Resolution of the identity approximation

Kendall, R. A., Friichtl, H. A., 1997, The Impact of the Resolution of the Identity Approximate Integral Method on Modern Ab Initio Algorithm Development , Theor. Chem. Acc., 97, 158. 

Hattig C, Weigend F (2000) CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J Chem Phys 113 5154... 

A. Kohn and C. Hattig, Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation, J. Chem. Phys., 119 (2003) 5021-5036. 

Till recently, computations of vibronic spectra have been limited to small systems or approximated approaches, mainly as a consequence of the difficulties to obtain accurate descriptions of excited electronic states of polyatomic molecules and to computational cost of full dimensional vibronic treatment. Recent developments in electronic structure theory for excited states within the time-dependent density functional theory (TD-DFT) and resolution-of-the-identity approximation of coupled cluster theory (R1-CC2) and in effective approaches to simulate electronic spectra have paved the route toward the simulation of spectra for significantly larger systems. 

Nonetheless, MP2 is quite a bit slower than HF theory. The resolution of the identity approximation (RI) makes MP2 nearly competitive with HF in terms of computational time. This approximation involves a simplification of the evaluation... 

Hattig, C., A. Hellweg, and A. Kohn. Distributed memory parallel implementation of energies and gradients for second-order Moller-Plesset perturbation theory with the resolution-of-the-identity approximation. Phys. Chem. Chem. Phys. 8 1159-1169, 2006. 

Kendall RA, Fruchtl HA (1997) The impact of the resolution of the identity approximate integral method on modem ab initio algorithm development. Theor Chem Acc 97 158-163... 

Calculations on Large Molecules using the Resolution of the Identity Approximation. 

These linear R12 approaches, while helpful for very careful benchmarking studies, have had the drawback that they are rather expensive to use. One of the main reasons for this is that the particular resolution of the identity approximation they have typically employed is valid only when a large basis set is used. However, a number of recent developments indicate that in the... 

Resolution of the Identity Approximate Integral Method on Modern Ab Initio Algorithm Development. 

---