A combined Monte Carlo simulation with semiempirical quantum mechanics calculations has been performed to investigate the structure of hydrated fullerene (C 60 HyFn) and the influence of hydration on its UV-vis spectra. The statistical information of the C 60 fullerene aqueous solution (C 60 FAS) is obtained from NPT ensemble including one C 60 fullerene immerses in 898 water molecules. To obtain an efficient ensemble average, the auto-correlation function of the energy has been calculated. The analyzed center-of-mass pair-wise radial distribution function indicates that, on average, there are 65 and 151 water molecules around the first and second hydration shells, respectively, of a single C 60 molecule. To calculate the average UV-vis transition energies of C 60 HyFn, only the statistically uncorrelated configurations are used in the quantum mechanical calculations (INDO/CIS). These involve hundreds of supramolecular structures containing one C 60 fullerene surrounded by the first hydration shell. The calculated average transitions at 268 and 350 nm are in very good agreement with the experimental prediction.

We propose the Woods-Saxon (WS) potential to simulate spatial confinement. The great advantage of our methodology is that it enables the study of a wide range of systems and confinement regimes by varying two parameters in the model potential. To test the methodology we have studied the confined harmonic oscillator in two different regimes: when the confinement potential exhibits a sudden jump; and when the confinement is described by a smooth function. We have also applied the present procedure to a realistic problem, a confined quantum dot-atom. The numerical calculation is performed with the equally spaced discrete variable representation (DVR). Our results are in close agreement with those available in the literature, and we believe our method to be a good alternative for studying confined quantum systems.

In this paper we review the correlation function quantum Monte Carlo (CFQMC) method. We describe the functional forms and the optimization of trial basis functions used to treat the vibrational and rotational motions. We discuss selected applications to di-, tri- and tetra-atomic molecules. Our main goal is to discuss the potentiality of the CFQMC method in the study of rovibrational excited states of polyatomic molecules. In particular, we focus our discussion on the generation of the trial basis functions for ground and excited states, and the guiding function used to perform the multidimensional integral sampling required by the method.

We develop a procedure for calculating an optimized Discrete Variable Representation DVR optimized for a given potential. The method leads to an e cient and compact way to obtain numerical solutions of quantum mechanical problems. The procedure is applied to several physical problems. To illustrate the strength of the algorithm in dealing with multidimensional calculations, we obtain accurate levels up to 19; 000 cm ,1 for the vibrational energies of the water molecule.The e ciency of quantum mechanical numerical calculations rely in great part on the right c hoice of basis functions. The solution of multidimensional problems requires the manipulation of large matrices and a bad choice of basis functions could easily turn the problem unfeasible. We should also be concerned with the matrix structure and the computer time for the computation of the matrix elements. The calculation of the elements of a matrix makes use of Gaussian quadratures and an excessive n umb e r o f p o i n ts may lead to prohibitive time consuming codes. This paper shows a procedure for optimizing all these aspects. The strength of the approach is easily seen when we deal with threedimensional problems.There are several ways of expanding the quantum mechanical wave function. The more traditional procedure is the expansion in terms of global basis functions 1-3 . Generally, w e c hoose the functions that diagonalize the kinetic energy operator and integrate numerically the potential using Gaussian quadratures. Another family of procedures are the nite element methods 4-12 . The basis functions are local and we h a ve to discretize the space in many elements to implement the calculation 6 . Finally, w e m a y c hoose a set of basis functions that have the feature of diagonalizing the potential. The great advantage in this case is that the kinetic energy operator may b e i n tegrated analytically, leading to a great e ciency during the evaluation of the matrix elements. The last procedure is called the Discrete Variable Representation" DVR 13-23 . The Discrete Variable Representation has been used extensively by Light and collaborators 13-16 who performed accurate calculations of the ro-vibrational energies of several triatomic molecules. Choi and Light 24 also used this procedure to study Van der Waals molecules. Le Quere and Leforestier 25 used a time dependent approach and a DVR implementation for studying the photodissociation of Ozone. More recently, the method for expanding the multidimensional quantum mechanical wave function 26-32 has appeared in other calculations. This paper develops a procedure for obtaining a Numerically Generated Discrete Variable Representation NG-DVR . All publications mentioned before, except the work of Echave and Clary 26 , do not use a numerically optimized Discrete Variable Representation for the potential of the system under consideration. In this way, the number of basis functions is not optimized for the particular problem to be solved. The procedure proposed by E c have and Clary 26 does not calculate e...

A variational method called discrete variable representation is applied to study the energy spectra of two interacting electrons in a quantum dot with a three-dimensional anisotropic harmonic confinement potential. This method, applied originally to problems in molecular physics and theoretical chemistry, is here used to solve the eigenvalue equation to relative motion between the electrons. The two-electron quantum dot spectrum is determined then with a precision of at least six digits. Moreover, the electron correlation energies for various potential confinement parameters are investigated for singlet and triplet states. When possible, the present results are compared with the available theoretical values.