplet states 62–63 time reversal symmetry 449 3 –SF2(b A2) 61–62 TIP3P model 509 1 ––OF2(X A1) 62 topological rules 119 1 –SF2(X A1) 58–59 transition metal compounds chemical 3 ––SF2(a B1) 59, 61 bonding. See also open-shell –SF3 and SF4 63–64 transition-metal complexes 175–176 –SF5 and SF6 64 – carbonyl complexes 181–187 single-orbital entropy 239 – cluster, complex, and electron-sharing solids 445–447 compound 203–211 – bonding 458 – ethylene and acetylene complexes 190, ––Ba7Ga4Sb9 470–473 192–195 – – covalent bonds in polar metallic solids – ferrocene and bis(benzene)chromium 459–462 199–203 – – crystal versus electronic structure – group-13 diyl complexes 195–199 466–470 – metal–metal multiple bonding 211–213 – – electronic localization 462–466 – phosphane complexes and N-heterocyclic – electronic structures 447 carbene complexes 187–190 – – Bloch orbitals, crystal orbitals, and band – valence orbitals and hybridization in structure 447–449 electron-sharing bonds 177–181 – – density of states and analysis 453–456 transition metal surface bonding and reactivity – – electronic localization 456–458 quantum chemistry 269–271 – – Fermi level and electron counting – adatom adsorption energy dependence on 449–451 coordinative unsaturation of surface – – Peierls distortions 451–452 atoms 276–283 spin density distributions 243 – – adatom adsorption energy as function of – multiconfigurational study 245–246 metal position in periodic system – one-determinant picture 243–245 284–286 stereo-chemically active versus inactive lone – – adsorbate coordination in relation to pairs 10–12 adsorbate valence 301–303 steric crowding and labile molecule – – molecular adsorption and CO adsorption 493–494 286–296 styx formalism 120, 122 – – surface group orbitals 296–301 substituted ethenes 492–493 – adsorbate bond activation and formation supermolecular density functional theory – – different metal surfaces reactivity 317, 488–490 318–321 544 Index

transition metal surface bonding and reactivity van der Waals (vdW) 477, 478, 481 quantum chemistry (contd.) – density function (vdW-DF) 488–490 – – quantum-chemical view of bond activation van Hove singularity 453 321–328 VSEPR model 10, 19, 179 – analysis 328–333 – elementary quantum-chemical model w 272–276 Wade’s rules 114–119, 122 – lateral interactions and reconstructions Woodward–Hoffman rules 330 310–317 – metal particle composition and size y dependence ylides 72 – – alloying 303–305 – – particle size dependence 305–310 z Zintl phases 456, 458, 459, 468, 470–474 v valence bond 508–509 valence orbitals and hybridization in electron-sharing bonds 177–181