Quantum second-order Moller-Plesset perturbation

Over the decade 1995-2005, ab initio quantum chemistry has become an important tool in studying imidazole derivatives. Two highly productive approaches are often utilized for the calculations the wave function-based methods (e.g., Hartree-Fock theory and second-order Moller-Plesset perturbation theory (MP2)) and the density functional theory (DFT) based methods (e.g., gradient-corrected (BLYP) and hybrid (B3LYP) methods). 

Second-order Moller-Plesset perturbation theory correlated static quantum chemical method see [2]... 

In many cases electronic properties calculated at the Hartree-Fock level do not have the accuracy sufficient to make them useful in chemical predictions. For example, as revealed in a recent study,the stability of the cage isomer of the C20 carbon cluster relative to that of the cyclic isomer is underestimated at the Flartree-Fock level by as much as 200 kcal/mol. In such systems, the electron correlation effects have to be taken into account in quantum chemical calculations through application of approximate methods. One such approximate electron correlation methods that has gained a widespread popularity is the second-order Moller-Plesset perturbation theory (MP2). Until recently calculations involving the MP2 approach have used a traditional formulation in which the MP2 energy is evaluated as the sum... 

One of the most dramatic changes in the standard theoretical model used most widely in quantum chemistry occurred in the early 1990s. Until then, ab initio quantum chemical applications [1] typically used a Hartree-Fock (HF) starting point, followed in many cases by second-order Moller-Plesset perturbation theory. For small molecules requiring more accuracy, additional calculations were performed with coupled-cluster theory, quadratic configuration interaction, or related methods. While these techniques are still used widely, a substantial majority of the papers being published today are based on applications of density functional theory (DFT) [2]. Almost universally, the researchers use a functional due to Becke, whose papers in 1992 and 1993 contributed to this remarkable transformation that changed the entire landscape of quantum chemistry. 

Moller-Plesset many-body perturbation theory taken through second order in the energy is the most commonly used ab initio molecular electronic structure method in contemporary quantum chemistry. For this report on many-body perturbation theory and its application to the molecular electronic structure problem we restricted our survey of applications to second-order Moller-Plesset perturbation theory. Even with this restriction, the nmnber of pubhcations appearing in the period covered by our review - namely, June 1999 to May 2001 - is sizeable. We recorded in the introduction that 883 publications containing the string MP2 in the title or keywords appeared in the year 2000 alone. However, rather than review just a small subset of these publications we decided to try to convey the... 

The heat of combustion (AcH) of dinitrobiuret (DNB) was determined experimentally using oxygen bomb calorimetry AcH(DNB) = 5195 200kjkg The standard heat of formation (AfH°) of DNB was obtained on the basis of quantum chemical computations at the electron-correlated ab initio MP2 (second order Moller-Plesset perturbation theory) level of theory using a correlation consistent double-zeta basis set (cc-pV-DZ) AfPf°(DNB) =- 353 kj mol - 1829 kj kg (Fig. 34). The detonation velocity (D) and detonation pressure (P) of DNB was calculated using the empirical equations by Kamlet and Jacobs D(DNB) = 8.66 mm xs P(DNB) = 33.9 GPa. 

Ab initio correlated or so-called post Hartree-Fock methods provide a proper description of dispersion forces. Unfortunately, these methods are computationally limited to systems with few atoms. Only few CCSD(T) calculations of very small ionic liquid systems were reported so far. Second-order Moller Plesset perturbation theory (MP2) might be also a suitable ab initio method to study ionic liquids. Recent developments have made this approach available for systems with hundreds of atoms. However, calculations of medium sized ionic liquid systems need still enormous computational resources. Thus, MP2 and similar approaches seem to be limited to static quantum chemical calculations and are still too expensive for ab initio molecular dynamics simulations over an appropriate system size and time frame. 

Further, it is understood that each matrix element consists of the components originating in the pure QM, the est and the vdW contribution. The est components are conveniently computed by the quantum chemical calculation package. For instance, in GAUSSIAN program [25], several approximate methods of electronic state calculations are available, e.g., the Hartree-Fock (HF), second-order Moller-Plesset perturbation theory (MP2), conhguration interaction field (CIS), complete active space self-consistent field (CASSCF) method, and the density functional theory (DFT) methods. On the other hand, since the vdW components are expressed as such analytical functions of the mw Cartesian coordinate variables involved in the same atom (A = B) as follows. 

Second-order Moller-Plesset (MP2) perturbation theory is a widely used quantum chemical method for incorporating electron correlation. This chapter considers parallel computation of MP2 energies, comparing the performance achievable wifh simple and more sophisticated parallelization strategies. 

The quantum-mechanical energies and properties are calculated individually for each of the (1 1) structures extracted from the MC simulation of the liquid and for the optimized (1 1) complexes using many-body perturbation theory in second order with the Moller-Plesset partitioning [33], using the MP2/aug-cc-pVDZ theoretical model implemented in the Gaussian 98 program [34]. 

The question for a more systematic inclusion of electronic correlation brings us back to the realm of molecular quantum chemistry [51,182]. Recall that (see Section 2.11.3) the exact solution (configuration interaction. Cl) is found on the basis of the self-consistent Hartree-Fock wave function, namely by the excitation of the electrons into the virtual, unoccupied molecular orbitals. Unfortunately, the ultimate goal oi full Cl is obtainable for very small systems only, and restricted Cl is size-inconsistent the amount of electron correlation depends on the size of the system (Section 2.11.3). Thus, size-consistent but perturbative approaches (Moller-Plesset theory) are often used, and the simplest practical procedure (of second order, thus dubbed MP2 [129]) already scales with the fifth order of the system s size N, in contrast to Hartree-Fock theory ( N ). The accuracy of these methods may be systematically improved by going up to higher orders but this makes the calculations even more expensive and slow (MP3 N, MP4 N ). Fortunately, restricted Cl can be mathematically rephrased in the form of the so-called coupled clus-... 

Many-body methods, based on the linked-cluster expansion (LCE), were first developed by Brueckner [1] and Goldstone [2] in the 1950s for nuclear physics problems. Perturbation-theory applications to atomic and molecular systems (in a numerical, one-center frame) were pioneered by Kelly [3] in the early 1960s. Basis sets were later introduced, first in second-order [4] and then in third-order [5]. The 1970s saw a proliferation of molecular applications with basis sets, under the names of many-body perturbation theory (MBPT) [6] or the Moller-Plesset method [7]. Nowadays, many-body methods offer some of the most powerful tools in the quantum chemistry arsenal, in particular the coupled-cluster (CC) method, and are available in many widely used quantum chemistry program packages. 

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