As a part of an ongoing project devoted to the development of theoretical foundations and computational methods for treating systems in external electro-magnetic fields, we present a new method here for dealing with magnetic fields of arbitrary strength and for arbitrary systems. The method is based on leaving the commonly used Coulomb gauge and instead introducing an operator gauge. We show that this method avoids the obstacles related with using the Coulomb gauge in combination with GIAOs (gauge-invariant atomic orbitals) as basis functions, i.e., complicated matrix elements and oscillatory behavior for non-magnetic terms. Moreover, our approach shares many features with the "Modern Theory of Magnetization," which is based on the operator, ∇⃗k. However, our approach is not restricted to periodic systems and avoids many complications involved in the application of ∇⃗k. Our method is applicable for any system and field strength, and it readily provides an answer to the question of whether there is a surface/shape contribution to intensive magnetic responses for large systems. Test calculations on H2+ using a homemade ab initio program developed for small systems, and a simplified model for large systems, give mutually consistent and complementary results in support of our suggested approach, but not in complete agreement with results of GIAO calculations. We present a detailed analysis of this finding.

During the past years, organic solar cells (OSCs) have been at the center of a significant scientific interest. However, it is still a big challenge to identify organic molecules with the best performances due to the almost inexhaustible chemical space. We recently proposed an inverse-design approach, i.e.. poor man's materials optimization (PooMa), which combines global optimization based on genetic algorithms (GA) and a fast, efficient parametrized density-functional tight-binding (DFTB) method for the calculation of the electronic structure for each individual structure. Here, we applied this method to identify conjugated systems with low reorganization energies for charge-transfer processes. We have considered benzene and pyridine as two different simple test systems and selected 20 different functional groups for the construction of organic molecules. The results showed that our approach (PooMa) is able to construct numerous new structures and successfully identify molecules with good performance at a low computational cost. Furthermore, we present a simple theory that can capture the main results of our study.

DFT calculations using the B3LYP level of theory were carried out in order to determine the mechanisms of the hydromination reaction and of the cyclization reaction of 1-(2-aminophenyl)-3-phenylprop-2yn-1-one R1. Hydromination of R1 by diethylamine leads to 2-phenylquinolin-4 (1H)-one P1, while the catalytic cyclization using different palladium complexes as catalysts leads to the production of (2Z)-2-benzylidene-1,2-dihydro-3H-indol-3-one P2. Analyzing the potential energy surface indicates that the formation of the C-N bond in the presence of diethylamine is related to high activation energies. In addition, the calculations show that there are two reaction paths for the palladium-catalyzed cyclization reaction of R1; the first one is of [1,6]-H shift type while the second is of [1,5]-H shift type, followed by the formation of a C-N bond. In each case, this is the rate-determining step. We compare the Pd complexes and determine the one with the best catalytic performance in the production of P2.

We discuss theoretical methods with which the effects of static, homogenous, electromagnetic fields can be determined for systems that are extended and in the ultimate limit are infinite and periodic. We focus here on the finite field (FF) method, but there are obvious implications for perturbation theory approaches as well. The fact that including finite fields in electronic-structure calculations simultaneously introduces the coordinate r→ means that the translational invariance of the potential would be violated and therefore without modification this approach would be inapplicable to infinite, periodic systems. One such long-standing approach is to replace r→ by an operator that involves the derivative with respect to the crystal momentum k→. This is the primary procedure for electrostatic fields. For magnetostatic fields a number of suggestions have been made, all of which are or may be related to changing the gauge used to describe the fields. In the case of a large finite system, for non-vanishing electrostatic and/or magnetostatic field, the lowest energy orbitals are unbound. Thus, the bound states become resonances and the bound-state variational principle can no longer be applied. Instead, special methods for identifying the changes in the system properties due to the presence of these fields are evaluated. Our own simple method based on identifying those orbitals in the field-containing case that are most similar to the occupied orbitals in the field-free case seems to be a promising approach. Since methods for finite molecular systems exposed to static electromagnetic fields are more mature than those for the infinite, periodic crystals, an important issue is to establish that these methods give identical results when treating a crystal as being either large and finite or infinite and periodic. Finally it shall be mentioned that our presentation focuses on methods rather than results. Moreover, it concentrates on our own work that, in some cases, is not yet complete.

A computational investigation of the aerobic oxidative C-C bond cleavage reaction of glycol catalyzed by an Anderson-type heteropolyanion HPA [IMo6O24](5-) in the presence of acetonitrile as solvent has been performed at the WB97XD/6-31G(d,p)/lanl2dz level. Two reaction pathways have been identified. The catalytic cycle of each pathway consists of three steps: oxidation cleavage of a glycol molecule by the HPA, oxidation of the HPA by one dioxygen molecule, and, finally, oxidation of a second glycol and regeneration of the catalyst. These reaction pathways have been thoroughly investigated in terms of energetic, natural bond orbital (NBO), natural charges, and geometrical parameters. It is found that (i) even though the top oxygen atoms of the Anderson heteropolyanion are not the most negatively charged ones, they are more likely to react with the diol hydroxyl groups, (ii) a direct relationship between the presence of the iodine ion I(VII) and the studied oxidation reaction could not be identified, and (iii) in terms of energy, the transfer of the two hydrogen atoms is the most energetic step.

The synthetic bicyclic bis(hemiacetals) compounds 1,5-pyranose-9,7-pyranoses, with a structural analogy to the bicyclic monosaccharide Bradyrhizose, have been described here based on a theoretical approach, using DFT calculations with the B3LYP functional combined with the 6-311 + G(d,p) basis set. First, we have performed a geometrical and electronic properties description of (1 R,9S), (1S,9S) and (1S,9R)-1,5-pyranose-9,7-pyranoses. Results analysis indicated that, slight differences in the three-dimensional orientations of their atoms lead to an enormous difference in chemical reactivity. Consequently, (1S,9S) and (1S,9R) isomers are predicted to be the most resembling the natural bradyrhizose in structural features. To enhance the performance of these two isomers, a set of modifications through functional groups attached to the reactive sites were determined by local reactivity descriptors. Subsequently, in order to get more information on the obtained derivatives for both isomers, HOMO, LUMO, Egap and four electronic parameters were calculated and compared. The substituted systems show a good performance in chemical reactivity than the unmodified parent compounds.Communicated by Ramaswamy H. Sarma

In this work, the geometric and electronic parameters of pure and vanadium-substituted anions of Lindqvist polyoxometalates have been investigated using DFT calculations. Active sites of all anions are identified through results on local and global reactivity descriptors. The results indicate that bridging oxygen atoms in all clusters are the most active sites. Using this, the mechanism of the catalytic generation of the hydroxyl radical from water was studied for the di-substituted Lindqvist polyoxometalate [V2Mo4O19]4−. This study provides a detailed understanding of this important intermediate step in photo-oxidation reactions. The mechanistic route makes it possible to locate transition states and intermediates structures and demonstrates that the pre-association of the water molecule leads to an H abstraction with an energy barrier of 26.42 kcal/mol and OH radical and [HV2Mo4O19]4− as products in this step.

Results of a theoretical study devoted to comparing NLO (non-linear optics) responses of derivatives of tetracene, isochrysene, and pyrene are reported. The static hyperpolarizability β, the dipole moment μ, the HOMO and LUMO orbitals, and their energy gap were calculated using the CAM-B3LYP density functional combined with the cc-pVDZ basis set. The para-disubstituted NO2-tetracene-N(CH3)2 has the highest NLO response, which is related to a large intramolecular charge transfer. Adding vinyl groups to the para-disubstituted NO2-tetracene-N(CH3)2 results in an increase in the NLO responses. We further investigated the effect of the intercalation of various push–pull molecules inside an armchair single-walled carbon nanotube. The intercalation leads to increased NLO responses, something that depends critically on the position of the guest molecule and/or on functionalization of the nanotube by donor and attractor groups.

Using various approximate total-energy methods, we are studying the energetic and structural properties of clusters with more than one type of atoms of which at least one type is a metal. In order to study larger classes of sizes and/or stoichiometries, we have to rely on less accurate total-energy methods, most notably the density-functional tight-binding (DFTB) method and embedded-atom method (EAM). The structures that are studied are either parts of crystalline compounds or determined through unbiased structure optimizations. The goal is to study larger classes of sizes and/or stoichiometries and, therefore, various descriptors are employed in order to extract chemical and physical understanding from the large amount of data that result from such calculations.

In this paper we develop the shape effect, which is relevant for crystalline materials whose size is larger than that of the thermodynamic limit. According to this effect the electronic properties of one surface of a crystal depend upon all of its surfaces, i.e. on the overall shape. At first, qualitative mathematical arguments are presented for the existence of this effect based on the conditions for the stability of polar surfaces. Our treatment explains why such surfaces are observed even though earlier theory indicated that they should not exist. Then, models are developed from which it is found computationally that changing the shape of a polar crystal can substantially alter the magnitude of its surface charges. Apart from surface charges, it follows that the crystal shape will also significantly affect bulk properties, most notably polarization and piezoelectric responses. Additional model calculations show a strong shape effect on the activation energy for heterogeneous catalysis primarily through local surface charges rather than a non-local/long range electrostatic potential.

The structural and energetic properties of small silver clusters Agn with n = 2–100 atoms are reported. For n = 2–100 the embedded atom model for the calculation of the total energy of a given structure in combination with the basin-hopping search strategy for an unbiased structure optimization has been used to identify the energies and structures of the three energetically lowest-lying isomers. These optimized structures for n = 2–11 were subsequently studied further through density-functional-theory calculations. These calculations provide additional information on the electronic properties of the clusters that is lacking in the embedded-atom calculations. Thereby, also quantities related to the catalytic performance of the clusters are studied. The calculated properties in comparison to other available theoretical and experimental data show a good agreement. Previously unidentified magic (i.e., particularly stable) clusters have been found for n>80. In order to obtain a more detailed understanding of the structural properties of the clusters, various descriptors are used. Thereby, the silver clusters are compared to other noble metals and show some similarities to both copper and nickel systems, and also growth patterns have been identified. All vibrational frequencies of all the clusters have been calculated for the first time, and here we focus on the highest and lowest frequencies. Structural effects on the calculated frequencies were considered.

We present an improved inverse-design approach for automatically identifying molecular (or other) systems with optimal values for prechosen properties. The new approach uses SMILES (simplified molecular input line entry system) to describe molecular structures efficiently, a genetic algorithm to optimize the molecules automatically, and the DFTB+ (self-consistent charge density functional tight-binding) method to calculate electronic properties. Thereby, almost every class of materials─even macromolecules or monomers─can be studied easily. Without crossover operators but with only mutation operators, the genetic algorithm is more adaptive to SMILES while keeping its efficiency. DFTB+ is more accurate than the DFTB method used in our previous inverse-design approach for the study of excited states and charge transfer processes. The improved approach is applied to optimize benzene, pyridine, pyridazine, pyrimidine, and pyrazine derivatives for seven electronic properties, which all are highly relevant and important for the performance of molecules in solar cells. We found that for some electronic properties, the precise composition and structure of the backbone have remarkable impacts on the value of the electronic properties and/or on the set of functional groups that leads to the best performance. On the contrary, for other properties, these effects are less pronounced. The reasonable optimal functional groups and/or substitution patterns are reported.

Aldimine derivatives chromophores grafted on polyacetylene oligomers were first designed to investigate the nonlinear optical (NLO) response of the resulting materials using CAMB3LYP method. The effects of different factors such as the chain length separating the substitutions as well as the configurations and the orientations of these latter, were examined and discussed. In a second part of this paper, NLO responses, in particular the static hyperpolarizabilities of polyvinyl oligomers substituted by aldimine chromophores via carboxylic groups and by pyrrolidone groups were calculated for different configurations. The stability and the hydrogen bonding in each oligomer were also discussed.

Eight push–pull systems involving containing four transition metals (iron, ruthenium, cobalt, and nickel), metallocenes as donor groups, cyanoacrylate as electron attractor group, and thiophene-N = N- pyrimidine derivatives as π-conjugated bridges were designed and studied using DFT and TD-DFT methods involving B3LYP and CAM-B3LYP functionals combined with the cc-pVDZ/LANL2DZ basis sets. The main purpose of this work is to determine the effect of metallocene in improving the photosensitization property of such chromophores. This was done by calculating their light-harvesting efficiency LHE as well as other properties employed for DSSC application. The considered dyes were first studied in the gas phase, then in the presence of TiO2 nanoparticles representing the semi-conductor, and finally in the presence of a specific implicit solvent. The presence of iron as metal involved in the metallocene group supplemented by extending the π-conjugated bridge by a cyanovinyl spacer was demonstrated so as to give the most optimal response taking into account the lower cost and toxicity as well as the friendliness to the environment of iron as metal.

This textbook introduces the reader to quantum theory and quantum chemistry. The textbook is meant for 2 nd – 3 rd year bachelor students of chemistry or physics, but also for students of related disciplines like materials science, pharmacy, and bioinformatics. At first, quantum theory is introduced, starting with experimental results that made it inevitable to go beyond classical physics. Subsequently, the Schrödinger equation is discussed in some detail. Some few examples for which the Schrödinger equation can be solved exactly are treated with special emphasis on relating the results to real systems and interpreting the mathematical results in terms of experimental observations. Ultimately, approximate methods are presented that are used when applying quantum theory in the field of quantum chemistry for the study of real systems like atoms, molecules, and crystals. Both the foundations for the different methods and a broader range of examples of their applications are presented. The textbook assumes no prior knowledge in quantum theory. Moreover, special emphasis is put on interpreting the mathematical results and less on an exact mathematical derivations of those. Finally, each chapter closes with a number of questions and exercises that help in focusing on the main results of the chapter. Many of the exercises include answers.

Using a combination of genetic algorithms for the unbiased structure optimization and a Gupta many-body potential for the calculation of the energetic properties of a given structure, we determine the putative total-energy minima for all $$\hbox {Ag}_{m} \hbox {Rh}_n$$ Ag m Rh n clusters with a total number of atoms $$m+n$$ m + n up to 55. Subsequently, we use various descriptors to analyze the obtained structural and energetic properties. With the help of a similarity function, we show that the pure Ag and Rh clusters are structurally similar for sizes up to around 20 atoms. The same approach gives that the mixed clusters tend to possess a larger structural similarity with the pure Rh clusters than with the pure Ag clusters. However, for clusters with $$m\simeq n\ge 25$$ m ≃ n ≥ 25 , other structures dominate. The effective coordination numbers for the Ag and Rh atoms as well as the radial distributions of those atoms indicate that there is a tendency towards segregation with Rh atoms forming an inner part and the Ag atoms forming a shell. Only few clusters, all with a fairly large total number of atoms, are found to be particularly stable.

Molecular level insights into the mechanism and thermodynamics of CO oxidation by a (TiO2)6 cluster have been obtained through density functional calculations. Thereby, in this study, as an example, two different structural isomers of (TiO2)6 are considered with the purpose of understanding the interplay between local structure and activity for the CO oxidation reaction. Active sites in the two isomeric forms were identified on the basis of global and local reactivity descriptors. For the oxidation of CO to CO2, the study considered both sequential and simultaneous adsorption of CO and O2 on (TiO2)6 cluster through the ER and LH mechanisms, respectively. Three different pathways were obtained for CO oxidation by (TiO2)6 cluster, and the mechanistic route of each pathway were identified by locating the transition-state and intermediate structures. The effect of temperature on the rate of the reaction was investigated within the harmonic approximation. The structure-dependent activity of the cluster was rationalized through reactivity descriptors and analysis of the frontier orbitals.

Using a combination of genetic algorithms for the unbiased structure optimization and a Gupta many-body potential for the calculation of the energetic properties of a given structure, we determine the putative total-energy minima for all $$\hbox {Ag}_{m} \hbox {Rh}_n$$ clusters with a total number of atoms $$m+n$$ up to 55. Subsequently, we use various descriptors to analyze the obtained structural and energetic properties. With the help of a similarity function, we show that the pure Ag and Rh clusters are structurally similar for sizes up to around 20 atoms. The same approach gives that the mixed clusters tend to possess a larger structural similarity with the pure Rh clusters than with the pure Ag clusters. However, for clusters with $$m\simeq n\ge 25$$ , other structures dominate. The effective coordination numbers for the Ag and Rh atoms as well as the radial distributions of those atoms indicate that there is a tendency towards segregation with Rh atoms forming an inner part and the Ag atoms forming a shell. Only few clusters, all with a fairly large total number of atoms, are found to be particularly stable.