O THEORETICAL AND COMPUTATIONAL CHEMISTRY

Molecular Electrostatic Potentials Concepts and Applications

Edited by

Jane S. Murray

Department of Chemistry University of New Orleans

New Orleans, LA 70148, USA

Kalidas Sen

School of Chemistry University of Hyderabad

Hyderabad 500 046, India

1996

ELSEVIER

Amsterdam - Lausanne - New York - Oxford - Shannon - Tokyo

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TABLE OF CONTENTS

Chapter 1. MEP: A Tool for Interpretation and Prediction. From Molecular Structure to Solvation Effects, J. Tomasi, B. Mennucci, andR. Cammi 1

1. Introduction 1 2. Thirty Years Ago: The Evolution of Chemical Quantum Theory 2 3. The Molecular Electrostatic Potential as an Interpretative Tool

for Intermolecular Interactions 7 3.1. Simplified expressions for MEP from the global

molecular wavefunction 11 3.2. A closer look at the internal structure of charge

distributions 17 3.3. Other topological analysis 20 3.4. Some comments on topological partitions 22 3.5. Partition in terms of localized Orbitals 23 3.6. Some words of commentary 33

4. Intermolecular Energy: A Füll Decomposition at HF Level 35 4.1. Counterpoise corrections to the AE composition 44 4.2. Performances of the semiclassical model in describing

non-covalent interactions 54 4.3. A molecular function for Ep^ 59

4.4. Interaction with Li+ and other cations 60 4.5. Hydrogen bond interactions 62 4.6. Nucleophilic interactions. An example of Interpretation

and prediction 64 5. Molecular Electrostatics and Semiclassical Approximation in

Solvation Effects 68 5.1. N—body interactions and the solute-solvent potential 68 5.2. Partition of the solvation free energy „ 70 5.3. Comparison of W(M/S) with AE(A.B) 70 5.4. The electrostatic free energy of M in S, Gei 74

5.5. Gei and the group partition of AGS0;. Some methodological remarks 77

5.6. The problem of large solutes and the role of properties defined on the cavity 79

5.7. Further evolution of continuum solvation modeis 85

Chapter 2. Molecular Electrostatic Potentials from Density Functional Theory, A. M. Köster, M. Lebouf, and D. R. Salahub 105

1. Introduction 105 2. Calculation of Electrostatic Observables 106

2.1. Electrostatic moments 107 2.2. Electrostatic potential 112

3. Simplified Analytic Expressions for the Molecular Electrostatic Potential 116

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3.1. The multipole expansion 116 3.2. Cumulative atomic multipole moments 117 3.3. Asymptotic Density Model 121

4. Critical Points of the Molecular Electrostatic Potential 125 4.1. Location of critical points 125 4.2. Interpretation of electronic structure 126 4.3. Prediction of reactivity 131

5. Evolution of the Molecular Electrostatic Potential During Chemical Reactions 132

5.1. [4+2] Cycloaddition of ethylene and butadiene 133 5.2. Explosive reaction in ammonium nitrate 135

6. Conclusion 137

Chapter 3. The Use of Electrostatic Potential Fields in QSAR and QSPR, C. M. Breneman and M. Martinov 143

1. Introduction 143 2. QSAR and QSPR 146 3. EP-based 3D QSAR/QSPR approaches 156 4. Conclusions 175

Chapter 4. Generalization of the Molecular Electrostatic Potential for the Study of Noncovalent Interactions, M. Orozco and F. J. Luque 181

1. Introduction 181 2. Introduction of Environment Effects in the MEP 183

2.1. Discrete environment 184 2.2. Continuum environment 186

3. Introduction of Non-Electrostatic Energy Terms in the MEP 190 3.1. The polarization contribution to the interaction energy.... 190 3.2. "Steric" contributions to the interaction energy 193

4. Future Directions 210

Chapter 5. Molecular Recognition via Electrostatic Potential Topography, S. R. Gadre, P. K. Bhadane, S. S. Pundlik, and S.S.Pingale 219

1. Introduction 219 2. Models for Weak Intermolecular Interactions 223

2.1. Legon-Miller (LM) rules 223 2.2. Buckingham and Fowler (BF) model 224 2.3. Alhambra, Luque and Orozco model 225 2.4. Molecular mechanics for Clusters by Dykstra 226

3. Topography of Molecular Scalar Fields 226 3.1. Topography of molecular electron density and

electrostatic potential 228 4. Topography-Based Molecular Interaction Model 238

4.1. Electrostatic interaction model 238 4.2. Results and discussion 239

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5. Concluding Remarks 248

Chapter 6. Molecular Electrostatic Potentials and Fields: Hydrogen Bonding, Recognition, Reactivity and Modelling, P. C. Mishra and A. Kumar 257

1. Introduction 257 2. Definitions and Methods 258 3. Charge Distribution 262

3.1. Direct calculation of charges 262 3.2. Potential-derived charges 263 3.3. Hybridization displacement charges 264 3.4. Transferability of charges 266

4. Representation of MEP and MEF 267 5. Reactivity, Hydrogen Bonding and Other Properties 268

5.1. Neutral molecules 268 5.2. Anions and cations 272 5.3. Physical properties and related aspects 276 5.4. Biopolymers: DNA and its constituents 277

6. Recognition and Modelling 278 6.1. Complementarity 278 6.2. Similarity 279 6.3. Property—activity relationship 281

Chapter 7. Molecular Electrostatic Potentials for Large Systems, M. Krack and K. Jug 297

1. Introduction 297 2. Reactivity Concepts 298

2.1. Atomic net charges 300 2.2. Cumulative atomic multipole moments 301 2.3. The asymptotic density model (ADM) 301

3. Calculation of Cumulative Atomic Multipole Moments inSINDOl 303

4. Calculation of the MESP with SINDOl 305 5. The Molecular Surface 311

5.1. Van der Waals surface 311 5.2. Solvent accessible surface 312 5.3. Isodensity surface 312

6. Silicon Clusters 312 6.1. Small Silicon Clusters 313 6.2. Medium size Silicon Clusters 318

7. Solid Silicon 322 7.1. The unreconstructed S i ( l l l ) surface 324 7.2. The reconstructed Si(lll)-(7X7) surface 324 7.3. Simulation of the S i ( l l l ) surface 325 7.4. Reactivity of the S i ( l l l ) surface 326

8. Conclusions 329

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Chapter 8. Protein Electrostatics, G. Näray-Szabo 333 1. Introduction 333 2. Methodology 334

2.1. Protein energetics 334 2.2. The protein electrostatic potential 339 2.3. Reaction field theories 348 2.4. The Poisson-Boltzmann equation 350

3. Applications 352 3.1. Side-chain protonation 353 3.2. Ligand bindüig 355 3.3. Molecular recognition 358 3.4. Enzyme catalysis 360 3.5. Redox properties 364

4. Conclusions 365

Chapter 9. The Lorentz—Debye-Sack Theory and Dielectric Screening of Electrostatic Effects in Proteins and Nucleic Acids, E. L. Mehler 371

1. Introduction 371 2. Lorentz-Debye-Sack Theory of Polar Molecules and Radial

Permittivity Profiles 374 2.1. Radial permittivity profiles in polar media 374 2.2. Reaction field effects 377 2.3. Calculation of solvation energy 380 2.4. Final remarks 381

3. Electrostatic Screening in Macromolecular Systems 382 3.1. Electrostatic effects in acid-base equilibria 382 3.2. Radial dielectric Screening in proteins and nucleic acids ... 384

4. Application of Electrostatic Screening to the Calculation of Equilibrium Properties 388

4.1. Formulation 388 4.2. Shifted equilibrium constants in native structures 389 4.3. Effect of mutations on equilibrium constants 391

5. Electrostatic Screening in Molecular Dynamics and Monte Carlo Simulations 392

5.1. Efficacy of constant and linear, distance-dependent dielectric Screening 393

5.2. Sigmoidal forms of dielectric Screening 394 6. Conclusions 400

Chapter 10. Modelling Intrinsic Basicities: The Use of the Electrostatic Potentials and the Atoms-in-Molecules Theory, M. Alcami, O. Mo and M. Yänez 407

1. Introduction 407 2. Computational Details 410 3. Carbonyl vs. Thiocarbonyl Compounds 411

3.1. Li+Association 412

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3.2. H+ and CH3+ associations 422

3.3. Changes produced by cationization 430 4. Three-Membered Rings 436

4.1. Li+ association 437 4.2. H+ association 446

5. Concluding Remarks 452

Chapter 11. Computed Electrostatic Potentials in Molecules, Clusters, Solids and Biosystems Containing Transition Metals, M. Benard 457

1. Introduction 457 2. Lattice Energy and Cluster—Lattice Interaction in

Ionic Crystals 458 2.1. Ewald-like estimates of the lattice electrostatic energy „458 2.2. Extension of Ewald-like summations to molecular ions ...459 2.3. Achemist's analysis of thecrystal structure: the

Cluster—lattice interaction 461 2.4. Electrostatic potentials as a reactivity index in the solid

State: an example [87] 466 3. Electrostatic Potentials as a Reactivity Index for Complex Ions

and Molecules 468 3.1. Limitation of MEPs as a model of bonding 468 3.2. MEPs and the reactivities of transition metal

complexes: the case of [CoCCO)^" [96] 470 3.3. Miscellaneous cases 471 3.4. From MEPs to reactivity indices 474 3.5. MEPs of polyoxometallates 481

4. Polar Molecules in Solution 492 4.1. Methods for solving the Poisson—Boltzmann equation 492 4.2. Applications to metal-containing molecules 495

5. Experimental Electrostatic Potentials 497 6. Conclusion 499

Chapter 12. Studies on the Molecular Electrostatic Potential Inside the Microporous Material and Its Relevance to their Catalytic Activity, R. Vetrivel, R. C. Deka, A. Chatterjee, M. Kubo, E. Broclawik and A. Miyamoto 509

1. Introduction 510 2. Methodology 511 3. Applications 512

3.1. Acidity determination 512 3.2. Electrostatic catalysis 513 3.3. Representation of long ränge forces in MEP 517 3.4. Host-guest complexes 519 3.5. Activity correlations 525

4. Conclusions 538

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Chapter 13. X-ray Diflfraction and the Potential Distribution in Crystals, D.Feil 543

1. Introduction 543 2. Basic Theory 546

2.1. Diflfraction 546 2.2. Thermal motion 549 2.3. Potential 551

3. Multipole Analysis 554 4. Partitioning 561

4.1. Badens gradient vector field 562 4.2. Hirshfeld's stockholder scheine 562 4.3. Multipole populations 563

5. Data Collection 564 6. Results 567

6.1. Borates 567 6.2. Silicates and zeolites 570 6.3. Molecular Compounds 572 6.4. Hydrogenbond 575

7. Comparison with Theory 576

Chapter 14. Molecular Electrostatic Potentials vs. DFT Descriptors of Reactivity, P. Geerlings, W. Langenaeker, F. De Proft and A. Baeten 587

1. Introduction 587 2. DFT-Based Reactivity Descriptors: Conceptual and

Methodological Issues 588 2.1. Reactivity descriptors as response functions 588 2.2. Local hardness: looking for a true companion

Parameter to local softness 590 2.3. Methodological issues 592

3. Results and Discussion 596 3.1. MEP vs. local softness and hardness: the electrophilic

Substitution reaction on benzene as a case study 596 3.2. The MEP as local hardness indicator 605

4. Conclusions 613

Chapter 15. Electrostatic Potential, Bond Density and Bond Order in Molecules and Clusters, N. H. Maren 619

1. Introduction 619 2. Electrostatic Potential at the Nucleus of a Neutral Atom

Related to the Electronic Correlation Energies of Atomic Ions 620 2.1. Feynman's theorem and electron-nuclear potential

energy 620 2.2. Relation to 1/Z expansion of ground-state energy 621 2.3. Virial theorem and [dE^JdZ] at constant number of

electronsN 622 2.4. Experimental estimates of correlation energy

derivative 624

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3. Chemical Potential and Bond Mid-Point Properties 625 3.1. Euler equation of density functional theory 625 3.2. Low-order density gradient form 627 3.3. Some exact results for Hj 628

4. Cluster Properties 629 4.1. Homonuclear Clusters of alkali atoms 630 4.2. Dissociation energy related to bond midpoint properties:

density and electrostatic potential 633 5. Dissociation of Doubly-Charged Clusters: Study of

Supermolecular Ions (NaJo^ and (Kjo^ 634 5.1. Coulomb barriers in dissociation of doubly-charged

Clusters 634 5.2. Deviation from Coulomb barrier in terms of bond

midpoint density 636 6. Bond Density and Chemical Network Model 638 7. Correlation Energy and Electron Density 640

7.1. Atoms 640 7.2. Light diatomic molecules 641 7.3. Polyatomic molecules: characterization of correlation

energy by bond order 643

Chapter 16. Relationships of Electrostatic Potentials to Intrinsic Molecular Properties, P. Politzer and J. S. Murray 649

1. Introduction 649 2. Atomic and Molecular Energies as Functions of Electrostatic

Potentials at Nuclei 649 3. Electrostatic Potentials and Chemical Potentials 652 4. Topographical Analyses 654 5. Lattice Energies and Ionic Radii 655 6. Covalent Radii and Bond Dissociation Energies 655

6.1. Covalent radii 655 6.2. Bond dissociation energies 656

7. Electronic Densities and Electrostatic Potentials 657

Index 661