16 lines
1.7 KiB
TeX
16 lines
1.7 KiB
TeX
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\section{Summary}
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In the last chapter of this memoir, we have presented two lines of our current research.
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First, we have introduced a dressed version of the well-established CI method to incorporate explicitly the correlation between electrons.
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We have shown that the new CI-F12 method allows to fix one of the main issue of conventional CI methods, i.e.~the slow convergence of the electronic energy with respect to the size of the one-electron basis set.
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Albeit not variational, our method is able to catch a large fraction of the basis set incompleteness error at a low computational cost compared to other variants.
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In particular, one eschews the computation of four-electron integrals as well as some types of three-electron integrals.
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We believe that the present approach could be a significant step towards the development of an accurate and efficient explicitly-correlated FCI methods.
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Second, we have proposed a procedure to enforce the e-n cusp by augmenting conventional (cuspless) Gaussian basis sets with cusp-correcting Slater basis functions.
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Two types of procedure has been presented.
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In the one-shot procedure, the coefficients of the Slater functions are obtained by ensuring the correct e-n cusp at each nucleus.
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We have also designed a self-consistent procedure to optimise simultaneously the coefficients of the Gaussian and Slater basis functions by diagonalisation of an orbital-dependent effective Fock operator.
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The same procedure could potentially be employed to correct the long-range part of the electronic density with obvious application within DFT.
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