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WIREs Comput Mol Sci
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State‐specific multireference perturbation theory: development and present status

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The state‐specific multireference perturbation theory (SSMRPT), which provides one state at a time may now gradually become a new useful ab initio tool for studying electronic states with strong configurational quasidegeneracy owing primarily to its suitability toward numerical implementation in the presence of intruders and also to a great extent for its firm theoretical construct and the scope of a systematic and hierarchical improvement. The method works with a complete active space, and treats each of the model space functions on the same footing by exploiting Jeziorski–Monkhorst parametrization of the wavefunction. The SSMRPT is size‐extensive and size‐consistent (with the orbitals localized). The real challenge remains in developing MRPT methods capable of maintaining explicit size‐extensivity and avoiding intruders over a vast range of molecular geometries. Recently developed relativistic SSMRPT for the four‐component spinors is very promising to describe the near‐degenerate states of molecules containing heavy atoms. The analysis of the formal aspects and practical utility of the SSMRPT method vis‐à‐vis the other MRPT formalisms that bear kinship with the SSMRPT formulation is also presented. Illustrative results show high accuracy of the SSMRPT method in describing quasidegenerate situations such as those appearing when one or more covalent bonds in the molecule become stretched or broken. While actively pursuing SSMRPT method, it became apparent to us that this method encounters two major limitations: (1) the scaling of the computational cost with respect to the number of active orbitals and (2) the lack of invariance of the energy with respect to a unitary transformation of the active orbitals. The future will tell whether the SSMRPT method will be able to acquire the same faith as other widely used single‐root MRPT methods. WIREs Comput Mol Sci 2016, 6:266–291. doi: 10.1002/wcms.1248 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Dissociation energy curves of the ground state N2 molecule provided by CASSCF‐SSMRPT, IVO‐SSMRPT, CASPT2, MR‐ccCA, CCSD(T), and 8R‐RMRCCSD methods with cc‐pVTZ basis set. The CASPT2, MR‐ccCA, and CCSD(T) values are taken from Ref and 8R‐ RMRCCSD results are taken from Ref . Reproduced from Ref . Copyright 2015 Wiley Periodicals, Inc.
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Deviation of vibrational energies of the ground state of F2 molecule from the experimental values (Ref ) for the vibrational levels up to v = 22. Reproduced from Ref . Copyright 2015 Wiley Periodicals, Inc.
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Deviation of energies (ΔE = EEFCI) of IVO‐SSMRPT and various [such as SS‐MRCCSD, CR‐CCSD(T), CASPT2, and MRCI see Ref. ] methods from the FCI values for bond breaking in the ground state F2 [CAS(2,2) reference wave function with cc‐pVDZ basis set has been used in all MR‐based calculations considered here]. Reproduced from Ref . Copyright 2015 Wiley Periodicals, Inc.
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Generic representation of MR situations carrying both nondynamical (treated by CASSCF/CASCI/IVO‐CASCI ⋯) and dynamical (accounted by PT/CI/CC ⋯ method on top of the multiconfigurational wave function) correlations. Active–active space correlations describe nondynamical correlation effects, while the interaction between active–virtual, active–core, and core–virtual spaces provided the dynamic correlation. All configuration functions with a given space and spin symmetry are included in the multiconfigurational wave function. This is the concept of the complete active space.
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Structures of m‐benzyne, 2,6‐pyridyne, and 2,6‐pyridynium cation.
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Dissociation energy curves [in terms of ΔE(R) = E(R) − E(Re)] provided by the 4c‐IVO‐SSMRPT, and 4c‐CCSD methods with Dyall‐v2z and Dyall‐v3z basis sets for the ground state of the Rb2 molecule. Note that the energy value at the equilibrium internuclear distance is shifted to zero for all approaches. Reproduced from Ref . Copyright 2015 Wiley Periodicals, Inc
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