HISTORICAL INTRODUCTION TO CHEMISTRY
CONTENTS CHAPTER 1 INTRODUCTION 11 GENERAL INTRODUCTION 12 WHAT ARE DISPERSION FORCES? 13 WHEN ARE DISPERSION FORCES IMPORTANT? 14 HISTORICAL SUMMARY OF CONCEPTUAL DEVELOPMENTS 141 LATE 19TH CENTURY: DISCOVERY OF VDW FORCES 142 1900S: EARLY MICROSCOPIC EXPLANATIONS OF VDW FORCES 143 1920S–1930S: QUANTUM MECHANICAL EXPLANATION OF VDW DISPERSION FORCES 144 1920S: MODEL PAIR POTENTIAL BETWEEN ATOMS OR MOLECULES 145 1930S: EARLY PAIRWISE SUMMATION APPROACHES 146 1940S: ELECTROMAGNETIC RETARDATION AND THE CASIMIR EFFECT 147 1930S–1960S: THEORY AND EXPERIMENTS ON COLLOIDS 148 1950S AND 1960S: MACROSCOPIC LIFSHITZ THEORY 149 1960S ONWARDS: EXTENDING LIFSHITZ TO NON-PLANAR GEOMETRIES 1410 1950S ONWARDS: IS THERE LIFE AFTER LIFSHITZ? 1411 1960S–PRESENT: DISPERSION FORCES VIA THE PHYSICS OF MANY INTERACTING ELECTRONS 1412 1960S ONWARDS: MANY-ELECTRON QUANTUM PERTURBATION THEORY 1413 1960S ONWARDS: ELECTRON DENSITY FUNCTIONAL THEORY 1414 2000S ONWARDS: EXPLICITLY NON-LOCAL DENSITY FUNCTIONALS FOR DISPERSION INTERACTIONS 1415 TIME DEPENDENT DENSITY FUNCTIONAL THEORY AND INTERMOLECULAR DISPERSION ENERGY 1416 1990S ONWARDS: SYMMETRY ADAPTED PERTURBATION THEORY 1417 21ST CENTURY: MODERN APPROACHES TO PAIRWISE ADDITIVE VDW ANALYSIS 1418 21ST CENTURY: QUALITATIVE FAILURE OF PAIRWISE VDW ADDITIVITY IN POLARISABLE AND LOW-DIMENSIONAL SYSTEMS 1419 21ST CENTURY: RANDOM PHASE APPROXIMATION AND RELATED CORRELATION CALCULATIONS OF DISPERSION ENERGY 1420 2010S: “MANY BODY DISPERSION” 15 DIRECT EXPERIMENTAL MEASUREMENT OF DISPERSION FORCES 16 INDIRECT MEASUREMENTS OF VDW BINDING 17 NOMENCLATURE REFERENCES CHAPTER 2 BASIC CONCEPTS FROM TOY MODELS 21 ELECTROSTATIC INTERACTION BETWEEN PERMANENT DIPOLES 22 THE ELECTROSTATIC INDUCTION INTERACTION 23 QUANTUM AND THERMAL DIPOLE-MOMENT FLUCTUATIONS IN AN ISOLATED SYSTEM THAT HAS NO PERMANENT DIPOLE 24 SIMPLEST MODEL OF THE VAN DER WAALS/DISPERSION ENERGY: INDUCTION INTERACTION DUE TO TRANSIENT DIPOLES 25 LONDON FORMULA 26 VDW INTERACTION FROM ZERO-POINT ENERGY OF COUPLED OSCILLATORS 27 PHYSICAL UNDERSTANDING FROM THE TRANSIENT DIPOLE AND COUPLED OSCILLATOR MODELS 28 PAULI REPULSION 29 HIGHER TERMS MODIFYING THE R?6 DISPERSION INTERACTION 210 ELECTROMAGNETIC RETARDATION 211 THE FEYNMAN APPROACH TO VAN DER WAALS FORCES 212 DISPERSION INTERACTIONS FOR LARGER SYSTEMS – PAIRWISE ADDITIVE APPROACH 213 EFFECTS BEYOND PAIRWISE ADDITIVITY 214 DISPERSION INTERACTIONS FOR LARGER SYSTEMS: MACROSCOPIC METHODS 215 DIELECTRIC CONTRAST AS THE DRIVER OF MACROSCOPIC VDW INTERACTIONS 216 ATTRACTIVE AND REPULSIVE DISPERSION INTERACTIONS 2161 REPULSIVE INTERACTIONS WITH EXCITED MOLECULES 2162 REPULSIVE INTERACTIONS FROM NEGATIVE DIELECTRIC CONTRAST 2163 REPULSIVE INTERACTION FROM ELECTROMAGNETIC RETARDATION 2164 SUMMARY OF REPULSIVE DISPERSION INTERACTIONS 217 FINITE TEMPERATURE EFFECTS 218 ENTROPIC FORCES AND HYDROPHOBIC INTERACTIONS CHAPTER 3 MACROSCOPIC LIFSHITZ APPROACH 31 THE MACROSCOPIC APPROACH TO VDW FORCES: LIFSHITZ THEORY AND EXTENSIONS 32 DERIVATION OF THE T = 0 K, NON-RETARDED LIFSHITZ THEORY FROM ZERO-POINT ENERGIES 321 INFINITELY THICK SLABS: THE LIFSHITZ CASE 33 ANALYTIC DISPERSION ENERGY FOR THICK SLABS OF A MODEL METAL OR INSULATOR 34 GENERAL FORMULATION AS A FREQUENCY INTEGRAL 35 GENERALISATION TO T ? 0 K WITHOUT RETARDATION 36 GENERALISATION TO THE ELECTROMAGNETICALLY RETARDED CASE 37 THE ORIGINAL DERIVATIONS OF LIFSHITZ AND OF DZYALOSHINSKY ET AL 38 APPROXIMATE EXTENSION TO OTHER GEOMETRIES 39 ACCURATE TREATMENT OF MACROSCOPIC OBJECTS IN NON-PLANAR GEOMETRIES WITHIN QUANTUM ELECTRODYNAMICS CHAPTER 4 SUPERMOLECULAR WAVEFUNCTION METHODS 41 GENERAL CONSIDERATIONS 42 BASIS SET ISSUES 421 BASIS SET EXTRAPOLATION 422 EXPLICIT CORRELATION 423 BASIS SETS AND INTERMOLECULAR INTERACTIONS 43 WAVEFUNCTION METHODS AND INTERMOLECULAR INTERACTIONS 44 HARTREE–FOCK 441 THEORETICAL FOUNDATIONS 442 ORBITAL LOCALISATION AND SIZE-CONSISTENCY 443 LONG-RANGE INTERACTIONS 444 PAIR DENSITY AND FERMI CORRELATION 45 CONFIGURATION INTERACTION 451 THEORETICAL FOUNDATIONS 452 DISPERSION INTERACTIONS IN CI 453 SIZE-CONSISTENCY 46 MØLLER–PLESSET PERTURBATION THEORY 461 THEORETICAL FOUNDATIONS 463 HIGHER-ORDER MPPT 464 MP2 MODIFICATIONS 47 COUPLED-CLUSTER THEORY 471 THEORETICAL FOUNDATIONS 472 SIZE-CONSISTENCY 473 DISPERSION INTERACTIONS IN CCD 474 CCSD(T) AND INTERMOLECULAR INTERACTIONS 475 LOCAL CC CORRELATION 48 QUANTUM MONTE CARLO CHAPTER 5 INTERMOLECULAR PERTURBATION THEORY 51 INTERMOLECULAR PERTURBATION THEORY 511 POLARISATION APPROXIMATION 512 INTERACTION ENERGIES FROM MOLECULAR PROPERTIES, GENERALISED CASIMIR–POLDER FORMULA 513 MULTIPOLE EXPANSIONS 514 CONVERGENCE ISSUES 52 SYMMETRY-ADAPTED PERTURBATION THEORY 521 HEITLER–LONDON INTERACTION ENERGY 522 SYMMETRISED RAYLEIGH–SCHRÖDINGER PERTURBATION THEORY 523 IMPLEMENTATION OF SAPT 524 MODIFICATIONS AND EXTENSIONS OF SAPT CHAPTER 6 ADIABATIC CONNECTION, FLUCTUATION–DISSIPATION APPROACH: RPA AND RELATED CORRELATION ENERGY METHODS 61 ACFD: GROUNDSTATE EXCHANGE AND CORRELATION ENERGIES FROM THE DENSITY RESPONSE 62 THE RANDOM PHASE APPROXIMATION AND ITS VARIOUS VERSIONS 63 EXPANSION OF ?DRPA IN POWERS OF THE PAIR POTENTIAL W 64 FEYNMAN DIAGRAMS FOR THE EXPANSION OF ?DRPA 65 THE DIRECT RPA (DRPA) ENERGY: ACFD WITH TIME- DEPENDENT HARTREE RESPONSE 66 DRPA CORRELATION ENERGY AS A SUM OF ZERO POINT ENERGIES 67 EXPANSION OF THE DRPA ENERGY IN POWERS OF THE PAIR POTENTIAL W: FEYNMAN ENERGY DIAGRAMS 68 DRPA ENERGY BETWEEN TWO SEPARATED SYSTEMS 681 EXAMPLE: PLANAR GEOMETRY 682 RELATIONSHIP BETWEEN DRPA AND LIFSHITZ FOR THE TWO-SLAB PROBLEM 69 SCHEMES FOR EVALUATION OF EDRPA C 610 STERNHEIMER METHOD VERSUS SUM OVER EXCITED ORBITALS 611 DIELECTRIC EIGENFUNCTIONS AND EIGENVALUES 612 PLANE WAVE METHODS FOR DRPA 613 IMPLEMENTATION OF DRPA ENERGY IN LOCALISED CHEMICAL BASIS SETS 614 SUCCESSES OF DRPA 6141 SEAMLESSNESS 6142 GOOD RESULTS WITH SMALL-GAP AND METALLIC SYSTEMS 6143 SIZE CONSISTENCY 6144 CASIMIR–POLDER SIZE CONSISTENCY 6145 GEOMETRY AND ENERGETICS OF 3D CRYSTALS 6146 GEOMETRY AND ENERGETICS OF LAYERED SYSTEMS 6147 USES AS A BENCHMARK 615 DISEASES OF THE DRPA 6151 OVERESTIMATION OF TOTAL CORRELATION ENERGY 6152 BETTER DRPA PERFORMANCE FOR ENERGY DIFFERENCES 6153 DRPA TENDS TO UNDER-ESTIMATE RELEVANT ENERGY DIFFERENCES SLIGHTLY 6154 UNPHYSICAL ONE-ELECTRON SELF-INTERACTION 6155 AMBIGUOUS STARTING ORBITALS 616 RPA+, A SHORT-RANGED CORRECTION TO DRPA 617 RPAX 618 BEYOND THE DRPA VIA EXCHANGE-CORRELATION KERNELS 6181 ADIABATIC LDA 6182 CONCEPT OF AN ENERGY-OPTIMISED KERNEL 6183 KERNEL OF JUNG ET AL 6184 PGG KERNEL 6185 KERNEL OF OLSEN, THYGESEN AND PATRICK 6186 KERNEL OF BATES, LARICCHIA AND RUZSINSZKY 6187 CASIMIR POLDER SIZE CONSISTENCY WITH ACFD/FXC 6188 DOES FXC HAVE AN ULTRA-LONG-RANGED DEPENDENCE ON THE GROUNDSTATE DENSITY? 619 SOSEX 620 BEYOND-RPA EFFECTS AS A PERTURBATION TO DRPA 621 ISTLS 622 RANGE SEPARATION 623 OTHER CONCEPTIONS OF RPA CHAPTER 7 DISPERSION ENERGY FROM GROUNDSTATE ELECTRON “DENSITIES” ?( R?), ??( R?), ?( R?), ETC: EXPLICIT FUNCTIONALS 71 INTRODUCTION 72 LACK OF ASYMPTOTIC DISPERSION ENERGY IN LDA AND OTHER SEMI-LOCAL FUNCTIONALS 73 “SHORT TO MID-RANGE VDW”: PERFORMANCE OF LOCAL AND SEMI-LOCAL FUNCTIONALS 731 GORDON–KIM APPROACH 732 HARRIS FUNCTIONAL 733 KOHN–SHAM EQUATIONS WITH CONSTRAINED ELECTRON DENSITY 734 LDA AND DISPERSION 735 GGAS FOR MID-RANGE DISPERSION 736 META-GGAS FOR MEDIUM-RANGE DISPERSION 74 NEED FOR FULLY NON-LOCAL DENSITY FUNCTIONALS 75 LDA ENERGY FROM A PARTIALLY LOCAL APPROXIMATION FOR INTERACTING ? 76 REQUIREMENTS FOR OBTAINING VDW FUNCTIONALS VIA ACFD WITH APPROXIMATE RESPONSE 77 LIFSHITZ ENERGY FROM A LOCAL APPROXIMATION FOR ? OR ? 78 RA, ALL AND DD FUNCTIONALS: VDW ENERGY FROM A LOCAL APPROXIMATION FOR ?SCR XVII CONTENTS 79 THE CONCEPT OF A “SEAMLESS” VAN DER WAALS FUNCTIONAL 710 FUNCTIONAL OF DOBSON AND WANG: RPA-VDW ENERGY FROM LOCAL APPROXIMATION FOR ?KS 711 FUNCTIONAL OF RYDBERG ET AL FOR LAYERED SYSTEMS: CONTINUOUS LOCAL APPROXIMATION FOR ? 712 VDW-DF: SEMI-LOCAL APPROXIMATION FOR ?SCR AFTER PERTURBATIVE COULOMB TREATMENT 7121 FEATURES OF VDW-DF 713 VYDROV–VAN VOORHIS VDW FUNCTIONAL 714 SCAN–RVV10 FUNCTIONAL CHAPTER 8 DISPERSION ENERGIES VIA DIVISION INTO ATOMS OR LARGER UNITS 81 INTRODUCTION 82 LENNARD-JONES SUMMATION AND RELATED APPROACHES 821 SIMPLEST PAIRWISE APPROACH 822 BETTER EMPIRICAL TREATMENT OF NEAR- AND MID-RANGE INTERACTIONS 823 HIGHER ORDER MULTIPOLE CONTRIBUTIONS 83 ATOM-BASED PAIRWISE ADDITIVE DISPERSION TERMS AS A CORRECTION TO LDA, AND TO SEMI-LOCAL DENSITY FUNCTIONAL CALCULATIONS 831 DFT + D APPROACHES 84 THREE-UNIT INTERACTIONS IN THE GRIMME D3(ABC) METHOD 85 BRINGING IN THE DENSITY: XDM, TS AND DDSC 851 KEY APPROACHES 852 TKATCHENKO–SCHEFFLER APPROACH 853 XDM APPROACH 854 DDSC CORRECTION 86 MANY-UNIT THEORIES: BEYOND PAIRWISE SUMMATION 87 BEYOND PAIRWISE SUMMATION: GENERAL CONSIDERATIONS 871 TYPE A NON-ADDITIVITY (ORBITAL DEFORMATION) 872 TYPE B NON-ADDITIVITY (SCREENING BY SPECTATOR UNITS) 873 TYPE C NON-ADDITIVITY (INTER-UNIT ELECTRON HOPPING) 874 TYPE C POWER LAWS IN SMALL-GAP SYSTEMS 875 PERFORMANCE OF COMMON VDW FORMALISMS IN DESCRIBING TYPES A, B, C NON-ADDITIVITY 88 COLLECTIVE TYPE B DISPERSION PHYSICS – “MANY-BODY DISPERSION” (MBD) 881 VARIANTS OF MBD 89 EXPERIMENTAL VERIFICATION OF NON-PAIRWISE ADDITIVITY CHAPTER 9 SOME CHEMICAL EFFECTS OF DISPERSION INTERACTIONS 91 INTERMOLECULAR INTERACTIONS 911 ALKANE DIMERS 912 DIMERS OF AROMATICS 913 ENERGETICS OF OTHER VDW DIMERS 92 INTRAMOLECULAR DISPERSION INTERACTIONS 921 THERMODYNAMIC STABILITY OF ALKANES 922 STERIC HINDRANCE VERSUS LONDON DISPERSIVE ATTRACTION 923 VDW EFFECTS ON REACTION INTERMEDIARIES 93 AUROPHILIC AND METALLOPHILIC INTERACTIONS 94 CAT-CRACKING CHAPTER 10 PERIODIC SOLIDS 101 “NORMAL” STRONGLY BOUND SOLIDS 102 RARE GAS CRYSTALS 103 MOLECULAR CRYSTALS 1031 MOLECULAR CRYSTALS IN DFT+D 1032 POLYMORPHISM IN MOLECULAR CRYSTALS 104 LAYERED SOLIDS CHAPTER 11 LOW-DIMENSIONAL SYSTEMS: NANOLAYERS, NANOTUBES, NANOWIRES, ETC 111 INTRODUCTION TO LAYERED SYSTEMS 112 LAYERED MATERIALS: GRAPHENE, GRAPHITE AND BEYOND 113 MODELLING THE ENERGETICS OF LAYERED SOLIDS NEAR THEIR EQUILIBRIUM LAYER SPACING 114 “UNIVERSAL” GRAPHITIC POTENTIAL 115 DESCRIBING LAYERED SOLIDS BEYOND LENNARD- JONES APPROACHES 116 DISPERSION INTERACTIONS BETWEEN DISTANT PARALLEL 2D LAYERS 1161 SIMPLEST TREATMENT OF A 2D METAL 1162 VDW INTERACTION BETWEEN 2D INSULATORS 1163 SIMPLEST TREATMENT OF UNDOPED GRAPHENE AT T = 0 K 117 “LAYER RESPONSE THEORY”: SEMI-ANALYTIC BINDING CURVES FROM ASYMPTOTICS DOWN TO INTER-LAYER CONTACT 1171 THE SPECIAL CASE OF GRAPHENE 118 CAN LIFSHITZ THEORY WORK IN NANO-THIN LAYERED SYSTEMS NEAR EQUILIBRIUM SPACING? 119 FULLERENES (“BUCKY BALLS”) 1110 1D SYSTEMS 1111 1D STRUCTURES IN PAIRWISE-ADDITIVE THEORY 11111 TELESCOPED MULTIWALLED NANOTUBES 11112 WELL-SEPARATED LONG PARALLEL WIRES IN PAIRWISE ADDITIVE THEORY 11113 COLLINEAR NON-CONTACTING WIRES IN PAIRWISE ADDITIVE THEORY 1112 INFINITE PARALLEL CONDUCTING WIRES IN RPA 1113 HIGHER LEVEL THEORIES FOR 1D CONDUCTORS IN OTHER GEOMETRIES 1114 ZERO-DIMENSIONAL GAPLESS SYSTEMS? 1115 SUMMARY OF LOW-DIMENSIONAL SYSTEMS CHAPTER 12 INTERACTION OF MOLECULES WITH SURFACES AND LAYERS 121 ANALYTIC ATOM–SUBSTRATE DISPERSION INTERACTION IN THE ASYMPTOTIC REGIME 122 THE DIFFICULTIES IN PREDICTING ADSORPTION PHYSICS 123 AN ILLUSTRATION OF THE CHALLENGE 124 MOLECULES ON BULK SURFACES AND LAYERS 1241 OTHER SURFACES WORK 125 POROUS SURFACES–MOFS AND ZEOLITES 1251 SOLVENT EFFECTS CHAPTER 13 SUMMARY OF RECOMMENDED METHODS 131 LIFSHITZ-BASED APPROACHES 132 RECOMMENDATIONS FOR HIGH ACCURACY/COST 1321 SMALL MOLECULES AND ATOMS 1322 LARGE MOLECULES 1323 SOLIDS 1324 SURFACES 1325 THE NEAR FUTURE? 133 RECOMMENDATIONS FOR MEDIUM ACCURACY/COST 1331 SMALL MOLECULES AND ATOMS 1332 LARGE MOLECULES AND SURFACES 134 RECOMMENDATIONS FOR LOW ACCURACY/COST 1341 SMALL MOLECULES AND ATOMS 1342 LARGE MOLECULES 1343 SOLIDS 1344 SURFACES 135 A FINAL NOTE