THE QUANTUM THEORY OF ATOMS IN MOLECULES

By STEVEN MILLER

CONTENTS AN INTRODUCTION TO THE QUANTUM THEORY OF ATOMS IN MOLECULES INTRODUCTION THE TOPOLOGY OF THE ELECTRON DENSITY THE TOPOLOGY OF THE ELECTRON DENSITY DICTATES THE FORM OF ATOMS IN MOLECULES THE BOND AND VIRIAL PATHS, AND THE MOLECULAR AND VIRIAL GRAPHS THE ATOMIC PARTITIONING OF MOLECULAR PROPERTIES THE NODAL SURFACE IN THE LAPLACIAN AS THE REACTIVE SURFACE OF A MOLECULE BOND PROPERTIES THE ELECTRON DENSITY AT THE BCP (RB) THE BONDED RADIUS OF AN ATOM (RB), AND THE BOND PATH LENGTH THE LAPLACIAN OF THE ELECTRON DENSITY AT THE BCP (‘2 RB) THE BOND ELLIPTICITY (E) ENERGY DENSITIES AT THE BCP ELECTRON DELOCALIZATION BETWEEN BONDED ATOMS: A DIRECT MEASURE OF BOND ORDER ATOMIC PROPERTIES ATOMIC ELECTRON POPULATION [N(W)] AND CHARGE [Q(W)] ATOMIC VOLUME [VOL (W)] KINETIC ENERGY [T(W)] LAPLACIAN [L(W)] TOTAL ATOMIC ENERGY [EE(W)] ATOMIC DIPOLAR POLARIZATION [M(W)] ATOMIC QUADRUPOLAR POLARIZATION [Q(W)] ‘‘PRACTICAL’’ USES AND UTILITY OF QTAIM BOND AND ATOMIC PROPERTIES THE USE OF QTAIM BOND CRITICAL POINT PROPERTIES THE USE OF QTAIM ATOMIC PROPERTIES STEPS OF A TYPICAL QTAIM CALCULATION REFERENCES PART I ADVANCES IN THEORY THE LAGRANGIAN APPROACH TO CHEMISTRY FROM OBSERVATION, TO PHYSICS, TO QTAIM THE LAGRANGIAN APPROACH WHAT IS THE LAGRANGIAN APPROACH AND WHAT DOES IT DO? THE LAGRANGIAN AND THE ACTION PRINCIPLE – A RETURN TO THE BEGINNINGS MINIMIZATION OF THE ACTION STEPS IN MINIMIZING THE ACTION THE ACTION PRINCIPLE IN QUANTUM MECHANICS SCHRO¨DINGER’S APPEAL TO THE ACTION SCHRO¨DINGER’S MINIMIZATION TWO WAYS OF EXPRESSING THE KINETIC ENERGY OBTAINING AN ATOM FROM SCHRO¨DINGER’S VARIATION THE ROLE OF LAPLACIAN IN THE DE?NITION OF AN ATOM GETTING CHEMISTRY FROM DG(C,‘C; W) FROM SCHRO¨DINGER TO SCHWINGER FROM DIRAC TO FEYNMAN AND SCHWINGER FROM SCHWINGER TO AN ATOM IN A MOLECULE MOLECULAR STRUCTURE AND STRUCTURAL STABILITY DE?NITION OF MOLECULAR STRUCTURE PREDICTION OF STRUCTURAL STABILITY RE?ECTIONS AND THE FUTURE RE?ECTIONS THE FUTURE ATOMIC RESPONSE PROPERTIES APPARENT ORIGIN-DEPENDENCE OF SOME ATOMIC RESPONSE PROPERTIES BOND CONTRIBUTIONS TO ‘‘NULL’’ MOLECULAR PROPERTIES BOND CONTRIBUTIONS TO ATOMIC CHARGES IN NEUTRAL MOLECULES ATOMIC CONTRIBUTIONS TO ELECTRIC DIPOLE MOMENTS OF NEUTRAL MOLECULES ATOMIC CONTRIBUTIONS TO ELECTRIC POLARIZABILITIES ATOMIC CONTRIBUTIONS TO VIBRATIONAL INFRARED ABSORPTION INTENSITIES ATOMIC NUCLEAR VIRIAL ENERGIES ATOMIC CONTRIBUTIONS TO INDUCED ELECTRONIC MAGNETIC DIPOLE MOMENTS ATOMIC CONTRIBUTIONS TO MAGNETIZABILITIES OF CLOSED-SHELL MOLECULES QTAIM ANALYSIS OF RAMAN SCATTERING INTENSITIES: INSIGHTS INTO THE RELATIONSHIP BETWEEN MOLECULAR STRUCTURE AND ELECTRONIC CHARGE FLOW BACKGROUND TO THE PROBLEM CONCEPTUAL APPROACH TO A SOLUTION EXPERIMENTAL MEASUREMENT OF RAMAN SCATTERING INTENSITIES THEORETICAL MODELING OF RAMAN SCATTERING INTENSITIES: WHAT WE DID AND WHY METHODOLOGY MODELING A AND QA/QR RECOUPING A FROM THE WAVEFUNCTION, WITH QTAIM RECOVERING QA/QR FROM QTAIM SPECI?C EXAMPLES OF THE USE OF AIM2000 SOFTWARE TO ANALYZE RAMAN INTENSITIES ADDITIONAL EXERCISES FOR THE INTERESTED READER PATTERNS IN A THAT ARE DISCOVERED THROUGH QTAIM PATTERNS IN QA/QRCH THAT APPLY ACROSS DI?ERENT STRUCTURES, CONFORMATIONS, MOLECULAR TYPES: WHAT IS TRANSFERABLE? PATTERNS IN DA/DRCH REVEALED BY QTAIM QTAIM ANALYSIS OF DA/DRCH IN SMALL ALKANES WHAT DID WE LEARN FROM QTAIM THAT CAN BE TRANSFERRED TO THE OTHER MOLECULES? WHAT CAN WE DEDUCE FROM SIMPLE INSPECTION OF QA/QRCH AND QA/QRCC FROM GAUSSIAN? VARIATIONS IN QA/QRCH AMONG THE ALKANES DA/DRCH IN CYCLOALKANES, BICYCLOALKANES, AND HEDRANES PATTERNS THAT EMERGE IN DA/DRCC OF ALKANES UNSATURATED HYDROCARBONS AND THE SILANES: CAH, CBC, AND SIASI DERIVATIVES CONCLUSION TOPOLOGICAL ATOM–ATOM PARTITIONING OF MOLECULAR EXCHANGE ENERGY AND ITS MULTIPOLAR CONVERGENCE THEORETICAL BACKGROUND DETAILS OF CALCULATIONS RESULTS AND DISCUSSION CONVERGENCE OF THE EXCHANGE ENERGY CONVERGENCE OF THE EXCHANGE FORCE DIAGONALIZATION OF A MATRIX OF EXCHANGE MOMENTS THE ELF TOPOLOGICAL ANALYSIS CONTRIBUTION TO CONCEPTUAL CHEMISTRY AND PHENOMENOLOGICAL MODELS WHY ELF AND WHAT IS ELF? CONCEPTS FROM THE ELF TOPOLOGY THE SYNAPTIC ORDER THE LOCALIZATION DOMAINS ELF POPULATION ANALYSIS VSEPR ELECTRON DOMAINS AND THE VOLUME OF ELF BASINS EXAMPLES OF THE CORRESPONDENCE BETWEEN ELF BASINS AND THE DOMAINS OF THE VSEPR MODEL OCTET MOLECULES HYDRIDES (CH4, NH3, H2O) AX4 (CH4, CF4, SICL4) AX3E AND AX2E2 (NCL3, OCL2) HYPERVALENT MOLECULES AX7 AND AX6E MOLECULES MULTIPLE BONDS CONCLUSIONS PART II SOLID STATE AND SURFACES SOLID STATE APPLICATIONS OF QTAIM AND THE SOURCE FUNCTION – MOLECULAR CRYSTALS, SURFACES, HOST–GUEST SYSTEMS AND MOLECULAR COMPLEXES QTAIM APPLIED TO SOLIDS – THE TOPOND PACKAGE QTAIM APPLIED TO EXPERIMENTAL DENSITIES: TOPXD AND XD PACKAGES QTAIM APPLIED TO MOLECULAR CRYSTALS UREA UREA: PACKING E?ECTS QTAIM APPLIED TO SURFACES SI(111)(1 1) CLEAN AND HYDROGEN-COVERED SURFACES SI(111)(2 1) RECONSTRUCTED SURFACE QTAIM APPLIED TO HOST–GUEST SYSTEMS TYPE I INORGANIC CLATHRATES A8GA16GE30 (A ¼ SR, BA) SODIUM ELECTROSODALITE THE SOURCE FUNCTION: THEORY THE SOURCE FUNCTION AND CHEMICAL TRANSFERABILITY CHEMICAL INFORMATION FROM THE SOURCE FUNCTION: LONG AND SHORT-RANGE BONDING E?ECTS IN MOLECULAR COMPLEXES THE SOURCE FUNCTION: LATEST DEVELOPMENTS TOPOLOGY AND PROPERTIES OF THE ELECTRON DENSITY IN SOLIDS THE ELECTRON DENSITY TOPOLOGY AND THE ATOMIC BASIN SHAPE CRYSTALLINE ISOSTRUCTURAL FAMILIES AND TOPOLOGICAL POLYMORPHISM TOPOLOGICAL CLASSI?CATION OF CRYSTALS BOND PROPERTIES – CONTINUITY FROM THE MOLECULAR TO THE CRYSTALLINE REGIME BASIN PARTITION OF THE THERMODYNAMIC PROPERTIES OBTAINING THE ELECTRON DENSITY OF CRYSTALS ATOMS IN MOLECULES THEORY FOR EXPLORING THE NATURE OF THE ACTIVE SITES ON SURFACES IMPLEMENTING THE DETERMINATION OF THE TOPOLOGICAL PROPERTIES OF R(R) FROM A THREE-DIMENSIONAL GRID AN APPLICATION TO NANOCATALYTS – EXPLORING THE STRUCTURE OF THE HYDRODESULFURIZATION MOS2 CATALYSTS CATALYST MODELS THE FULL R(R) TOPOLOGY OF THE MOS2 BULK THE R(R) TOPOLOGY OF THE MOS2 EDGES PART III EXPERIMENTAL ELECTRON DENSITIES AND BIOLOGICAL MOLECULES INTERPRETATION OF EXPERIMENTAL ELECTRON DENSITIES BY COMBINATION OF THE QTAMC AND DFT SPECI?CITY OF THE EXPERIMENTAL ELECTRON DENSITY APPROXIMATE ELECTRONIC ENERGY DENSITIES KINETIC AND POTENTIAL ENERGY DENSITIES EXCHANGE AND CORRELATION ENERGY DENSITIES THE INTEGRATED ENERGY QUANTITIES CONCLUDING REMARKS TOPOLOGICAL ANALYSIS OF PROTEINS AS DERIVED FROM MEDIUM AND HIGH- RESOLUTION ELECTRON DENSITY: APPLICATIONS TO ELECTROSTATIC PROPERTIES METHODOLOGY AND TECHNICAL DETAILS ULTRA-HIGH X-RAY RESOLUTION APPROACH MEDIUM-RESOLUTION APPROACH 11 2 2 1 PROMOLECULAR ELECTRON DENSITY DISTRIBUTION CALCULATED FROM STRUCTURE FACTORS 11 2 2 2 PROMOLECULAR ELECTRON DENSITY DISTRIBUTION CALCULATED FROM ATOMS A TEST SYSTEM – HUMAN ALDOSE REDUCTASE TOPOLOGICAL PROPERTIES OF MULTIPOLAR ELECTRON DENSITY DATABASE ANALYSIS OF LOCAL MAXIMA IN EXPERIMENTAL AND PROMOLECULAR MEDIUM- RESOLUTION ELECTRON DENSITY DISTRIBUTIONS EXPERIMENTAL AND PROMOLECULAR ELECTRON DENSITY DISTRIBUTIONS CALCULATED FROM STRUCTURE FACTORS PROMOLECULAR ELECTRON DENSITY DISTRIBUTIONS CALCULATED FROM ATOMS (PASA MODEL) CALCULATION OF ELECTROSTATIC PROPERTIES FROM ATOMIC AND FRAGMENT REPRESENTATIONS OF HUMAN ALDOSE REDUCTASE MEDIUM- AND HIGH-RESOLUTION APPROACHES OF ELECTROSTATIC POTENTIAL COMPUTATIONS ELECTROSTATIC POTENTIAL COMPARISONS ELECTROSTATIC INTERACTION ENERGIES CONCLUSIONS AND PERSPECTIVES FRAGMENT TRANSFERABILITY STUDIED THEORETICALLY AND EXPERIMENTALLY WITH QTAIM – IMPLICATIONS FOR ELECTRON DENSITY AND INVARIOM MODELING EXPERIMENTAL ELECTRON-DENSITY STUDIES EXPERIMENTAL REQUIREMENTS RECENT EXPERIMENTAL ADVANCES 12 2 2 1 SYNCHROTRON RADIATION COMPARED WITH LABORATORY SOURCES 12 2 2 2 DATA COLLECTION AT ULTRA-LOW TEMPERATURES (10–20 K) STUDYING TRANSFERABILITY WITH QTAIM – ATOMIC AND BOND TOPOLOGICAL PROPERTIES OF AMINO ACIDS AND OLIGOPEPTIDES INVARIOM MODELING INVARIOM NOTATION, CHOICE OF MODEL COMPOUNDS, AND PRACTICAL CONSIDERATIONS SUPPORT FOR PSEUDOATOM FRAGMENTS FROM QTAIM APPLICATIONS OF ASPHERICAL INVARIOM SCATTERING FACTORS MOLECULAR GEOMETRY AND ANISOTROPIC DISPLACEMENT PROPERTIES USING THE ENHANCED MULTIPOLE MODEL ANOMALOUS DISPERSION SIGNAL MODELING THE ELECTRON DENSITY OF OLIGOPEPTIDE AND PROTEIN MOLECULES PART IV CHEMICAL BONDING AND REACTIVITY INTERACTIONS INVOLVING METALS – FROM ‘‘CHEMICAL CATEGORIES’’ TO QTAIM, AND BACKWARDS THE ELECTRON DENSITY IN ISOLATED METAL ATOMS – HINTS OF ANOMALIES TWO-CENTER BONDING THE DATIVE BOND 13 3 1 1 METAL CARBONYLS 13 3 1 2 DONOR–ACCEPTOR INTERACTIONS OF HEAVY ELEMENTS DIRECT METAL–METAL BONDING THREE-CENTER BONDING P-COMPLEXES S-COMPLEXES 13 4 2 1 DIHYDROGEN AND DIHYDRIDE COORDINATION 13 4 2 2 AGOSTIC INTERACTIONS 13 4 2 3 HYDRIDE BRIDGES CARBONYL-SUPPORTED METAL–METAL INTERACTIONS APPLICATIONS OF THE QUANTUM THEORY OF ATOMS IN MOLECULES IN ORGANIC CHEMISTRY – CHARGE DISTRIBUTION, CONFORMATIONAL ANALYSIS AND MOLECULAR INTERACTIONS ELECTRON DELOCALIZATION THE PAIR-DENSITY 3JHH COUPLING CONSTANTS AND ELECTRON DELOCALIZATION CONFORMATIONAL EQUILIBRIA ROTATIONAL BARRIERS 14 3 1 1 ROTATIONAL BARRIER OF ETHANE 14 3 1 2 ROTATIONAL BARRIER OF 1,2-DISUBSTITUTED ETHANES ANOMERIC E?ECT ON HETEROCYCLOHEXANES AROMATIC MOLECULES ELECTRONIC STRUCTURE OF POLYBENZENOID HYDROCARBONS AROMATICITY ANALYSIS BY MEANS OF THE QUANTUM THEORY OF ATOMS IN MOLECULES THE FERMI HOLE AND THE DELOCALIZATION INDEX ELECTRON DELOCALIZATION IN AROMATIC SYSTEMS AROMATICITY ELECTRONIC CRITERIA BASED ON QTAIM THE PARA-DELOCALIZATION INDEX (PDI) THE AROMATIC FLUCTUATION INDEX (FLU) THE P-FLUCTUATION AROMATIC INDEX (FLUP) APPLICATIONS OF QTAIM TO AROMATICITY ANALYSIS AROMATICITY OF BUCKYBOWLS AND FULLERENES E?ECT OF SUBSTITUENTS ON AROMATICITY ASSESSMENT OF CLAR’S AROMATIC P-SEXTET RULE AROMATICITY ALONG THE DIELS–ALDER REACTION THE FAILURE OF SOME AROMATICITY INDEXES TOPOLOGICAL PROPERTIES OF THE ELECTRON DISTRIBUTION IN HYDROGEN-BONDED SYSTEMS TOPOLOGICAL PROPERTIES OF THE HYDROGEN BOND TOPOLOGICAL PROPERTIES AT THE BOND CRITICAL POINT (BCP) INTEGRATED PROPERTIES ENERGY PROPERTIES AT THE BOND CRITICAL POINT (BCP) TOPOLOGICAL PROPERTIES AND INTERACTION ENERGY ELECTRON LOCALIZATION FUNCTION, H(R) COMPLETE INTERACTION RANGE DEPENDENCE OF TOPOLOGICAL AND ENERGY PROPERTIES ON THE INTERACTION DISTANCE PERTURBED SYSTEMS RELATIONSHIPS BETWEEN QTAIM AND THE DECOMPOSITION OF THE INTERACTION ENERGY – COMPARISON OF DI?ERENT KINDS OF HYDROGEN BOND DIVERSITY OF HYDROGEN-BONDING INTERACTIONS THE DECOMPOSITION OF THE INTERACTION ENERGY RELATIONSHIPS BETWEEN THE TOPOLOGICAL AND ENERGY PROPERTIES OF HYDROGEN BONDS VARIOUS OTHER INTERACTIONS RELATED TO HYDROGEN BONDS HÞP INTERACTIONS HYDRIDE BONDS SUMMARY PART V APPLICATION TO BIOLOGICAL SCIENCES AND DRUG DESIGN QTAIM IN DRUG DISCOVERY AND PROTEIN MODELING QSAR AND DRUG DISCOVERY ELECTRON DENSITY AS THE BASIC VARIABLE ATOM TYPING SCHEME AND GENERATION OF THE TRANSFERABLE ATOM EQUIVALENT (TAE) LIBRARY TAE RECONSTRUCTION AND DESCRIPTOR GENERATION QTAIM-BASED DESCRIPTORS TAE DESCRIPTORS RECON AUTOCORRELATION DESCRIPTORS PEST SHAPE–PROPERTY HYBRID DESCRIPTORS ELECTRON DENSITY-BASED MOLECULAR SIMILARITY ANALYSIS SAMPLE APPLICATIONS QSAR/QSPR WITH TAE DESCRIPTORS PROTEIN MODELING WITH TAE DESCRIPTORS FLESHING-OUT PHARMACOPHORES WITH VOLUME RENDERING OF THE LAPLACIAN OF THE CHARGE DENSITY AND HYPERWALL VISUALIZATION TECHNOLOGY COMPUTATIONAL AND VISUALIZATION METHODS COMPUTATIONAL DETAILS VOLUME RENDERING OF THE LAPLACIAN OF THE CHARGE DENSITY THE HYPERWALL HYPER-INTERACTIVE MOLECULAR VISUALIZATION SUBATOMIC PHARMACOPHORE INSIGHTS HYDROGEN-BONDING DONOR SITES INNER-VALENCE SHELL CHARGE CONCENTRATION (I-VSCC) FEATURES IN TRANSITION-METAL ATOMS MISDIRECTED VALENCE IN THE LIGAND SPHERE OF TRANSITION-METAL COMPLEXES