Handbook of Computational Chemistry

Quantum chemical calculations rely on a few fortunate circumstances like usually small relativistic and negligible electrodynamic (QED) corrections and large nuclei-to-electron mass ratio. The fast progress in computer technology revolutionized theoretical chemistry and gave birth to computational chemistry. The computational quantum chemistry provides for experimentalists the ready-to-use tools of new kind offering powerful insight into molecular internal structure and dynamics. It is important for the computational chemistry to elaborate methods, which look at molecule in a multiscale way, which provide first of all its global and synthetic description such as shape and charge distribution, and compare this description with those for other molecules. Only such a picture can free researchers from seeing molecules as a series of case-by-case studies. Chemistry represents a science of analogies and similarities, and computational chemistry should provide tools for seeing this. This is especially useful for the supramolecular chemistry, which allow chemists to planify and study intermolecular interactions. Some of them, involving concave and convex moieties, represent molecular recognition, which assures a perfect fitting of the two molecular shapes. A sequence of molecular recognitions often leads to self-assembling and self-organization, typical to nanostructures.

A short survey of the general principles and selected applications of molecular mechanics (MM) is presented. The origin of molecular mechanics and its evolution is followed starting from “pre-computer” and the first computer-aided estimations of the structure and potential energy of simple molecular systems to the modern force fields and software for the computations of large biomolecules and their complexes. Analysis of the current state of physicochemical study of biological processes suggests that MM simulations based on empirical force fields have an ever-increasing impact on understanding the structure and functions of biomolecules. The problem of “classic mechanics” description of essentially quantum properties and processes is considered. Various approaches to a selection of force field mathematical expressions and parameters are reviewed. The relation between MM simplicity and “physical nature” of the properties and events is examined. Quantum chemistry contributions to MM description of complex molecular systems and MM contribution to quantum mechanics computations of such systems are considered.

Arguments are advanced to support the view that at present it is not possible to derive molecular structure from the full quantum mechanical Coulomb Hamiltonian associated with a given molecular formula that is customarily regarded as representing the molecule in terms of its constituent electrons and nuclei. However molecular structure may be identified provided that some additional chemically motivated assumptions that lead to the clamped nuclei Hamiltonian are added to the quantum mechanical account.

Methods of computational chemistry seem to often be simply a melange of undecipherable acronyms. Frequently, the ability to characterize methods with respect to their quality and applied approximations or to ascribe the proper methodology to the physicochemical property of interest is sufficient to perform research. However, it is worth knowing the fundamental ideas underlying the computational techniques so that one may exploit the approximations intentionally and efficiently. This chapter is an introduction to quantum chemistry methods based on the wave function search in one-electron approximation.

A detailed derivation of the adiabatic approximation and the Born-Oppenheimer approximation is presented, the difference between these two approximations is discussed and the circumstances under which the adiabatic approximation collapses are discussed. It is shown that the solution of the Schrödinger equation in the adiabatic approximation can be divided into one representing the motion of electrons in the field of fixed nuclei and another one representing the motion of nuclei in the potential generated by the presence of the electrons. The shapes of the potential energy curves generated by the electrons and the motion of the nuclei in these potentials are also analyzed. Finally, the state-of-the-art highly accurate calculations for diatomic molecules performed without the use of the Born-Oppenheimer approximation is presented.

Two aspects are quintessential if one seeks to successfully perform DFT calculations: a basic understanding of how the concepts and models underlying the various manifestations of DFT are built and an essential knowledge of what can be expected from DFT calculations and how to achieve the most appropriate results. This chapter expands on the development and philosophy of DFT and aims to illustrate the essentials of DFT in a manner that is intuitively accessible. An analysis of the performance and applicability of DFT focuses on a representative selection of chemical properties, including bond lengths, bond angles, vibrational frequencies, electron affinities and ionization potentials, atomization energies, heats of formation, energy barriers, bond energies, hydrogen bonding, weak interactions, spin states, and excited states.

This chapter provides a concise introduction to quantum chemical response theory as implemented in a number of widely used electronic structure software packages. While avoiding technical derivations of response functions, the fundamental idea of response theory, namely, the calculation of field-induced molecular properties through changes in expectation values, is explained in a manner equally valid for approximate wave function and density functional theories. Contrasting response theory to textbook treatments of perturbation theory, key computational concepts such as iterative solution of response equations and the identification and calculation of electronic excitation energies are elucidated. The wealth of information that can be extracted from approximate linear, quadratic, and higher-order response functions is discussed on the basis of the corresponding exact response functions. Static response functions and their identification and numerical calculation as energy derivatives are discussed separately. Practical issues related to the lack of gauge and origin invariance in approximate calculations are discussed without going into too much theoretical detail regarding the sources of these problems. Finally, the effects of nuclear motion (molecular vibrations, in particular) and how to include them in computational studies are treated in some detail.

Van der Waals interactions determine a number of phenomena in the fields of physics, chemistry and biology. As we seek to increase our understanding of physical systems and develop detailed and more predictive theoretical models, it becomes even more important to provide an accurate description of the underlying molecular interactions. The goal of this chapter is to describe recent developments in the theory of intermolecular interactions that have revolutionised the field due to their comparatively low computational costs and high accuracies. These are the symmetry-adapted perturbation theory based on density functional theory (SAPT(DFT)) for interaction energies and the Williams–Stone–Misquitta (WSM) method for molecular properties in distributed form. These theories are applicable to systems of small organic molecules containing as many as 30 atoms each and have demonstrated accuracies comparable to the best electronic structure methods. We also discuss the numerical aspects of these theories and recent applications which demonstrate the range of problems that can now be approached with these accurate ab initio methods.

This chapter provides an overview of different hierarchical levels of molecular dynamics (MD) spanning a wide range of time and length scales – from first-principles approaches via classical atomistic methods to coarse-graining techniques. The theoretical background of the most widely used methods and algorithms is briefly reviewed, and practical instructions are given on the choice of input parameters for an actual computer simulation. In addition, important postprocessing procedures such as data analysis and visualization are discussed.

Single molecule force spectroscopy constitutes a robust method for probing the unfolding of biomolecules. Knowledge gained from statistical mechanics is helping to build our understanding about more complex structure and function of biopolymers. Here, we have review some of the models and techniques that have been employed to study force-induced transitions in biopolymers. We briefly describe the merit and limitation of these models and techniques. In this context, we discuss statistical models of polymer along with numerical techniques, which may provide enhanced insight in understanding the unfolding of biomolecules.

This chapter deals with two very important aspects of modern ab initio computational chemistry: the determination of molecular structure and the calculation, and visualization, of vibrational spectra. It deals primarily with the practical aspects of determining molecular structure and vibrational spectra computationally. Both minima (i.e., stable molecules) and transition states are discussed, as well as infrared (IR), Raman, and vibrational circular dichroism (VCD) spectra, all of which can now be computed theoretically.

The theory and applications of ab initio methods for the calculation of molecular properties are reviewed. A wide range of properties characterizing the interactions of molecules with external or internal sources of static or dynamic electromagnetic fields (including nonlinear properties and those related to nuclear and electron spins) is considered. Emphasis is put on the properties closely connected to the parameters used to describe experimentally observed spectra. We discuss the definitions of these properties, their relation to experiment, and give some remarks regarding various computational aspects. Theory provides a unified approach to the analysis of molecular properties in terms of average values, transition moments, and linear and nonlinear responses to the perturbing fields. Several literature examples are given, demonstrating that theoretical calculations are becoming easier, and showing that computed ab initio molecular properties are in many cases more accurate than those extracted from experimentally observed data.

Weak intermolecular interactions, which are ubiquitous in biological and materials chemistry, are fast becoming more routinely and accurately investigated owing to the increased performance of computational methods being actively developed. A vast array of pragmatic methods have been proposed using empirical, semi-empirical, density functional theory, and ab initio approaches, which all serve to widen the scope of feasible problems. Especially for the calculation of the important London dispersion interactions, significant progress has been achieved. Herein, we present a general overview on a number of illustrative strategies used to routinely investigate structures and energies of such systems. The composition and advantages/disadvantages of different benchmark sets, which have been found to be of crucial importance in assessing such a wide range of methods is discussed. Finally, a number of experience-based perspectives are provided in relation to the scaling and accuracy of the “more popular” methods used when investigating non-covalent interactions.A present trend in quantum chemistry is on cheap and reliable methods that effectively solve present-day problems in biological and materials chemistry. Quantum chemistry now confidently looks beyond small polyatomic molecules and toward large supramolecular complexes; this represents an area on the cutting edge of simulation sciences.This chapter deals with weak intermolecular (non-covalent) interactions between molecules in the gas phase. These interactions are essential for the quantitative description and understanding of complex molecular aggregates in physics (e.g., surface science), chemistry, and molecular biology. The same interactions also occur in an intramolecular fashion between atoms or groups in one molecule. One of the big advantages of the supermolecular approach described herein is that it can handle both situations on an equal footing. Just for convenience and due to space limitations, we will consider here only intermolecular cases (complexes of at least two molecules). The reader should, however, keep in mind that much of what we are saying about quantum chemical methods similarly holds for the quantum chemical simulation of protein folding.The following chapter is a pragmatic overview on “current” methods that are useful in obtaining reliable data from quantum chemical calculations, with a strong focus on methods used (and developed) primarily to study such non-covalent interactions. Weak intermolecular interactions in the solid or solution phase are almost completely neglected here, this is by no means a reflection on their importance, rather a way of restricting the scope of this chapter to a particular stream of research. A thorough description of the underlying theory of molecular interactions is presented in Volume I written by Alston Misquita. Only a succinct overview of weak intermolecular interactions is given below to “set the scene.”

This chapter provides an introduction to the calculation of thermochemical data for chemical reactions using quantum chemical methods. The basic procedure is first described, namely, obtaining molecular structures and electronic energies of reactants and products, followed by vibrational frequency calculations and evaluation of thermal corrections. Since it is harder to obtain a given accuracy for some types of reactions than others, some discussion is provided on classes of reactions (e.g., isodesmic reactions) for which a given accuracy is easier to achieve than for a general reaction. Three examples illustrate different aspects of thermochemical calculations. The first example, the formation of ammonia from its elements, illustrates a variety of basis set and correlation effects on calculated data. The second example is concerned with calculations on small fluorine-oxygen species and a systematic side-by-side comparison of coupled-cluster and density-functional methods, including the use of isodesmic reactions. The third example describes the use of high-level coupled-cluster calculations to predict the standard enthalpy of formation of S(OH)₂.

Excited states participate in photoinduced events as well as in thermally activated reactions, even in many cases in which only the ground state is believed to be involved. Life on Earth also depends, both directly and indirectly, on the influence that light has on chemistry. The energy of the Sun’s visible and ultraviolet radiation promotes processes that not only permit the continued existence of life on the planet, but which are keys for evolution by means of mutations. To study a system in an excited state, far away from its optimum situation, is a challenge for chemists, both experimentalists and theoreticians. This chapter is focused on the practical aspects related to the calculation of excited states in molecular systems by using quantum-chemical methods, a type of study that escapes in many cases from the well-established computational strategies used for the molecular ground states, both because of the complexity of the problem itself and for the methodological requirements. A short review of the spectroscopic and photochemical panorama will be provided first in order to explain which are the main parameters and processes to be determined, followed by a compact description of the most relevant and employed quantum-chemical methods and computational strategies for excited states. A number of applied examples of actual calculations on paradigmatic excited state problems will be provided in the different subchapters, followed in each case by comments on practical issues occurring in the calculations. With these cases we will try to demonstrate that in the last years the quantum-chemical studies on excited states have reached the required maturity to interpret and predict, at a molecular level, different types of chemical situations.

The properties of a molecule may change quite substantially when passing from the isolated state to a solution, and computational chemistry requires the possibility of taking into account the effects of a solvent on molecular properties. These changes are mainly due to long range interactions, and electrostatics involving a large number of solvent molecules play the major role in the phenomenon and free energy changes have to be evaluated. Statistical calculations by means of usual Monte Carlo or molecular dynamics coupled with a full quantum chemical description of a sample representative of the solution is still out of reach for standard molecular modeling computations nowadays. Nevertheless, several simplified approaches are available to evaluate the free energy changes which appear when an isolated molecule, as described by standard quantum computations, undergoes the influence of a solvent and to predict the changes in the molecular properties which are the consequences of solvation. In this chapter, we develop the principles of the most usual methods that a computational chemist can find in standard codes or can implement more or less easily to approach the solvent effects in quantum chemistry investigations.

Theoretical background and applications of methods for the calculation of solvent effects on molecular electric properties are reviewed. Macroscopic linear and nonlinear susceptibilities are defined, and their relationship to microscopic properties, i.e., (hyper)polarizabilities, is described. The role of specific intermolecular interactions in property calculations is demonstrated in terms of interaction-induced properties. Two categories of models for the description of solvent effects are presented. The first category comprises continuum models, in which the solvent is described as a homogeneous medium with the solute molecule located inside a cavity. Within this category, the polarizable continuum model and the multipole expansion method are described in more detail. The second group of approaches is based on discrete solvent models in which the solvent molecules are explicitly considered. Selected representative methods such as the supermolecular approach, polarizable embedding, and frozen-density embedding are presented. The possibility to combine explicit and implicit methods is demonstrated on the discrete reaction field and the Langevin dipole approaches. Finally, two illustrative examples (liquid water and p-nitroaniline in 1,4-dioxane) of the application of the presented methods for (non)linear property calculations are given.

The working equations of auxiliary density functional theory (ADFT) and auxiliary density perturbation theory (ADPT) are derived in the framework of the linear combination of Gaussian-type orbital expansion. The inclusion of hybrid functionals into ADFT is presented. Its extension for the calculation of magnetic properties is outlined. The ADFT and ADPT implementations in the density functional theory program deMon2k are discussed. Special attention is given to the efficient calculation of electron repulsion integrals in nanostructures. The use of ADFT and ADPT in first-principles Born-Oppenheimer molecular dynamics at the pico- to nanosecond time scale is reviewed. In particular, the long-standing mystery of the discrepancy between experiments and computations for the polarizability of small sodium clusters is resolved. Applications of the parallel deMon2k ADFT implementation to systems on the nanometer scale are reviewed. This includes Al-zeolites and giant fullerenes. It is shown that structures as large as C₅₄₀ can be fully optimized within a few days without any symmetry constraints in the ADFT framework employing all-electron basis sets. The successful application of a hierarchical transition state finder for the study of selected sodium cluster rearrangements is presented, too.

This chapter reviews most of the widely used nonrelativistic quantum chemistry program packages. Considering that information about availability and capabilities of the free quantum chemistry programs is more limited than that of the commercial ones, the authors concentrated on the free programs. More specifically, the reviewed programs are free for the academic community. Features of these programs are described in detail. The capabilities of each free program can generally be categorized into five fields: independent electron model; electron correlation treatment; excited state calculation; nuclear dynamics including gradient and hessian; and parallel computation. Examples of input files for the Møller–Plesset calculation of formaldehyde are presented for most of the free programs to illustrate how to create the input files. The main contributors of each free program and their institutions are also introduced, with a brief history of program development if available. All the key references of the cited algorithms and the hyperlinks of the home page of each program (both free and commercial) are given in this review for the interested readers. As the most important information of every cited free program’s documentation has been extracted here, it is appropriate to consider this chapter to be the manual of manuals.

In this chapter, we briefly discuss the theoretical foundations of relativistic two-component methods used in quantum chemistry calculations. Specifically, we focus on two groups of methods. These are (i) methods based on the elimination of the small component, such as the zeroth-order regular approximation (ZORA), the first-order regular approximation (FORA), and the normalized elimination of small component (NESC) formalisms, and (ii) approaches that use a unitary transformation to decouple the electronic and positronic states such as the Douglas–Kroll–Hess (DKH) and the infinite-order two-component (IOTC) Hamiltonians. Furthermore, we describe the algebraic approach to IOTC and scrutinize pure algebraic schemes that paved the way to the eXact 2-Component (X2C) Hamiltonians taking advantage of the nonsymmetric algebraic Riccati equation (nARE). Finally, we assess the accuracy of the aforementioned methods in calculating core and valence properties of heavy-element compounds and discuss some challenging examples of computational actinide chemistry.

The accurate description of electronically excited states remains a challenge for theoretical chemistry. Among the vast body of quantum mechanical methods available to perform this task, time-dependent density functional theory (TD-DFT) currently remains the most widely applied method, a success that one can explain not only by its very interesting accuracy/effort ratio but also by the ease to perform TD-DFT calculations for a large number of compounds and properties (absorption and emission spectra, band shapes, dipole moments, electron and proton transfers, etc.) in various environments. In the present chapter, we present TD-DFT as a tool for modeling such excited-state properties, with a focus on several practical aspects (choosing an exchange-correlation functional and an atomic basis set, analyzing the nature of the electronic transitions, comparing results with experiments, including environmental effects, etc.) that are useful to get a quick start. In that framework we rely on a series of examples of increasing complexity considering both organic and inorganic compounds as well as biomolecules.

The majority of organic and inorganic chemical reactions relevant for synthesis or industrial applications take place in the solution phase. Similarly, almost all biological reactions proceed in an aqueous environment. Theoretical descriptions of chemical reactions in solution differ in the way they treat the surrounding solvent molecules. Their large number excludes an explicit treatment. Nevertheless, the elucidation of the solvated structure plays a key role in obtaining an accurate description of chemical reactions as well as the activity of biomolecules. In this chapter, we review recent theoretical developments for the description of solvated molecules during chemical reactions, employing statistical physics to treat the solvent. The reference interaction-site model (RISM) theory, and some of its extensions, coupled with recent quantum mechanical theories, are described, and applications to various systems in solution, from conventional chemical reactions to the activities of biomolecules in biological systems, are presented. The solvent distribution around the solute and solute–solvent interactions is critical for the reactions and structures of such systems. The theories described here offer the possibility to obtain detailed information on the molecular origin of solvation and may contribute to discover and elucidate novel phenomena in chemistry, physics, and bioscience.

This chapter reports experimental investigations and theoretical approaches devoted to analyze the electronic, optical, and vibrational properties occurring in semiconducting photoactive materials in their bulk form or as nanosized objects. An original cluster approach was developed to describe the physical features of nanoparticles and the impact of their surface on photoinduced charge transfer phenomena.Photovoltaic and photocatalysis are two major applications for both clean environment and sustainable sources of energy as well. In this context, semiconducting nanocrystals from defined oxide families have attracted increasing interest during the last decade for their promising potential in renewable energy applications because of their versatile and coupled optical and electronic properties. More specifically, the semiconductor oxides as titanium oxide and bismuth vanadate-based materials can be tailored in nanosized and mesoporous structures. The electronic and optical features may be modulated in large extents when dye molecules are used as sensitizing vectors enhancing the efficiency of solar cells, energy storage, and photocatalyst. These applications depend on the reactive surface area, morphology and nanostructuration, doping and sensitizing agents, as well as controlled vacancy rates acting on the charge transferpeculiarities.In parallel to experimental investigations dedicated to selected forms of photoactive semiconducting oxides, original theoretical approaches were developed to analyze the key features of the considered functional systems. Using an integrated approach associating theoretical models and numerical simulations, the influence of the size and morphology of nanoparticles on their electronic and optical properties was pointed out. The cluster approach methodology was developed to simulate the electronic properties of semiconducting nanocrystalline materials as isolated objects or functionalized by organic dye molecules. The construction of the system proceeds by the crystal structure frozen in the cluster core while the surface is modified according to the environmental interactions. Theoretically, it was proved that nanostructures exhibit patchwork properties coming from the bulk material including core crystal structure and from surface effects caused by environment. On the other hand, the role of doping of the considered structures by metallic elements was investigated on the photoactivity mechanism involved in nanoparticles. The nature of vacancies located close to the dopants plays a crucial role on the electronic and optical features in the photoactive materials. Thus, the theoretical approaches and the carried out numerical simulations contribute to draw quantitative insights of the physical properties of functional semiconducting oxides in agreement with relevant experimental analyses.

This chapter describes general principles in the stability and bonding of empty fullerenes, endohedral fullerenes, and exohedral derivatives of empty fullerenes. First, an overview of the structural properties of empty fullerenes is given. The problem of isomers’ enumeration is described and the origin of the intrinsic steric strain of the fullerenes is discussed in terms of POAV (π-orbital vector analysis) leading to the isolated pentagon rule (IPR). Finally, theoretical studies of the isomers of fullerenes are discussed. In the second part of the chapter, bonding phenomena and molecular structures of endohedral metallofullerenes (EMFs) are reviewed. First, the bonding situation in EMFs is discussed in terms of ionic/covalent dichotomy. Then, the factors determining isomers of EMFs, including those favoring formation of non-IPR cage isomers, are reviewed. In the third part, general principles governing addition of atomic addends and trifluoromethyl radicals to fullerenes are analyzed.

Materials that exhibit an electrical resistivity between that of conductor and insulator are called semiconductors. Devices based on semiconductor materials, such as transistors, solar cells, light-emitting diodes, digital integrated circuits, solar photovoltaics, and much more, are the base of modern electronics. Silicon is used in most of the semiconductor devices while other materials such as germanium, gallium arsenide, and silicon carbide are used for specialized applications. The obvious theoretical and technological importance of semiconductor materials has led to phenomenal success in making semiconductors with near-atomic precision such as quantum wells, wires, and dots. As a result, there is a lot of undergoing research in semiconductor clusters of small and medium sizes both experimentally and by means of computational chemistry since the miniaturization of devices still continues. In the next pages, we are going to learn which the most studied semiconductor clusters are, we will explore their basic structural features and visit some of the most representative ab initio studies that are considered as works of reference in this research realm. Also, we are going to be introduced to the theory of the electric properties applied in the case of clusters by visiting some of the most illustrative studies into this research area. It is one of the purposes of this presentation to underscore the strong connection between the electric properties of clusters and their structure.

This chapter discusses the structures, energetics, and vibrational spectra of the first few (n ≤ 24) water clusters obtained from high-level electronic structure calculations. The results are discussed in the perspective of being used to parameterize/assess the accuracy of classical and quantum force fields for water. To this end, a general introduction with the classification of those force fields is presented. Several low-lying families of minima for the medium cluster sizes are considered. The transition from the “all surface” to the “fully coordinated” cluster structures occurring at n = 17 and its spectroscopic signature is presented. The various families of minima for n = 20 are discussed together with the low-energy networks of the pentagonal dodecahedron (H₂O)₂₀ water cage. Finally, the low-energy networks of the tetrakaidecahedron (T-cage) (H₂O)₂₄ cluster are shown and their significance in the construction of periodic lattices of structure I (sI) of the hydrate lattices is discussed.

This chapter provides information on various carbon allotropes and in-depth details of structural, electronic, and chemical properties of graphene, fullerenes, and single-walled carbon nanotubes (SWCNTs). We have written an overview of different computational methods that were employed to understand various properties of carbon nanostructures. Importance of application of computational methods in exploring different sizes of fullerenes and their isomers is given. The concept of isolated pentagon rule (IPR) in fullerene chemistry has been revealed. The computational and experimental studies involving Stone–Wales (SW) and vacancy defects in fullerene structures are discussed in this chapter. The relationship between the local curvature and the reactivity of the defect-free and defective fullerene and single-walled carbon nanotubes has been revealed. We reviewed the influence of different defects in graphene on hydrogen addition. The viability of hydrogen and fluorine atom additions on the external surface of the SWCNTs is revealed using computational techniques. We have briefly pointed out the current utilization of carbon nanostructures and their potential applications.

This chapter reviews the fundamental concepts of excitons and excitonic polaritons and their extraordinary optical properties in quantum dot nano-composite materials. By starting with the optical excitation of an exciton in the nanostructure we show that the effective dielectric constant of the nanostructure becomes significantly modified due to the exciton generation and recombination, resulting in high positive and negative dielectric constants. We also discuss single exciton generation by multiple photons and multiple exciton generation by single photon. All these nonlinear optical properties of quantum dot nano-composite materials offer novel possibilities and are expected to have deep impact in nanophotonics.

The purpose of this chapter is to describe and review examples of how theoretical investigations can be applied to elucidate the behavior of carbon nanostructures and to understand the physical mechanisms taking place at the molecular level. We will place a special emphasis in theoretical works utilizing density functional theory. We assume that the reader is familiar with the basics of density functional theory as well as the electronic properties of single-walled carbon nanotubes and graphene nanoribbons (GNRs). We do not intend to present an extensive review; instead, we focus on several examples to illustrate the powerful predictive capabilities of current computational approaches.

Recent computer simulations have indicated that there is a linear relationship between the melting and the Curie temperatures for Ni _n (n ≤ 201) clusters. In this chapter, it is argued that this result is a consequence of the fact that the surface and the core (bulk) contributions to the cluster properties vary with the cluster size in an analogous way. The universal aspect of this result is also discussed. Among the many interesting consequences resulting from this relationship is the intriguing possibility of the coexistence of melting and magnetization. As demonstrated, these conclusions have as their origin the major contribution coming from the melting/magnetization ratio arising from surface effects and appear to overshadow all other contributions. As a result, this can be quantified with approximate methods which are suitable for describing any major surface contribution to a cluster property.

Clusters contain more than just some few atoms but not so many that they can be considered as being infinite. By varying their size, their properties can often be varied in a more or less controllable way. Often, however, the precise relation between size and property is largely unknown: the sizes of the systems are below the thermodynamic limit so that simple scaling laws do not apply. Theoretical studies of such systems can provide relevant information, although in many cases idealized systems have to be treated. The challenge of such calculations is the combination of the relatively large size of the systems together with an often unknown structure. In this presentation, different theoretical methods for circumventing these problems shall be discussed. They shall be illustrated through applications on various types of clusters. These include isolated metal clusters with one or two types of atoms, metal clusters deposited on a surface, nanostructured HAlO, semiconductor nanoparticles, and metallocarbohedrenes. Special emphasis is put on the construction of descriptors that can be used in identifying general trends.

We present an overview of our understanding of how extended materials exposed to an electrostatic field can be treated theoretically. We concentrate on materials that are regular so that they can be approximated as being infinite and periodic. We show how expressions for the dipole moment per unit that were suggested previously within the so-called modern theory of polarization can be obtained. Subsequently, we present the single-particle equations that describe how the electrons respond to an external, electrostatic field and present a numerically efficient method of solution. We also discuss how structural responses in the presence of an electrostatic field can be calculated automatically. We demonstrate that bulk properties of macroscopic systems will depend upon the surfaces and demonstrate how these properties may be evaluated from calculations on the infinite and periodic system even though the latter does not contain surfaces. As one example, we show how the surfaces will contribute to the so-called converse piezoelectric effect. In addition, the polarizabilities induced by the structural response may be larger than the corresponding electronic polarizabilities. Finally, problems related to the description of the responses within density-functional theory are briefly discussed.

Materials properties show a dependence on the dimensionality of the systems studied. Due to the increased importance of surfaces and edges, lower-dimensional systems display behavior that may be widely different from their bulk counterparts. As a means to complement the newly developed experimental methods to study these reduced dimensional systems, a large fraction of the theoretical effort in the field continues to be channeled toward computer simulations. This chapter reviews briefly the computational methods used for the low-dimensional materials and presents how the materials properties change with dimensionality. Low-dimensional systems investigated are classified into a few broad classes: 0D nanoparticles, 1D nanotubes, nanowires, nanorods, and 2D graphene and derivatives. A comprehensive literature will guide the readers’ interest in computational materials sciences.

Recent extensions of the coupled-cluster (CC) theory for molecular solute described within the polarizable continuum model (PCM) were summarized. The advances covered in this review regard (i) the analytical gradients for the PCM-CC theory at the single and double excitation level, (ii) the analytical gradients for the PCM-EOM-CC theory at the single and double excitation level for the descriptions of the excited-state properties of molecular solute, and (iii) the coupled-cluster theory for the linear and quadratic molecular response functions of molecular solutes. These computational advances can be profitably used to study molecular processes in condensed phase, where both the accuracy of the QM descriptions and the influence of the environment play a critical role.

We review the general concept of nonadiabatic quantum spin transitions in biochemistry. A few important examples are highlighted to illustrate the concept: the role of spin effects in oxidases, cytochromes, in dioxygen binding to heme, in photosynthesis, and in tentative models of consciousness. The most thoroughly studied of these effects are connected with dioxygen activation by enzymes. Discussion on the mechanisms of overcoming spin prohibitions in dioxygen reactions with flavin-dependent oxygenases and with hemoglobin and myoglobin is presented in some detail. We consider spin-orbit coupling (SOC) between the starting triplet state from the entrance channel of the O₂ binding to glucose oxidase, to ferrous heme, and the final singlet open-shell state in these intermediates. Both triplet (T) and singlet (S) states in these examples are dominated by the radical-pair structures D+−O2−$$ {\mathrm{D}}^{+}-{\mathrm{O}}_2^{-} $$ induced by charge transfer; the peculiarities of their orbital configurations are essential for the SOC analysis. An account of specific SOC in the open π_g-shell of dioxygen helps to explain the probability of T-S transitions in the active site near the transition state. Simulated potential energy surface cross-sections along the reaction coordinates for these multiplets, calculated by density functional theory, agree with the notion of a relatively strong SOC induced inside the oxygen moiety by an orbital angular momentum change in the π_g-shell during the T-S transition. The SOC model explains well the efficient spin inversion during the O₂ binding with heme and glucose oxidase, which constitutes a key mechanism for understanding metabolism. Other examples of nontrivial roles of spin effects in biochemistry are briefly discussed.

Proteins play a crucial role in biological processes; therefore, understanding their structure and function is very important. In this chapter, we give an overview on computer models of proteins. First, we treat both major experimental structure determination methods, X-ray diffraction and NMR spectroscopy. In subsequent sections, computer modeling techniques as well as their application to the construction of explicit models are discussed. An overview on molecular mechanics and structure prediction is followed by an overview of molecular graphics methods of structure representation. Protein electrostatics and the concept of the solvent-accessible surface are treated in detail. We devote a special section to dynamics, where time scales of molecular motions, structures, and interactions are discussed. Protein in relation to its surroundings is especially important, so protein hydration, ligand binding, and protein-protein interactions receive special attention. The case study of podocin provides an example for the successful application of molecular dynamics to a complex issue. At last, computer modeling of enzyme mechanisms is discussed. It is demonstrated that protein representation by computers arrived to a very high degree of sophistication and reliability; therefore, even lots of experimental studies make use of such models. A list with a large number of up-to-date bibliographic references helps the reader to get informed on further details.

The present advanced state of the computer hardware offers superb opportunities for further explorations of protein structure and dynamics. Sound and well-established theoretical models are successfully used for searching new biochemical phenomena, correlations, and protein properties. In this chapter, the fast-growing field of computer simulations of protein dynamics is panoramically presented. The principles of currently used computational methods are briefly outlined, and representative examples of their recent advanced applications are given. In particular protein folding studies, intrinsically disordered proteins, protein-drug interactions, ligand transport phenomena, ion channel activity, molecular machine mechanics, origins of molecular diseases, and simulations of single-molecule AFM experiments are addressed. Special attention is devoted to emerging methods of enhanced molecular dynamics.

Molecular dynamics (MD) simulations based on a classical force field are increasingly being used to study the structure and dynamics of nucleic acids. Simulation studies are limited by the accuracy of the force field description and by the time scale accessible by current MD approaches. In case of specific conformational transitions, it is often possible to improve the sampling of possible states by adding a biasing or umbrella potential along some coordinate describing the conformational transition. It is also possible to extract the associated free energy change along the reaction coordinate. The development of advanced sampling methods such as the replica-exchange MD (REMD) approach allows significant enhancement of conformational sampling of nucleic acids. Recent applications of umbrella sampling and REMD simulation as well as combinations of both methodologies on nucleic acids will be presented. These approaches have the potential to tackle many open questions in structural biology such as the role of nucleic acid structure during recognition and packing and the function of nucleic acid fine structure and dynamics.

Mixed-quantum classical dynamics simulations have recently become an important tool for investigations of time-dependent properties of electronically excited molecules, including non-adiabatic effects occurring during internal conversion processes. The high computational costs involved in such simulations have often led to simulation of model compounds instead of the full biochemical system. This chapter reviews recent dynamics results obtained for models of three classes of biologically relevant systems: protonated Schiff base chains as models for the chromophore of rhodopsin proteins; nucleobases and heteroaromatic rings as models for UV-excited nucleic acids; and formamide as a model for photoexcited peptide bonds.

Low-energy electrons (LEE) have been experimentally found to structurally alter DNA by induction of base damage, base release, and strand breaks. This has engendered a considerable number of theoretical studies of the mechanisms involved in this DNA damage. In this chapter, we discuss the various pathways for LEE interaction with DNA and the theoretical treatments most suited to unravel these pathways. For example, inelastic electron scattering produces excitation, ionization, and transient negative ions (TNI) via shape, core-excited, and vibrational Feshbach resonances, which can all lead to DNA damage. Each of these pathways is distinguished, and their pertinence to the experimental results observed is described. Theoretical approaches used to explain these pathways are also described. Shape resonances can be understood as interactions with the electron with unoccupied molecular orbitals of neutral molecule, while core-excited states involve excitation of inner shell electrons and can be treated with theoretical methods such as time-dependent density functional theory (TD-DFT) or CASSCF. In treating the electron–molecule interaction, special care is needed to distinguish between diffuse and valence states of the TNI. The role of the vertical and adiabatic states of the radical anion is important as the electron adds to the neutral molecular framework, and reactions induced likely occur before equilibration to the adiabatic state. The effect of solvation is critical to both energetics of the interaction and the nature of the TNI formed. For example, gas-phase calculations show diffuse dipole-bound character for adenine, guanine, and cytosine anion radicals, but each of these is found to be in a valence state in aqueous solution by experiment. DNA base anion radicals often show ground states that are diffuse in character and that collapse to valence states on solvation. Such processes are shown to be accounted for inclusion of the polarized continuum model (PCM) for solvation. TD-DFT excited-state calculations including solvation show that the diffuse states rise in energy on solvation as expected. For LEE in the aqueous phase, new energy states become available such as conduction band or presolvated electrons, which may have sufficient energy to cause DNA damage. DNA radiosensitizers such as halogen-substituted uracils are being used to produce highly reactive uracil-5-yl radical, a precursor of DNA strand breaks, through its reaction with LEE.

A comprehensive analysis of the benefits and pitfalls of quantum chemical methods used to determine the structures, properties, and functions of DNA and RNA fragments is presented. Main emphasis is given to the application of different ab initio quantum chemical methods. An overview of computations reveals that quantum chemical methods provide an important means to investigate structures and interactions in nucleic acids. However, judicious selection of computational approach is necessary, depending upon the nature of the problem under investigation.

This chapter concerns some of the computational studies devoted to interactions of metal cations with nucleobases, nucleotides, and short oligonucleotides considered as DNA/RNA models. Our topic is fairly complex, therefore the results obtained using mainly ab initio and DFT methods are discussed. The first part focuses on the interactions of isolated bases with metal cations either in bare, hydrated, or ligated forms. We begin with interactions of naked cations with nucleobases in gas phase. Subsequently, solvation effects using polarizable continuum models are analyzed together with a comparison to explicitly hydrated ions. In the second part, adducts of various metals with base pairs and oligomeric models of DNA/RNA are discussed. Separate sections are devoted to complexes of promising anticancer drugs. Stacked bases and larger systems (quadruplexes) studied by semiempirical and QM/MM methods are mentioned in the last part.

Two-photon absorption (TPA) leads to higher-energy excited electronic states via the simultaneous absorption of two photons. In TPA, the absorption is directly proportional to the square of incident light intensity, and thus lasers are required for excitation. The advantages of TPA microscopy include better focus and less out-of-focus bleaching, together with absorption at longer wavelengths than in one-photon absorption, which leads to deeper penetration in scattering media, such as tissues. However, TPA probes are usually associated with less sensitivity, and thus designing TPA fluorophores with large absorption probability is an important area of research. TPA of biological molecules like fluorescent proteins and nucleic acids is of particular interest. These molecules are experimentally produced through utilization of the naturally present transcription mechanism in the cell and thus pose less cell toxicity. In this chapter, we review the theory of TPA highlighting the computational approaches used to study biological molecules. We discuss the computational methods available for exploring TPA and recent computational studies on the TPA of fluorescent proteins and nucleic acid base analogues. The chapter concludes by highlighting possible research avenues and unanswered questions.

Radiotherapy is still one of the most common modalities employed in anticancer treatment. However, hypoxia, a hallmark of solid tumor cells, makes cancer significantly more resistant than the adjacent healthy tissues toward ionizing radiation. In order to overcome this detrimental situation, radiosensitizers, i.e., substances that lower the lethal dose of ionizing radiation, should be used in clinics concomitantly with radiotherapy. In the current review, one class of radiosensitizers – modified nucleosides – are discussed in terms of their mode of action. As radiosensitizers, these modified nucleosides must employ a reaction with hydrated electrons that leaves behind the reactive radicals of nucleobases in DNA. The latter species, in turn, lead to serious DNA damage and the electron affinity of nucleosides and their ease to undergo dissociative electron attachment decide their efficiency. The mechanistic details of the process beginning from electron attachment to a nucleobase and ending with DNA damage are analyzed with the help of molecular modeling at the quantum chemistry (QM) level. First, the mechanism of action of ionizing radiation on biological matter, with particular emphasis on the formation of solvated electrons ubiquitously created under hypoxic condition, is discussed. Then, electron attachment to the modified nucleosides, to their halogen derivatives in particular, coupled to radical processes resulting in DNA damage are described in terms of the results of QM calculations. Finally, the perspectives of computer-based design of electrophilic nucleoside radiosensitizers are shortly discussed.

Excited-state molecular dynamics is a branch of theoretical physics and chemistry dedicated to simulating phenomena induced in molecules upon UV-visible light absorption. This includes the determination of nuclei positions evolution in time along with the calculation of electronic excited-states potential energy surfaces. This chapter presents both adiabatic molecular dynamics and nonadiabatic molecular dynamics simulation methods as used in photochemistry. Ab initio molecular dynamics methods are briefly reviewed. A particular emphasis is on the recent developments in semiclassical algorithms and their applicability to studies of large molecular systems evolving in electronic excited states.

This chapter focuses on the computational investigations of light-induced chemical reactions in different systems ranging from organic molecules in vacuo to chromophores in complex protein environments. The aim is to show how the methods of computational photochemistry can be used to attain a molecular-level understanding of the mechanisms of photochemical and photophysical transformations. Following a brief introduction to the field, the most frequently used quantum chemical methods for mapping excited state potential energy surfaces and for studying the mechanism of photochemical reactions in isolated molecules are outlined. In the following sections, such methods and concepts are further developed to allow the investigation of photo-induced reactions in solution and in the protein environment.

Molecular descriptors and properties are two basic forms of chemical information representing compounds in the computer. Chemical space is a structure for the mapping of these information types. It is not always easy to distinguish between descriptors and properties which are the rare annotations of chemical compounds and often need to be predicted. However, this distinction helps in understanding structure-property approaches and the possible origins for their failures. A variety of molecular descriptors is available both for storing molecules and for their processing in computers and we do not have here a sharp differentiation. The trend in property prediction goes away from pure modeling and prediction endeavors to the development of models that can also be interpreted and thus help us in increasing chemical insight and knowledge.

Quantum chemical and molecular mechanics-generated structure and reactivity parameters comprise a part of chemoinformatics, where such parameters are stored and properly indexed for search-information of a related molecule or a set of molecular systems. The present review makes a general survey of the various computable quantum chemical parameters for molecules. These could be used for quantitative structure activity relation (QSAR) modeling. The applicability of various quantum chemical techniques for such property (QSAR parameters) is also discussed and density functional theory (DFT)-related techniques have been advocated to be quite useful for such purposes. Molecular mechanics methods, although mostly useful for less time consuming structure calculations and important in higher level molecular dynamics and Monte-Carlo simulations, are sometimes useful to generate structure-related descriptors for QSAR analysis. A brief discussion in this connection with molecular mechanics-related QSAR modeling is included to show the use of such descriptors.

Despite the number of available chemicals growing exponentially, testing of their toxicological and environmental behavior is often a critical issue and alternative strategies are required. Additionally, there is the need to predict properties of not yet synthesized compounds to reduce the costs of synthesis, selecting only those that have the maximal potential to be active and nontoxic compounds. In order to evaluate chemical properties avoiding chemical synthesis and reducing expensive and time-demanding laboratory testing, it is necessary to build in silico models establishing a mathematical relationship between the structures of molecules and the considered properties (quantitative structure–activity relationships, QSARs). Molecular descriptors play a fundamental role in QSAR and other in silico models since they formally are the numerical representation of a molecular structure. Molecular descriptors can be classified using different criteria. Among them, there are two main categories, experimental and theoretical descriptors. The basis to understand and perform molecular descriptor calculation, the different theoretical descriptor categories together with their perspectives are described in this chapter.

In this chapter, we present an overview of various chemometric methods, appropriate for analyzing and interpreting data from social media, industry, academia, medicine, and other sources. We discuss unsupervised machine-learning techniques used for grouping (hierarchical cluster analysis, k-means) and exploring (principal component analysis, self-organizing Kohonen maps) all types of data, both quantitative and qualitative. For each method described in this chapter, we explain the basic concepts, provide a rudimentary algorithm, and present practical applications. All the examples are based on a set of molecular descriptors calculated for a selected group of persistent organic pollutants (POPs).

The development of quantitative structure–activity relationship (QSAR) methods is going very fast for the last decades. OSAR approach already plays an important role in lead structure optimization, and nowadays, with development of big data approaches and computer power, it can even handle a huge amount of data associated with combinatorial chemistry. One of the recent developments is a three-dimensional QSAR, i.e., 3D QSAR. For the last two decades, 3D-OSAR has already been successfully applied to many datasets, especially of enzyme and receptor ligands. Moreover, quite often 3D QSAR investigations are going together with protein–ligand docking studies and this combination works synergistically. In this review, we outline recent advances in development and applications of 3D QSAR and protein–ligand docking approaches, as well as combined approaches for conventional organic compounds and for nanostructured materials, such as fullerenes and carbon nanotubes.

Ontologies are structured controlled vocabularies which encode domain knowledge, backed by sophisticated logic-based computational tools. They enable knowledge-based applications which harness automated reasoning for inference and knowledge discovery. They also enable the semantic and standard annotation of large-scale data, which is ever relevant in the modern age of increased high-throughput data generation and sharing in scientific research. Established chemical ontologies include ChEBI, which encodes the structural classification of chemical entities of biological interest together with their roles. More recently, the chemical information ontology was created to standardize the annotation of cheminformatics software and descriptors. In this chapter, the technology, structure and applications of ontologies within cheminformatics will be described.

Force fields are empirical energy functions that are designed to compute the properties of molecular systems at a relatively low cost, subject to the condition that there are no chemical changes in a system. A force field is a sum of various energy contributions which were developed and parameterized using small model systems. A long-sought goal in designing a force field is that the simulation of a biomolecular system (mainly globular proteins) reproduces the native structure(s) and the folding/assembly process of the system. A systematic way to achieve this goal is to train a force field using a number of macromolecules (e.g., proteins) to determine the balance among constituting energy terms by adjusting force-field parameters so that the force field properly reproduces the native structures of the training molecules. In this chapter, we discuss the principles and methods used for the calibration of a force field suitable for various applications.

In this chapter, we present a brief description of compound datasets and programs developed to serve chemoinformatics as well as, more specifically, nanoinformatics purposes. Emphasis has been placed on publicly available tools and particularly on KNIME (Konstanz Information Miner), the most widely used freely available platform for data processing and analysis. Among a multitude of studies that have demonstrated the usefulness of chemoinformatics tools to chemical and medicinal applications, herein we present indicative cases of five successful KNIME-based approaches. The first two studies include the risk assessment of nanoparticles (NPs) through the Enalos InSilicoNano platform, namely, (1) the prediction of the toxicity of iron oxide NPs and (2) the cellular uptake prediction of computationally designed NPs with the aid of reliable quantitative nanostructure–activity relationships (QNAR) models. The third case study deals with the recognition of organic substances as corrosion inhibitors though the construction of predictive quantitative structure–property relationships (QSPR) models with Enalos KNIME nodes. Finally, two more cases are briefly described and involve the accurate prediction of yellow fever inhibitors from the ChEMBL database and the de novo design of compounds with the reaction vectors methodology. The aim of this work is to familiarize the interested reader with the freely available in silico tools in KNIME analytics platform and to demonstrate their value and effectiveness toward specific computational applications.

Several different chemical properties/activities must be contemporaneously taken into account to prioritize compounds for their hazardous behavior. Examples of application of chemoinformatic methods, such as principal component analysis for obtaining ranking indexes and hierarchical cluster analysis for grouping chemicals with similar properties, are summarized for various classes of compounds of environmental concern. These cumulative endpoints are then modeled by validated quantitative structure–activity relationships, based on theoretical molecular descriptors, to predict the potential hazard of new chemicals.

Since many drug development projects fail during clinical trials due to poor ADME properties, it is a wise practice to introduce ADME tests at the early stage of drug discovery. Various experimental and computational methods have been developed to obtain ADME properties in an economical manner in terms of time and cost. As in vitro and in vivo experimental data on ADME have accumulated, the accuracy of in silico models in ADME increases and thus, many in silico models are now widely used in drug discovery. Because of the demands from drug discovery researchers, the development of in silico models in ADME has become more active. In this chapter, the definitions of ADME endpoints are summarized, and in silico models related to ADME are introduced for each endpoint. Part I discusses the prediction models of the physicochemical properties of compounds, which influence much of the pharmacokinetics of pharmaceuticals. The prediction models of physical properties are developed based mainly on thermodynamics and are knowledge based, especially QSAR (quantitative structure activity relationship) methods. Part II covers the prediction models of the endpoints in ADME which include both in vitro and in vivo assay results. Most models are QSAR based and various kinds of descriptors (topology, 1D, 2D, and 3D descriptors) are used. Part III reviews physiologically based pharmacokinetic (PBPK) models.

Quantitative structure–activity relationship (QSAR) modeling is the major chemin- formatics approach to exploring and exploiting the dependency of chemical, biological, toxicological, or other types of activities or properties on their molecular features. QSAR modeling has been traditionally used as a lead optimization approach in drug discovery research. However, in recent years QSAR modeling found broader applications in hit and lead discovery by the means of virtual screening as well as in the area of drug-like property prediction, and chemical risk assessment. These developments have been enabled by the improved protocols for model development and most importantly, model validation that focus on developing models with independently validated external prediction power. This chapter reviews the predictive QSAR modeling workflow developed in this laboratory that incorporates rigorous procedures for QSAR model development, validation, and application to virtual screening. It also provides several examples of the workflow application to the identification of experimentally confirmed hit compounds as well as to chemical toxicity modeling. We believe that methods and applications considered in this chapter will be of interest and value to researchers working in the field of computational drug discovery and environmental chemical risk assessment.

A thorough antimicrobial review of an increasing number of reports reveals a broad spectrum of research activity in the development practices that are used to treat a variety of diseases. The quantitative relationship between chemical structure and biological activity has received considerable attention in recent years because it allows one to predict theoretically bioactivity without an inordinate amount of experimental time and effort. In this chapter we collect and discuss critically published results concerning the QSAR research on antimicrobial compounds. Finally, we present an updated perspective about the future trends in this area.