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\title{CONSTRUCTION OF NESTED CONTRACTED BASIS FUNCTIONS USING DIMENSIONALITY-REDUCTION TECHNIQUES IN CONJUNCTION WITH GROUP-THEORETICAL METHODS }

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\author{\underline{\FirstName MICHA\"{E}L \LastName REY}}
\address{Groupe de Spectrom\'etrie Mol\'eculaire et Atmosph\'erique UMR CNRS 7331, UFR Sciences BP 1039, 51687 Reims Cedex 2, France}

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\author{\FirstName TUCKER \LastName CARRINGTON, Jr.}
\address{Chemistry Department, Queen's University Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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The construction of contracted basis functions for solving the time-independent Schr\"odinger equation
 is revisited\footnote{M. Rey and T. Carrington, Jr., to be submitted}. 
First, an extensive use of symmetry {\it via} the irreducible tensor operator formalism  allows a unified treatment of molecules belonging to both Abelian and 
non-Abelian molecular symmetry groups. Second, a suitable combination of pruned basis sets and Kronecker products with relevant reduction techniques based on 
a tree-like structure allows to control the memory cost during each contraction. 
The dimension of the matrices to be diagonalized is thus substantially reduced, making it still possible to use direct eigensolvers, even for molecules with more than 5 atoms. 

As a validation test, the proposed method is used to compute the  energy levels of CH$_3$CN (C$_{3v}$) and 
C$_2$H$_4$O (C$_{2v}$) and the results are compared to the best available calculations. 




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