Reviews in Computational Chemistry, Volume 30 E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Reviews in Computational Chemistry
- Sprache: Englisch
The Reviews in Computational Chemistry series brings together leading authorities in the field to teach the newcomer and update the expert on topics centered on molecular modeling.
• Provides background and theory, strategies for using the methods correctly, pitfalls to avoid, applications, and references
• Contains updated and comprehensive compendiums of molecular modeling software that list hundreds of programs, services, suppliers and other information that every chemist will find useful
• Includes detailed indices on each volume help the reader to quickly discover particular topics
• Uses a tutorial manner and non-mathematical style, allowing students and researchers to access computational methods outside their immediate area of expertise
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Veröffentlichungsjahr: 2017
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Table of Contents
COVER
TITLE PAGE
COPYRIGHT
LIST OF CONTRIBUTORS
PREFACE
CONTRIBUTORS TO PREVIOUS VOLUMES
CHAPTER 1: CHEMICAL BONDING AT HIGH PRESSURE
HIGH-PRESSURE SCIENCE
PRESSURE EFFECTS IN MATERIALS
ELECTRONIC STRUCTURE CALCULATIONS ON MATERIALS UNDER PRESSURE
PROPERTIES OF MATERIALS UNDER PRESSURE
CONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES
CHAPTER 2: MOLECULAR DYNAMICS SIMULATIONS OF SHOCK LOADING OF MATERIALS: A REVIEW AND TUTORIAL
INTRODUCTION
MOLECULAR SIMULATIONS OF SHOCKWAVES IN SOLIDS
SHOCK-INDUCED PLASTICITY AND FAILURE
SHOCK-INDUCED AND SHOCK-ASSISTED CHEMICAL REACTIONS
SUMMARY AND OUTLOOK
ACKNOWLEDGMENTS
APPENDIX
REFERENCES
CHAPTER 3: BASIS SETS IN QUANTUM CHEMISTRY
INTRODUCTION
THE BASIS SET APPROXIMATION
BASIS SET DESIDERATA
TYPES OF BASIS FUNCTIONS
STRUCTURE AND CLASSIFICATION OF GAUSSIAN TYPE BASIS SETS
BASIS SET AUGMENTATION
FITTING FUNCTIONS
NONATOM-CENTERED BASIS SETS
EXAMPLES OF BASIS SETS
PROPERTY BASIS SETS
RELATIVISTIC BASIS SETS
PSEUDOPOTENTIALS
BASIS SET CONVERGENCE
BASIS SET INCOMPLETENESS AND SUPERPOSITION ERRORS
ASPECTS OF CHOOSING A SUITABLE BASIS SET
AVAILABILITY OF BASIS SETS
ACKNOWLEDGMENT
REFERENCES
CHAPTER 4: THE QUANTUM CHEMISTRY OF OPEN-SHELL SPECIES
INTRODUCTION AND OVERVIEW
QUANTUM CHEMISTRY METHODS FOR OPEN- AND CLOSED-SHELL SPECIES
SOME ASPECTS OF ELECTRONIC STRUCTURE OF OPEN-SHELL SPECIES
HIGH-SPIN OPEN-SHELL STATES
OPEN-SHELL STATES WITH MULTICONFIGURATIONAL CHARACTER
DIRADICALS, TRIRADICALS, AND BEYOND
EXCITED STATES OF OPEN-SHELL SPECIES
METASTABLE RADICALS
BONDING IN OPEN-SHELL SPECIES
PROPERTIES AND SPECTROSCOPY
OUTLOOK
ACKNOWLEDGMENT
APPENDIX: LIST OF ACRONYMS
References
CHAPTER 5: MACHINE LEARNING, QUANTUM CHEMISTRY, AND CHEMICAL SPACE
INTRODUCTION
KERNEL RIDGE REGRESSION
REPRESENTATION
DATA
KERNEL
ELECTRONS
-MACHINE LEARNING
ATOMS IN MOLECULES
CRYSTALS
CONCLUSIONS AND OUTLOOK
ACKNOWLEDGMENTS
REFERENCES
CHAPTER 6: THE MASTER EQUATION APPROACH TO PROBLEMS IN CHEMICAL AND BIOLOGICAL PHYSICS
INTRODUCTION
THE GENERAL FORM OF A MASTER EQUATION AND ITS SOLUTION
MICROSCOPIC REVERSIBILITY, DETAILED BALANCE, AND THEIR CONSEQUENCES
THE KINETIC MONTE CARLO (KMC) METHOD
QUANTUM MASTER EQUATIONS
KINETIC MONTE CARLO FOR QUANTUM MASTER EQUATIONS
PHYSICAL SIGNIFICANCE OF THE QUANTUM KINETIC MONTE CARLO SCHEME
CONCLUDING REMARKS
ACKNOWLEDGMENTS
REFERENCES
CHAPTER 7: CONTINUOUS SYMMETRY MEASURES: A NEW TOOL IN QUANTUM CHEMISTRY
INTRODUCTION
CONTINUOUS SYMMETRY MEASURES
CSM IN MOLECULAR QUANTUM CHEMISTRY
APPLICATIONS
CONCLUSIONS
ACKNOWLEDGMENT
REFERENCES
INDEX
End User License Agreement
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Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
CHAPTER 1: CHEMICAL BONDING AT HIGH PRESSURE
Figure 1 Schematics of static high-pressure cells. Left: Piston cylinder cell with Bridgman seal (dark gray); diamond anvil cell (DAC); and double-stage DAC. In all cases, samples are shown in black.
Figure 2 Schematics of shock-wave generation. From left: chemical (guns), electrical discharge (capacitor banks), or optical means (laser-generated plasmas). Flyer plates are drawn in black, shocked and unshocked sample material are shown in gray and white, and the direction of flight and the shock wave is indicated by arrows.
Figure 3 (a) Incommensurate host–guest phase Rb-IV at 16.8 GPa; (b) Incommensurate phase Ca-VII at 241 GPa. Guest atoms arrange in channels provided by the host, which is drawn as connected network.
Figure 4 Predicted crystal structures of cubic S (a) and tetragonal (b), both drawn to the same scale at GPa.
Figure 5 (a) Common tangent approach to identify a high-pressure phase transition using the equations-of-state of two phases; (b) The same transition from the enthalpies .
Figure 6 Schematics of a convex hull construction, based on first-principles enthalpies of formation (open squares). Note that the shape of the convex hull (and thus phase stability) is pressure dependent.
Figure 7 Stable phases in the ternary phase diagram Li–O–H, at ambient and elevated pressure. Stable phases are indicated and connected by solid lines; color shading refers to absolute binding enthalpies (dark gray is largest), and dashed lines indicate isenthalpic phases.
Figure 8 Compressed fcc-Lithium, isosurfaces of the charge density (a, ) and the electron localization function (b, ).
CHAPTER 2: MOLECULAR DYNAMICS SIMULATIONS OF SHOCK LOADING OF MATERIALS: A REVIEW AND TUTORIAL
Figure 1 (a) Schematic representation of a sustained shock with piston (or particle) velocity propagating at velocity . The loading takes the unshocked material with temperature, pressure, and density , , and to the shock state (, , and ). (b) Shock Hugoniot is the representation of the final shocked states in
P–V
space.
Figure 2 Shock simulations in the cloud using the MD shock tool in nanoHUB (https://nanohub.org/tools/mdshocks). Setup, run, and analyze MD simulations of shock loading using a standard web browser from your laptop or tablet.
Figure 3 curves for elastic waves (denoted by diamonds) and plastic waves (denoted by crosses) for different crystallographic orientations.
Figure 4 Average pressure as a function of position in the sample along the shock direction, at an instant in time, for different crystallographic orientations.
Figure 5 curves showing the plastic and elastic waves in a molecular crystal of -HMX.
Figure 6 Shock-induced collapse of a void of radius 1.5 nm in Cu at a shock strength of 8 GPa. Collapse is accompanied by the emission of dislocation loops. Only non-FCC atoms are shown.
Figure 7 Copper sample with 3% porosity shocked at 10 GPa showing multiple, interacting loop emissions from the preexisting porosity. Only defective atoms are shown.
Figure 8 Granular nanocomposite of Ni/Al prepared for dynamical loading under MD conditions.
Figure 9 Transition from (a) plastic deformation at and (b) plastic and fluid flow at to (c) fluid flow with Rayleigh instability in the front at and (d) jetting into the pore at . Only defective atoms shown in (a) in red are hcp; white are unclassified. (b–d), Al atoms are colored red, and Ni atoms are green.
Figure 10 Spall strength as a function of strain rates for tantalum and copper.
Figure 11 (a) Snapshots showing spallation on tantalum with an impact speed of . (b) Stress in the load direction versus time.
Figure 12 Comparison of photomicrographs from soft recovery experiments and MD simulations; green color corresponds to fcc structure, blue denotes stacking-faults, and red atoms have undefined structure. Top and bottom Figure are for single-crystal and polycrystalline samples, respectively.
Figure 13 (a) Void volume distribution of Ta at various stages of the spallation process.
Figure 14 Shock ejection from a roughened Cu surface.
Figure 15 Iron phase diagram adapted from predictions made by Hasegawa and Pettifor
49
with a superimposed Hugoniot (dashed line) from Brown and McQueen.
50
Inset is the phase diagram from experiment that observes a higher triple point temperature.
Figure 16 (a) Shocked single-crystal iron from Kadau et al.,
53
u
p
= 0.471 km/s. Here atoms are colored by coordination number;
n
. Gray atoms are unshocked (
n
= 8), blue are compressed bcc (
n
= 10), red are transformed hcp grains (
n
= 12), and grain boundaries are shown in yellow (
n
= 11). (b) A higher piston velocity for the same structure at
u
p
= 1.087 km/s.
Figure 17 Assembled Figure from Henning et al.
52
(a) Calculated phase diagram for pure Ti. (b) Calculated energy barriers for the alpha to omega transition for C, N, and O interstitial contaminants. (c) Calculated energy barriers for Al and V alloying elements.
Figure 18 Shocked copper metal. (a) Stress–strain relationship during uniaxial compression, virtual melting, and release. (b) Calculated melt temperatures for the isotropically (thin line) and uniaxially (dark line) compressed single crystal;
T
< 0 implies an unstable crystal and should be thought of as the driving force for the transformation. (c) Simulation snapshot along the shock direction, . Atoms colored by local order parameter: red is FCC Cu and blue is molten Cu. Local pressures (d) and temperatures (e) are shown along the shock direction matching the view in panel (c).
Figure 19 Si
P–T
phase diagram from Kraus et al.
69
Figure 20 Nanostructure obtained by (a) deposition and (b) mechanical activation.
Figure 21 Initial structure used in symmetric-shock MD simulations. Ni atoms are in light gray and Al atoms are in dark gray (red in the ebook version).
Figure 22 (a) Atomic snapshots of the porous Ni/Al structure following shock loading, colors as defined in the legend for Figure 21. (b) Temperature evolution for the defect free and porous case, showing faster kinetics in the presence of pores.
Figure 23 Shocks in a model porous AB chemistry solid. Atom colors correspond to reactants (blue), products (green), radicals (red), and clusters (purple). The shock direction in each panel is perpendicular to the thick black lines. In panels (a–c) are a time series of the same simulation showing the shock-to-detonation transition. The cooperation of multiple voids induces hot spots leading to the formation of a chemical wave shown in detail in (d).
Figure 24 Energetics of transition states and intermediates during the unimolecular decomposition in RDX obtained using the ReaxFF (full lines with filled symbols) and with quantum mechanics (dashed lines with open symbols). Circles represent the sequential HONO elimination, triangles show the decomposition process following homolytic NN bond breaking (NO
2
elimination), and diamonds represent the concerted ring-opening pathway.
Figure 25 Time dependence of the local temperature on a slab of a coarse-grained molecular crystal as a shock passes through. (a) Intermolecular temperature (dashed lines) and internal temperature (solid lines). (b) Effect of classical and quantum specific heat on the internal temperature.
Figure 26 Intramolecular energy landscape of a mesoparticle versus effective particle size for a family of model materials. The difference in energy between the two local minima in each curve governs the energetics of the chemical reactions. The dashed line denotes a chemically “inert” mesoparticle with a single minimum.
Figure 27 Spatial profiles of velocity, temperature, pressure, and density changes that take place under a sustained shock with an impact speed of 1.25 km/s. The inert material is shown in solid lines. The SWED material is simulated using an endothermicity value of 20 kcal/mol (small dashed lines) and no endothermicity (large dashed lines).
Figure 28 Tersoff, EAM, and REBO potentials can be compared to the more recent BOP and ReaxFF in this graph. Solid line represents a doubling of computational power every 2 years akin to Moore's law for the density of transistors. All timings were done on a Cray XT5 computer.
CHAPTER 3: BASIS SETS IN QUANTUM CHEMISTRY
Figure 1 Illustrating the difference between STO and GTO functions.
Figure 2 Illustrating how a linear combination of three GTOs can model a STO function.
Figure 3 The energy-optimized s-exponents (a) and the convergence of the energy contribution (b) for basis sets of increasing size for the He atom.
Figure 4 The energy-optimized s-exponents (a) and the convergence of the energy contribution (b) for basis sets of increasing size for the Ne atom.
Figure 5 The CISD correlation energy contribution for different types of functions for the Ne atom.
Figure 6 (a) The Kr s-orbitals. (b) The same orbitals when scaled such that the 2s-, 3s-, and 4s-orbitals match the value for the 1s-orbital at the origin. Note the logarithmic
x
-axis.
Figure 7 A (16s) → [6s] general contraction can be transformed into a segmented contraction with only 10, 4, 2, and 1 primitive GTOs instead of 14 primitive GTOs in the general contraction.
Figure 8 The Kr 4s-orbital radial behavior in an all-electron basis set, and with a small and large core potential.
Figure 9 Illustrating the components and procedure for estimating the electron correlation and basis set converged energy with the G4 and W4 procedures. Black dots indicate actual calculations and open circles indicate results obtained as intermediate results, while shaded circles indicate extrapolated results. Full arrows indicate explicit extrapolation using formulas such as Eqs [
43
] and [
45
], while dashed arrows indicate extrapolation procedures relying on additivity. The HLC (high-level correction) in the G4 Figure indicates an empirical correction based on the number of valence electrons.
CHAPTER 4: THE QUANTUM CHEMISTRY OF OPEN-SHELL SPECIES
Figure 1 Examples of closed-shell and open-shell species. Dinitrogen in its ground electronic state is a closed-shell molecule. All electrons are paired and degenerate molecular orbitals (MOs) such as the two -orbitals are completely filled. Vinyl is an example of a doublet radical with one unpaired electron (). Triplet methylene, which has two unpaired electrons, is a diradical (the high-spin component in which of the triplet state is shown).
Figure 2 Closed-shell molecules acquire open-shell character at stretched geometries, where degeneracy between frontier MOs develops. At equilibrium geometry, the coefficient is small and the wave function is dominated by . At the dissociation limit, both configurations become equally important resulting in an open-shell singlet radical pair, .
Figure 3
para
-Benzyne is an example of a singlet diradical. Its open-shell character derives from the fact that the two nearly degenerate frontier MOs are only partially occupied in each of the two leading electronic configurations.
Figure 4 Molecules with partially broken bonds can be described as diradicals. This cartoon depicts a diradical transition state often encountered in cis–trans isomerization around double bonds and a diradical intermediate in a cycloaddition reaction.
Figure 5 Examples of molecular magnets. (a) Molecular structure of a Cr(III) horseshoe complex. Each of the six chromium atoms has three unpaired electrons. (b) Structure of a nickel complex with the nickel-cubane core (). Each of the four nickel atoms has two unpaired electrons.
Figure 6 (a) Hierarchy of ab initio methods for ground electronic states. The simplest approximation of an -electron wave function is a single Slater determinant, , built of orbitals that are variationally optimized. The description can be systematically improved by including excited determinants up to the exact solution of the Schrödinger equation by full configuration interaction (FCI). Operators and generate -tuply excited determinants from the reference, for example, . The amplitudes (, , ) are determined either by solving coupled-cluster equations or by perturbation theory. In the case of closed-shell species, and spin-orbitals have the same spatial parts and the resulting wave functions are naturally spin-pure. (b) Reference determinant (also called the Fock-space vacuum state) determines the separation of the orbital space into the occupied and virtual subspaces. Traditionally, indices are used to denote occupied orbitals and are used for virtuals. General-type orbitals are denoted by . In single-reference methods, excitation operators (such as and ) are determined with respect to .
Figure 7 Hierarchy of ab initio methods for electronically excited states. The excited-state model corresponding to the Hartree–Fock ground-state wave function is configuration interaction singles (CIS) in which excited states are described as a linear combination of all singly excited Slater determinants, . For CCSD, the excited-state ansatz is a linear combination of all single and double excitations from the reference CCSD wave function, and so on.
Figure 8 Molecular orbitals in symmetric and asymmetric . By virtue of Koopmans' theorem, the shapes of the MOs represent the charge localization in the two electronic states of the ionized dimer, (the electronic configurations of the two cationic states are shown in the box). When the two molecules are identical (a), the charge is equally delocalized in the ground () and lowest excited () states of the cation. When the bond is stretched in one , the MOs become localized, that is, in the ground state of the cation, the positive charge is localized on the stretched moiety. At low symmetry, and can mix, resulting in multiconfigurational wave functions.
Figure 9 Two examples of Jahn–Teller systems. (a) Highest occupied MOs of benzene molecule (both and labels are given). (Reproduced with permission from Ref.
36
. Copyright 2008 American Institute of Physics). The two lowest states of the benzene radical-cation form a Jahn–Teller pair. (b) Molecular orbitals and the ground-state electronic configuration of cyclic ( structure, labels are given in parentheses). Both HOMO and LUMO are doubly degenerate. The two lowest electronic states of the doublet radical form a Jahn–Teller pair.
Figure 10 Potential energy surfaces illustrating JT effect in cyclic . Exact definition of coordinates and can be found in Ref.
38
. Point corresponds to equilateral triangle; this is the point of conical intersection. At , displacements lead to an obtuse isosceles triangle, whereas displacements result in an acute isosceles triangle. The motion connecting the three symmetry-equivalent minima is called pseudo-rotation. (a) A surface plot of the PES (in eV). (b) Electronic state symmetries. (i) A cross section of the PES shown on the left along the line. TS, MIN, and CI mark the points of the transition state, minimum, and conical intersection, respectively. The electronic state symmetry of the adiabatic ground-state PES changes at the point of CI. (ii) A contour map of the PES shown in (a). Three solid and three dashed lines cross at the point of CI and indicate and electronic state symmetries, respectively. Open and filled circles mark minima and transition states.
Figure 11 Geometric phase effect. (a) Illustration of the sign change in the lowest state adiabatic (Born–Oppenheimer) electronic wave function. The drawing represents a contour plot of the cyclic PES as in Figure 10, but with only two contour lines: one contour line is given at 0.16 eV, which is also the highest energy contour line in Figure 10. It forms two concentric loops, which encompass the white area, at the inner and outer parts of the well. The second contour line is given exactly at the energy of the transition state 0.0386 eV; it defines the colored area. This contour line exhibits a Möbius-like shape with the nodes at the transition state points and serves here as a reflection of the electronic wave function symmetries. The wave function is symmetric across the lines and is antisymmetric across the lines. This is indicated as “+/+” or “+/” across each symmetry line. (b) Demonstration of the changes in the nodal structure of vibrational wave functions due to the geometric phase effect. The wave functions for the (0,0,0) state of the symmetry and state of the symmetry obtained from calculations that neglect or account for geometric phase are shown on (a) (marked as BO) and (b) (marked as GBO), respectively. Accounting for the geometric phase changes the nodal structure of the vibrational wave function. The correct nodal structure of the generalized Born–Oppenheimer wave functions leads to the total molecular wave functions (a product of electronic and vibrational wave functions) that are single valued and have the correct permutation symmetry.
Figure 12 Frontier MOs (a) and leading electronic configurations (b) of the two lowest electronic states of the
para
-benzyne anion at and geometries.
Figure 13 Schematic depictions of (a) weak, (b) intermediate, and (c) strong second-order Jahn–Teller interactions along a symmetry-breaking coordinate .
Figure 14 Reference () and target configurations for EOM-IP-CCSD and EOM-EA-CCSD wave functions.
Figure 15 Comparison of EOM-IP-CCSD and CCSD/EOM-EE-CCSD description of the electronic states of along charge-transfer coordinate at the 3.0 Å (a–c) and 5.0 Å (d–f) separations using aug-cc-pVTZ. Errors against FCI in ground-state energy (a and d), excitation energy (b and e), and ground-state charge (c and f) are shown.
Figure 16 Comparison of EOM-IP-CCSD, CCSD, and B3LYP description of the ground electronic state of the ethylene dimer cation along the charge-transfer coordinate at the 4.0 Å (a) and 6.0 Å (b) separations using aug-cc-pVTZ. (a) Highly reliable MR-CISD and EOM-IP-CC(2,3) results. On the left, potential energy along the charge-transfer coordinate is shown. On the right, the charge on the left moiety is shown.
Figure 17 Ionized states of -stacked uracil dimer. (a) Molecular orbitals diagram. In-phase and out-of-phase overlap between the fragments' MOs results in bonding (lower) and antibonding (upper) dimer's MOs. Changes in the MO energies, and, consequently, IEs, are demonstrated by the Hartree–Fock orbital energies (hartrees). The correlated IEs follow the same trend. The ionization from the antibonding orbital changes the bonding from noncovalent to covalent and enables a new type of electronic transitions, which are unique to the ionized dimers. (b) Vertical electronic spectra of the stacked uracil dimer cation at two different geometries: the geometry of the neutral (bold lines) and the cation's geometry (dashed lines). MOs hosting the unpaired electron in each electronic states are shown for each transition.
Figure 18 The MOs and respective VIEs (eV, EOM-IP-CCSD/6-311+G(d,p) extrapolated to cc-pVTZ) for the two stacked thymine dimers, symmetric (a) and nonsymmetric (b). The energy difference (eV) between the dimer IE and corresponding IE of the monomer and leading EOM amplitudes for the shown orbitals are given in parenthesis.
Figure 19 Possible structural forms of
meta
-benzyne: a monocyclic singlet diradical 1 versus a bicyclic closed-shell singlet 2. Structure 1 can be described as the -allylic motif. Structure 2 has delocalized character. The distance between the two radical centers provides a measure of the competition between the two structures.
Figure 20 High-spin reference () and low-spin target configurations for the EOM-SF-CCSD wave functions. (a) EOM-SF using the triplet reference describes the states of diradicals. Note that both open-shell and closed-shell states can be described. (b) The electronic states of triradicals can be described by using the high-spin quartet reference ().
Figure 21 Frontier MOs and the leading configurations of the low-lying electronic states of methylene, , (closed-shell singlet), (open-shell singlet), and (also closed-shell singlet, which is doubly excited with respect to ). The wave functions of the components of all four states can be described as single SF excitations from the high-spin () triplet reference.
Figure 22 Molecular orbitals (a) and low-lying electronic states (b) of the 1,3,5-TMB, 5-DMX, and 2-DMX triradicals. 1,3,5-TMB and 2-DMX feature a quartet ground state, whereas 5-DMX has an unusual open-shell doublet ground state.
Figure 23 Procedure for extracting exchange coupling constants from single SF calculations. (a) Start with the Boys-localized ROHF orbitals for the highest multiplicity state (). (b) A single SF excitation operator generates all configurations necessary to describe the manifold. From this set, only the neutral (noncharge-transfer) subset is retained. (c) After site-by-site block diagonalization, the eigenstates are now linear combinations of three local quartet states, , , and . The tilted gray arrows indicate the component of the local quartet spin states. (d) In the local eigenstate basis, the effective Hamiltonian is now full rank and contains the exchange coupling constants, , as off-diagonal elements divided by , where denotes local spin on center .
Figure 24 Comparison of the low-energy spectrum taken from direct ab initio 4SF-CAS(S) calculations (gray) and the 1SF-CAS(S) + Heisenberg diagonalization (black). The -axis is the energy from the ground state in . The -axis is the for each state.
Figure 25 Doublet reference, (1), and target configurations for the EOM-EE-CCSD wave functions for vinyl radical. Configurations (2)–(5) are single excitations from reference (1), whereas determinants (6)–(8) are formally double excitations. Note that open-shell configurations, (4)–(6), needed to describe doublet and quartet states of vinyl radical, appear at different excitation levels in the EOM-EE-CCSD ansatz.
Figure 26 Electron-attached states of AgF ( debye) (see Ref. 135). Theoretical values are computed by EOM-EA-CCSD augmented by CAP. Experimental values are shown in parentheses. The ground state of the anion, , is strongly bound. Because of the strongly polar character, AgF also supports a dipole-bound state (bound by 0.014 eV). Three resonance states have been identified by the CAP-EOM-EA-CCSD calculations and experimentally.
135
The character of the target orbital hosting the attached electron reveals dipole-stabilized nature of the two upper resonance states.
Figure 27 Dyson orbitals and vertical IEs (eV) for the four lowest states of the cluster computed using EOM-EA-CCSD/aug-cc-pVDZ. The two lowest IEs of the bare sodium atom are 4.96 and 2.98 eV. The orbitals reveal that the unpaired electron resides on the surface of the cluster and that its states resemble atomic s and p states perturbed by the solvent molecules.
Figure 28 Bicopper molecular magnet. (a) Molecular structure (copper atoms are shown in gold). (b) Difference spin-density plot for the triplet state computed using B5050LYP/LANL2DZ. The excess electrons (purple) can be clearly associated with copper atoms, with some degree of delocalization along the Cu-ligand bonds.
Figure 29 Relative change of the distance between radical centers in benzynes () and tridehydrobenzenes () with respect to benzene. For each species, (in %) for the ground (low-spin) state and for the lowest high-spin state is shown. For the isomers, all possible distances between two radical centers are considered; for example, in 1,2,4-, the distances between centers in ortho (), meta (), and para () positions are used.
Figure 30 Illustration of Franck–Condon progressions in electronic and photoelectron spectroscopy. (a) Initial and final electronic states and the corresponding photoelectron spectrum for a diatomic molecule (or, more generally, a single Franck-Condon active mode). The definitions of adiabatic and vertical energy differences are shown. In this case, the most intense vibronic peak corresponds to vertical . (b) Photodetachment spectrum of the phenolate anion: calculated Franck–Condon factors (gray) and experimental spectrum (black).
164
The most intense band corresponds to the 00 transition, which is shifted by 0.05–0.08 eV from the vertical . The theoretical spectrum is computed using .
Figure 31 Photodetachment spectrum for
para
-benzyne anion. (a) Singlet (black) and triplet (gray) bands of the photoelectron spectra computed using SF methods and double-harmonic approximation. (b) The experimental (black) and the calculated (gray) spectra, which include singlet and triplet states of the diradical, using the CCSD-optimized geometry and normal modes for the anion.
Figure 32 Photoionization of thymine–water clusters. (a) Equilibrium structures of ionized thymine monohydrate (lowest energy structures, ). Bond lengths and changes in bond lengths due to ionization are shown (in Å). (b) Computed and experimental photoelectron spectra. The latter is derived from the photoionization efficiency curves. (c) Computed photoelectron spectrum of water–thymine cluster. Calculated FCFs for the first ionized state of (lower panel). Upper panel: FCFs due to water–thymine motion computed using curvilinear coordinates. Middle panel: FCFs due to thymine moiety computed using double-harmonic parallel mode approximation. Bottom: Overall photoelectron spectrum computed as a product of the thymine and water–thymine FCFs.
Figure 33 Simulated photoelectron spectra of the 1-imidazolyl radical, superimposed on the experimental spectrum (dots). (A) Adiabatic simulations roughly similar to double-harmonic calculations within the Franck–Condon model. The spectrum shown in (b) includes vibronic interactions between the radical states that lead to the breakdown of the Condon approximation. Inclusion of vibronic effects has noticeable effect on relative peak intensities (peaks , and ) and new (“vibronic”) peaks appear in the spectrum, resulting in better agreement with the experiment.
Figure 34 Absolute total cross sections for , Ne, and formaldehyde. The theoretical values are computed using EOM-IP-CCSD Dyson orbitals (shown in the insets) and ezDyson. Light and dark gray lines denote cross sections computed using plane wave () and Coulomb wave () wave functions of the free electron. Plane waves give a good description of photodetachment cross sections, while Coulomb waves give a better description for photoionization from atoms (and some small molecules). For formaldehyde, the orange line following the experimental points denotes cross section computed using a Coulomb wave with partial charge ().
Figure 35 The values of coupling elements for hole transfer (HT) and electron transfer (ET) for model ethylene dimers.
Figure 36 Schemes for computing the couplings using EOM-SF, EOM-IP, and EOM-EA wave functions, with orbitals depicted for two ethylenes as an example. Shown in panel (A) is the scheme for hole transfer and in panel (B) that for electron transfer. Configurations in panels (a) are the charged quartet configuration (for SF) and those in panels (d) are neutral singlet (IP and EA) reference states. In panels (b) and (c) are the target charged, doublet configurations.
Figure 37 Errors against FCI for diabatic Mulliken–Hush coupling in model charge- transfer systems. (a and b) at 3.0 and 5 Å separation. EOM- IP-CCSD/aug-cc-pVTZ (solid line) and EOM-EE-CCSD/aug-cc-pVTZ (dotted line) results are shown. (c) . EOM-IP-CCSD/aug-cc-pVDZ (solid line) and EOM-EE-CCSD/aug-cc-pVDZ (dotted line) results are shown.
CHAPTER 5: MACHINE LEARNING, QUANTUM CHEMISTRY, AND CHEMICAL SPACE
Figure 1 Flow chart showing the basic machinery of a Kernel-Ridge–Regression ML setup. Vertical flow corresponds to training the model by calculating regression coefficients through inversion of the symmetric square kernel matrix with the dimensionality of training set size . Horizontal flow corresponds to out-of-sample predictions of properties of query compounds, using the regression coefficients to scale the distance-dependent contribution of each training instance. Input compounds are denoted by R, their ML representations, also known as descriptors, by , and properties by P. and correspond to hyperparameters that control kernel width and noise level, respectively. Their optimization is discussed in the section
Kernel
.
Figure 2 Distribution of molecular size (in terms of number of occupied orbitals, that is, electron pairs, ). The height of each black box denotes the number of constitutional isomers for one out of 621 stoichiometries present in 134 k molecules. The two left-hand-side insets correspond to zoom-ins for smaller compounds. The right-hand-side inset zooms in on the predominant stoichiometry, HO, and features a scatter plot of G4MP2 relative (with respect to global minimum) potential energies of atomization versus molecular radius of gyration, , as well as joint projected distributions.
Figure 3 Learning curves for single-kernel ML models (with au and ) for thirteen molecular properties including thermochemical (a) as well as electronic (b) properties of molecules. For each training set size, a single kernel has been inverted and trained and tested on thirteen properties. Left and Right refer to the use of the aforementioned descriptors Coulomb matrix (CM) and bag-of-bonds (BOB), respectively. Out-of-sample relative mean absolute errors (RMAE), that is, MAE relative to standard quantum chemistry accuracy thresholds, are plotted for test and training sets drawn from the 112 k GDB-17 subset of molecules with exactly 9 heavy CONF atoms.
77
See Ref. 60 for further details of quantum chemistry accuracy thresholds. See Refs. 57, 60 for a color version.
Figure 4 Training coefficients in ML models of transmission coefficients plotted as a function of kinetic energy index of the incoming electron, as published in Ref. 61. Shown are the coefficients of four (out of 8000) nanoribbon compounds used for training (NR 1–4). These materials were selected because their coefficients exhibit the largest (NR 2 and NR 3) or smallest (NR 1 and 4) fluctuations in . The standard deviation (SD) over all 8000 training compounds is shown as well. Reproduced with permission of American Physical Society from Ref. 61.
Figure 5 (a) Flow chart for -machine learning. The input to the model typically consists of structures at a baseline level, , and properties are modeled using training data corresponding to properties
and
geometries consistent with targetline level, . (b) Baseline and targetline property function. The -ML model (arrow) accounts for both difference in property and geometry due to difference in level of theory.
Figure 6 Calculated enthalpy differences at 298.15 K between the most stable molecule with HO stoichiometry (inset), and its 10 energetically closest isomers in increasing order, according to targetline method G4MP2 (black). 1 k -ML model predictions are the center bar for each isomer, and B3LYP is the right bar for each isomer. Reproduced with permission of American Chemical Society from Ref. 64.
Figure 7 Density distributions of electronic excitation energies (top) and predicted errors (bottom). Top: Densities of first (a) and second (b) singlet–singlet transition energies of 17 k organic molecules with up to eight CONF atoms, at the CC2/def2TZVP targetline, and TDPBE0/def2SVP baseline levels of theory. Bottom: Densities of errors in predicting the values of and using -ML models based on 1 k (orange), and 5 k (red) training molecules. Reproduced with permission of American Institute of Physics from Ref. 65.
CHAPTER 6: THE MASTER EQUATION APPROACH TO PROBLEMS IN CHEMICAL AND BIOLOGICAL PHYSICS
Figure 1 When an individual protein jumps, randomly, between its folded (
F
) and unfolded (
U
) states with the transition probabilities obeying Eq. [3], a large collection of such proteins, each evolving independently, will obey the first-order kinetic equations, Eq. [1].
Figure 2 A network of interconnected states is described in terms of rate coefficients of jumping from state
i
to a state
j
.
Figure 3 A long, time-reversible trajectory contains as many jumps from state
i
to state
j
as from
j
to
i
. Indeed, each jump, say, from 1 to 4 in this trajectory (arrows) will become a jump from 4 to 1 in the time-reversed trajectory, and the statistical indistinguishability of the trajectory and its time-reversed counterpart necessitates equal numbers of jumps in both directions. Of course, this statement is only exact when applied either to an infinitely long trajectory or to the
average
numbers of jumps observed during a finite time interval: the actual numbers of 1 to 4 and 4 to 1 jumps observed during a given finite period of time are not necessarily equal.
Figure 4 The lifetime of the molecule in some state
i
is determined by the sum of all the rate coefficients for processes that lead from
i
to any other state. It has an exponential distribution and can be predicted using Eq. [36].
Figure 5 From all the possible states that the molecule can jump to from a state
i
, the new state
j
must be selected at random, with a probability equal to . A practical way of doing so involves a procedure resembling a roulette wheel: Align all the probabilities within a segment of unit length and draw a uniform random number that also falls within this segment. Select the new state
j
according to which of the probability segments falls into, as shown.
CHAPTER 7: CONTINUOUS SYMMETRY MEASURES: A NEW TOOL IN QUANTUM CHEMISTRY
Figure 1 “Octahedral” coordination compounds for which the five d-block molecular orbitals are assumed to be split in a two (
e
g
) over three (
t
2
g
) pattern.
Figure 2 Relation between the actual symmetry group of an object and the group adopted in a pseudosymmetry analysis where (a) a common pseudosymmetry group
G
0
is used for a set of related structures with different symmetries or (b) different pseudosymmetry groups are used for a single structure to find the best suiting pseudosymmetry group for a structure with a given symmetry
G
1
.
Figure 3 Dependence of the inversion symmetry measure for the centered Hückel Hamiltonian for a two s-orbital diatomic molecule on the difference between the energy of the two atomic orbitals (2δ) for several values of the interaction energy, β. Energies are given in arbitrary units.
Figure 4 Schematic representation of the orbital interaction for the Hückel model of a diatomic molecule with two
s
-type AOs.
Figure 5 Dependence of the inversion symmetry of the Hamiltonian and the two molecular orbitals on
δ
(the difference between the average energy and the energy of the atomic orbitals) for
β
= −10. Energies are given in arbitrary units.
Figure 6 Six-membered ring systems obtained from benzene, C
6
H
6
, or hexazine, N
6
, by replacing CH groups for N atoms.
Figure 7 Relative
C
6
Hamiltonian (empty circles and solid line) and the π-system's Fock matrix (solid circles) for the C
6-m
H
6-m
N
m
heterocycles shown in Figure 6.
Figure 8
C
6
continuous symmetry measures for the ground state electron density calculated using the Hückel method (empty circles) and HF/ STO-3G calculations (solid circles) for the C
6-m
H
6-m
N
m
heterocycles in Figure 6. The solid line corresponds to a least squares parabolic fit of the Hückel values.
Figure 9 Molecular geometries of phenanthrene and the [
n
]helicene series with 4–6 fused rings.
Figure 10 Lowest energy σ- and π-type CC bonding MOs for phenanthrene and [
n
]helicenes (
n
= 4–6).
Figure 11 Weights
ω
(Γ) of the two IRs of the pseudosymmetry group
C
s
,
A′
(white bars) and
A″
(gray bars), in the σ- and π-type orbitals of [
n
]helicenes and phenanthrene (
n
= 3).
Figure 12 d-block molecular orbitals for a [CoH
6
]
3−
ion with a perfect octahedral geometry. The levels highlighted in red correspond to other molecular orbitals that appear in the region of the d-block that are not represented in the figure.
Figure 13 d-block molecular orbitals for the[Co(NH
3
)
6
]
3+
ion.
Figure 14 d-block molecular orbitals for a
cis
-[CoCl
2
(NH
3
)
4
]
+
ion. The levels highlighted in gray correspond to other molecular orbitals that appear in the region of the d-block that are not represented in the figure.
Figure 15 d-block molecular orbitals for a [Co(Cp)
2
]
+
ion. The levels highlighted in gray correspond to other molecular orbitals that appear in the region of the d-block that are not represented in the figure.
Figure 16 Spread or planarization path to interconverts a tetrahedral ML
4
coordination compound into a square planar one through a continuous series of
D
2
d
geometries.
Figure 17 (a) Generalized interconversion pathway between two polyhedra P and T in the shape map referred to their ideal structures
P
and
T
. (b) Positions of the structures of tetracoordinate transition metal complexes in a shape map. The arrow indicates the path from the perfect tetrahedron (shape measures 0 and 33.3) to the perfect square (shape measures 33.3 and 0).
Figure 18 Walsh diagram for the d-block molecular orbitals of the [MnF
4
]
2−
anion along the spread pathway. The energies and compositions of the molecular orbitals obtained through density functional theory (B3LYP/Def2-TZVP) calculations are drawn as 0.04 probability contours. The symmetry labels given correspond to the
D
2
d
point group. For the sake of clarity, only one of the two equivalent orbitals of the (
xz, yz
) set is shown at each side of the diagram.
Figure 19 Inversion measures of the d-block MOs of [MnF
4
]
2−
along the spread pathway from square planar (0%) to tetrahedral (100%). The inversion measure for the nuclear framework is represented as a dashed line, for the sake of comparison.
Figure 20 Weights of the pseudo-symmetry representations for the d-based molecular orbitals of the [NiF
4
]
2−
anion along the square to tetrahedron pathway, relative to (a and c) the
D
4
h
pseudosymmetry group and (b and d) the
T
d
pseudosymmetry group.
Figure 21 Calculated Δ
E
-weighted oscillator strength for the
z
2
→
x
2
−
y
2
transition in [NiF
4
]
2−
along the spread pathway from the square to the tetrahedron (circles), compared to the variation of the pseudo-symmetry coefficients (fitted to Eq. [91] with
κ
= 0.064) along the same path (squares).
List of Tables
CHAPTER 3: BASIS SETS IN QUANTUM CHEMISTRY
Table 1 Highest Angular Momentum Function Included in Basis Sets with Cardinal Number
X
for Different Blocks of Elements in the Periodic Table
Table 2 Basis Set Compositions for a Second-Row Element (B–Ne) for Three Families of Basis Sets Optimized for DFT, Electron Correlation, and Explicitly Correlated Methods, Respectively
Table 3 Optimization Criteria for Commonly Used Basis Sets
Table 4 Criteria for Assigning Diffuse Functions for Commonly Used Basis Sets
Table 5 Selected Basis Sets for Second-Row s- and p-Block Elements (Li–Ne)
Table 6 Selected Basis Sets for Third-Row s- and p-Block Elements (Na–Ar)
Table 7 Selected Basis Sets for Fourth-Row s-, p-, and d-Block Elements (K–Kr)
CHAPTER 4: THE QUANTUM CHEMISTRY OF OPEN-SHELL SPECIES
Table 1 Adiabatic Singlet–Triplet Gaps
a
(eV) in
ortho
-,
meta
-, and
para
-Benzyne Isomers
Table 2 Adiabatic Excitation Energies (eV) Relative to the State of Methylene
Table 3 Different Types of the Electronic States in the Vinyl Radical and Appropriate CC/EOM-CC Models
CHAPTER 5: MACHINE LEARNING, QUANTUM CHEMISTRY, AND CHEMICAL SPACE
Table 1 Comparison of Mean Absolute Errors (MAEs, in kcal/mol) for ML-Predicted Energetic Properties () across Data Sets, and Baseline/Targetline Combinations for a Fixed Training Set Size of 1 k
CHAPTER 7: CONTINUOUS SYMMETRY MEASURES: A NEW TOOL IN QUANTUM CHEMISTRY
Table 1
C
6
Symmetry Measures for the Hückel Hamiltonian of the C
6-m
H
6-m
N
m
Series of Molecules Expressed as a Function of the Relative Electronegativity Perturbation Factor
f
Table 2 Contribution of the Irreducible Representations of the
O
h
Group to the Frontier Orbitals of
cis
-[CoCl
2
(NH
3
)
4
]
3+
Table 3 Contribution of the Irreducible Representations of the
O
h
Group to the Frontier Orbitals of the Alternated (
C
5
v
) Structure of [CoCp
2
]
+
Reviews in Computational ChemistryVolume 30
Edited by
Abby L. Parrill
College of Arts and SciencesThe University of MemphisMemphis, TN, U.S.A.
Kenny B. Lipkowitz
Office of Naval ResearchArlington, VA, U.S.A.
This edition first published 2017
© 2017 John Wiley & Sons, Inc.
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Library of Congress Cataloging-in-Publication Data
ISBN: 9781119355434
Serial. LCCN 93642005, ISSN 1069-3599
Cover Design: Wiley
LIST OF CONTRIBUTORS
Pere Alemany
, Departament de Química Física and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franquès, Barcelona, Spain
Santiago Alvarez
, Departament de Química Inorgànica and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franquès, Barcelona, Spain
Edwin Antillon
, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States
David Avnir
, Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel
David Casanova
, Donostia International Physics Center (DIPC), Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia, Spain; IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
Mathew J. Cherukara
, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States
Chaim Dryzun
, Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel
Andreas Hermann
, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, United Kingdom
Frank Jensen
, Department of Chemistry, Aarhus University, Aarhus, Denmark
Anna I. Krylov
, Department of Chemistry, University of Southern California, Los Angeles, CA, United States
Dmitrii E. Makarov
, Department of Chemistry and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, United States
Balazs Nagy
, Department of Chemistry, Aarhus University, Aarhus, Denmark
Raghunathan Ramakrishnan
, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Basel, Switzerland
Alejandro Strachan
, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States
O. Anatole von Lilienfeld
, Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Basel, Switzerland; General Chemistry, Free University of Brussels, Brussels, Belgium
Mitchell A. Wood
, School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, United States
PREFACE
This book series traditionally includes reviews of current topics in computational chemistry and provides minitutorials for novices initiating new directions in their own research along with critical literature reviews highlighting advanced applications. Volume 30 is no exception to that longstanding tradition. While each chapter has a unique focus, two themes connect some of the chapters in this volume: modeling of phenomena under extreme conditions in Chapters 1 and 2 and quantum chemistry in Chapters 3–5.
Chapter 1 focuses on the effects of high pressure on chemical bonding, as pressure is a variable with a range of observed values spanning 50 orders of magnitude between interstellar space and the interior of a neutron star. Andreas Hermann reviews the responses of materials to pressure and provides an important tutorial describing appropriate modeling approaches applicable to the study of high-pressure phases. Applications of computational chemistry to investigate mechanical, electronic, and spectroscopic properties of molecules round out the chapter.
Chapter 2, by Mitchell Wood, Mathew Cherukara, Edwin Antillon, and Alejandro Strachan, focuses on the behavior of materials under the extreme conditions of stress and temperature induced by shock loading. Of particular benefit to the reader is that the authors present examples that can be reproduced using an online simulation tool accessible using a standard web browser that runs on computing resources at Purdue University. The authors introduce the topic through MD simulations of shockwaves in solids. This tutorial aids in understanding material responses to shock such as plastic deformation and failure. Additional attention is paid to shock-induced phase transformations, synthesis, and chemical reactions.
In Chapter 3, Balazs Nagy and Frank Jensen provide a thorough and informative review on basis sets in quantum chemistry. This chapter will be an excellent resource for graduate students new to the field of computational chemistry faced with choosing methods for their first quantum calculations and for the experienced researcher who wants to identify the most suitable property basis set for a new research question. This chapter provides a basic introduction to the basis set approximation and desirable features of a basis set before enumerating the types of basis functions in common use today. Performance comparisons of basis set size, function type, general versus segmented contraction, and core potential size provide evidence-based guidance in the selection of suitable basis sets, which the authors augment with advice for practitioners regarding the compromise between accuracy and efficiency.
Systems with unpaired electrons offer particular challenges to the computational chemistry community. Anna Krylov details these challenges and reviews methods best suited to address each of these challenges in Chapter 4. Examples illustrate applications of computational methods to simple high-spin states, charge-transfer systems, di- and triradicals, and excited states. Computation of molecular properties for comparison to spectroscopic observables has been reviewed due to the importance of such comparisons in validating and benchmarking the suitability of various methods for use on open-shell systems.
Chapter 5 rounds out the quantum chemistry theme by discussing machine learning to overcome efficiency problems hindering quantum chemical methods in the search of chemical space of synthetically accessible species in a high-throughput manner. Raghunathan Ramakrishnan and Anatole von Lilienfeld review appropriate molecular representations that relate to quantum mechanical inputs, and the application of supervised machine learning methods to generalize from large training sets of molecules and their associated quantum mechanical results to previously unobserved examples that comprise a test set or out-of-sample set. This chapter demonstrates that even quantum chemistry is moving into the regime of “Big Data,” in which thousands of predictions can rapidly be made using the trained machine learning model.
Chapter 6, by Dmitrii Makarov, will introduce many readers to the use of master equations to describe the time evolution of a system, with probabilistic treatment of transitions between potential states of the system. Systems modeled using master equations might be simply represented by two states, such as folded and unfolded protein conformations, or might be represented by a much more complex network of states. The use of master equations to investigate kinetic properties for both classical and quantum systems using kinetic Monte Carlo (KMC) is reviewed, and the difference in the physical meaning of the KMC scheme in these two cases is articulated.
Chapter 7 introduces a new way for chemists in general, and computational chemists specifically, to think about symmetry. Symmetry provides chemists with an important mechanism to describe chemical structures and computational chemists with simplifications that improve computing efficiency. However, we often assume ideal symmetry for chemical systems that typically deviate from the ideal case and electronic structure changes may accompany those deviations from ideal symmetry. This train of thought demonstrates the importance of being able to quantify how well a given chemical system matches various ideal symmetries. Pere Alemany, David Casanova, Santiago Alvarez, Chaim Dryzun, and David Avnir present continuous symmetry measures (CSMs) as this quantitative tool and demonstrate continuous symmetry measures in the context of the atomic framework, matrices and operators, functions, and irreproducible representations. Applications of CSMs demonstrate the value in shifting from a binary representation of symmetry (symmetric or not) toward a quantitative reflection of the degree of symmetry.
The value of Reviews in Computational Chemistry stems from the pedagogically driven reviews that have made this ongoing book series so popular. We are grateful to the authors featured in this volume as well as to the authors that contributed to prior volumes.
Volumes of Reviews in Computational Chemistry are available in an online form through Wiley InterScience. Please consult the Web (http://www.interscience.wiley.com/onlinebooks) or contact [email protected] for the latest information.
Abby L. ParrillMemphis
Kenny B. LipkowitzWashingtonAugust 2016
CONTRIBUTORS TO PREVIOUS VOLUMES
Volume 1 (1990)
David Feller
and
Ernest R. Davidson
, Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions
James J. P. Stewart
, Semiempirical Molecular Orbital Methods
Clifford E. Dykstra, Joseph D. Augspurger, Bernard Kirtman
, and
David J. Malik
, Properties of Molecules by Direct Calculation
Ernest L. Plummer
, The Application of Quantitative Design Strategies in Pesticide Design
Peter C. Jurs
, Chemometrics and Multivariate Analysis in Analytical Chemistry
Yvonne C. Martin, Mark G. Bures
, and
Peter Willett
, Searching Databases of Three-Dimensional Structures
Paul G. Mezey
, Molecular Surfaces
Terry P. Lybrand
, Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods
Donald B. Boyd
, Aspects of Molecular Modeling
Donald B. Boyd
, Successes of Computer-Assisted Molecular Design
Ernest R. Davidson
, Perspectives on Ab Initio Calculations
Volume 2 (1991)
Andrew R. Leach
, A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules
John M. Troyer
and
Fred E. Cohen
, Simplified Models for Understanding and Predicting Protein Structure
J. Phillip Bowen
and
Norman L. Allinger
, Molecular Mechanics: The Art and Science of Parameterization
Uri Dinur
and
Arnold T. Hagler
, New Approaches to Empirical Force Fields
Steve Scheiner
, Calculating the Properties of Hydrogen Bonds by Ab Initio Methods
Donald E. Williams
, Net Atomic Charge and Multipole Models for the Ab Initio Molecular Electric Potential
Peter Politzer
and
Jane S. Murray
, Molecular Electrostatic Potentials and Chemical Reactivity
Michael C. Zerner
, Semiempirical Molecular Orbital Methods
Lowell H. Hall
and
Lemont B. Kier
, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure–Property Modeling
I. B. Bersuker
and
A. S. Dimoglo
, The Electron-Topological Approach to the QSAR Problem
Donald B. Boyd
, The Computational Chemistry Literature
Volume 3 (1992)
Tamar Schlick
, Optimization Methods in Computational Chemistry
Harold A. Scheraga
, Predicting Three-Dimensional Structures of Oligopeptides
Andrew E. Torda
and
Wilfred F. van Gunsteren
, Molecular Modeling Using NMR Data
David F. V. Lewis
, Computer-Assisted Methods in the Evaluation of Chemical Toxicity
Volume 4 (1993)
Jerzy Cioslowski
, Ab Initio Calculations on Large Molecules: Methodology and Applications
Michael L. McKee
and
Michael Page
, Computing Reaction Pathways on Molecular Potential Energy Surfaces
Robert M. Whitnell
and
Kent R. Wilson
, Computational Molecular Dynamics of Chemical Reactions in Solution
Roger L. DeKock, Jeffry D. Madura, Frank Rioux
, and
Joseph Casanova
, Computational Chemistry in the Undergraduate Curriculum
Volume 5 (1994)
John D. Bolcer
and
Robert B. Hermann
