The purpose of the work is to calculate accurate values of molecular properties of tetracyanoquinodimethane (TCNQ) and anions using the complete active space self-consistent field and complete active space second-order perturbation theory methods. The accuracy has been evaluated using several basis sets and active spaces. The calculated properties have, in many cases, been confirmed by experimental data (within parentheses), e.g., 9.54 eV (9.61 eV) and 3.36 eV (3.38 eV) for the ionization potential and electron affinity, respectively, of TCNQ; 3.12 eV (3.01 eV) and 3.54 eV (3.42 or 3.60 eV) for transition energies to the two lowest-lying excited singlet states of TCNQ; − 0.03, 0.46 and 1.44 eV (0, 0.5 and 1.4 eV) for electronic energies in electron attachment of TCNQ forming $$\hbox {TCNQ}^-$$; and 3.88 eV (3.71 eV) for the transition energy to the second lowest-lying excited singlet state of $$\hbox {TCNQ}^{2-}$$. Further, the calculations have brought insight into some experimental observations, e.g., the shape of the fluorescence spectrum of TCNQ at 3–4 eV.

Using the CASSCF/CASPT2 methodology the electronic transitions HOMO → LUMO, HOMO → LUMO+1, HOMO-1 → LUMO and HOMO-2 → LUMO are determined for C₆₀.Comparison to experiment suggests an accuracy better than 0.3 eV. Some illustrative examples are (with experimental data within parentheses) the first excited state, ³T_2g, at 1.54 eV (1.60 eV), the two lowest-lying ¹T_1u states (for spin- and symmetry-allowed transitions) at 3.09 eV (3.08 eV) and 3.19 eV (3.30 eV) and the lowest singlet excited states (¹G_g, ¹T_1g, ¹T_2g , ¹H_g) at [1.84, 1.95] eV (1.90 eV with mainly ¹G_g and ¹T_1g and minor ¹T_2g character).

The problem addressed concerns the determination of the average numberof successive attempts of guessing a word of a certain length consisting of letters withgiven probabilities of occurrence. Both first- and second-order approximations to a naturallanguage are considered. The guessing strategy used is guessing words in decreasing orderof probability. When word and alphabet sizes are large, approximations are necessary inorder to estimate the number of guesses. Several kinds of approximations are discusseddemonstrating moderate requirements regarding both memory and central processing unit(CPU) time. When considering realistic sizes of alphabets and words (100), the numberof guesses can be estimated within minutes with reasonable accuracy (a few percent) andmay therefore constitute an alternative to, e.g., various entropy expressions. For manyprobability distributions, the density of the logarithm of probability products is close to anormal distribution. For those cases, it is possible to derive an analytical expression for theaverage number of guesses. The proportion of guesses needed on average compared to thetotal number decreases almost exponentially with the word length. The leading term in anasymptotic expansion can be used to estimate the number of guesses for large word lengths.Comparisons with analytical lower bounds and entropy expressions are also provided.

Cellular automata have a widespread use in the description of complex phenomena in disciplines as disparate as for example physics and economics. They are described by a lattice of cells, states of the cells, and rules for updating the states of the cells. One characteristics of a cellular automaton is the simplicity of the rules that determine how the cellular automaton evolves in time. These rules are local, are applied in parallel to all the cells and despite their simplicity they may give rise to a complex macroscopic behaviour. In this paper this is illustrated by examples from hydrodynamics and it is shown that cellular automata might provide powerful alternatives to partial differential equations

Cellular automata have a widespread use in the description of complex phenomena in disciplines as disparate as, for example, physics and economics. A cellular automaton is a lattice of cells, and the cells can be in a finite number of states. By using simple local rules the states of the cells are updated in parallel at discrete time steps. In short, a cellular automaton can be characterised by the three words - simple, local, and parallel. These three words are one of the reasons for the attractiveness of cellular automata. They are simple to implement and they are well suited for parallel computers (computations). Another reason for using cellular automata are for their spatio-temporal properties. The lattice may represent space and the updating of the cells gives a

dimension of time.



In spite of the simplicity of cellular automata they may give rise to a complex macroscopic behaviour. This is illustrated, in this thesis, by an hydrodynamic example, namely the creation of vortices in flow behind a cylinder.



Although cellular automata have the ability to describe complex phenomena it is sometimes hard to find the proper rules for a given macroscopic behaviour. One approach which has been successfully employed is to let cellular automata rules evolve (for example, through genetic algorithms) when finding the desired properties. In this thesis this is demonstrated for two-dimensional cellular automata with two possible states of the cells. A genetic algorithm is used to find rules that evolve a given initial configuration of the cells to another given configuration.

In this paper properties and behavior of cellular automata are considered. Cellular automata can simply be described as lattices of cells, where the cells can be in a finite number of states. By using simple rules the states of the cells are updated in parallel at discrete time steps. Depending on the rule and, to a certain degree, the initial states of the cells, the evolution of a cellular automaton is restricted to a small number a ways. Some cellular automata evolve uniformly, meaning that all cells end up in the same state, while others evolve randomly, meaning that the states of the cells appear to be totally randomized during evolution. Intermediate behavior, displaying repetitiveness or nesting, also occurs.Properties of cellular automata that are discussed in the paper are, for instance, sensitivity to initial conditions, randomness, reversibility, entropy, and conservation. These properties also appear in the physical world and cellular automata provide good examples in the understanding of these properties.The evolution of cellular automata can be used for computations. Some cellular automata even display the property of universality, a term well known from the universal Turing machine, meaning that there is no limit to the sophistication of the computations they can perform.

Properties and behavior of cellular automata are considered. Cellular automata can simply be described as lattices of cells, where the cells can be in a finite number of states. By using simple rules the states of the cells are updated at discrete time steps. The evolution of cellular automata can be used for computations. Some cellular automata display universality meaning that there is no limit to the sophistication of the computations they can perform.

The electronic spectrum of VCr has been studied using the complete-active-space self-consistent field complete-active-space second-order perturbation theory approach. Potential energy curves for 12 electronic states have been computed. Transition energies, with respect to the X^2Delta ground state, for some of the calculated electronic states are (with possible experimental values within parentheses): 0.53 eV (0.56) for A^2Sigma+, 1.03 eV (1.14) for A^4Delta, 1.20 eV (1.14) for B^2Delta, 1.45 eV (1.51) for B^4Delta, 1.60 eV (1.51, 1.78) for C^2Delta, and 1.61 eV (1.63) for A^4Sigma^-.