Quantum Chemical Methods for the Design of Molecular Non-Linear Optical Materials
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INTRODUCTION
Historically, molecular design in the pharmaceutical, agrochemical and other areas has relied heavily upon empirical and intuitive methods for modifying molecular structures in appropriate ways to achieve or approach desired properties. Not. infrequently, success has occurred through chance or accidental observations and for this reason these methods have been referred to by some as 'molecular roulette.' In the mid 1960s, with the development of digital computers, computer aided methods began to be applied and both molecular mechanics and quantum mechanics were applied to problems in molecular design. Molecular mechanics models molecules by sets of atomns of specified mass coupled together by springs of specified force constant (one spring for each vibrational degree of freedom). These models were totally empirical but could give useful information, particularly about the shape of large molecules. This was valuable, especially in the design of new phamaceutical molecules where there is a need to tailor molecular shape to the intended receptor site. For our purposes, however, molecular mechanics has little use since it provides no electronic structure information. For that level of detail we must have recourse to quantum mechanical techniques.
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QUANTUM CHEMISTRY
Quantum chemistry' aims to provide the most fundamental understanding of molecular electronic properties which is possible, and this is achieved through solutions describing the microscopic quantum behaviour of the electrons and nuclei which make up molecules. 3 Mat. Res. Soc. Symp. Proc. Vol. 374 01995 Materials Research Society
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Systems of Schridinger equations
In usual applications, the methodology is predicated upon the BornOppenheimer approximation. Because the nuclear and electronic masses are so different, the electronic and nuclear subsystems can be treated separately to a very high degree of approximation. The total Hamiltonian can be written as a sum of two operators, one for each subspace, and the Schr6dinger equation for the complete system is replaced by a pair of equations. The motion of the nuclei is described by the electronic Schr6dinger equation
H(r, Q),P(x; Q) = E(Q)'I(x; Q)
(1)
for which a clamped nucleus approximation is invoked. The positions of the A nuclei are fixed at some predetermined values specified by the 3Adimensional vector Q. Solution of the electronic equation for this molecular geometry gives the total energy of the molecule, E(Q), and the total electronic wavefunction, i(x; Q), where x is a 6a-dimensionad vector in spin (a) and space (r) coordinates for the a electrons in the molecule. For each different electronic state n there is a different solution, specified by a subscript n. The equilibrium geometry Q(') of the molecule in the nth. electronic state is determined by OE=. (2)
OQ IQ=Q~o.
Some care must be exercised in determining Qo for large molecules since there will be many local minima associated with individual conformations of the molec(ule which lie above the absolute minimum of t
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