Adiabatic connection models

Models which include exact exchange are often called hybrid methods, the names Adiabatic Connection Model (ACM) and Becke 3 parameter functional (B3) are examples of such hybrid models defined by eq. (6.35). The <, d and parameters are determined by fitting to experimental data and depend on the form chosen for typical values are a 0.2, d 0.7 and c 0.8. Owing to the substantially better performance of such parameterized functionals the Half-and-Half model is rarely used anymore. The B3 procedure has been generalized to include more filling parameters, however, the improvement is rather small. 

Adamo, C., Barone, V., 1997, Toward Reliable Adiabatic Connection Models Free from Adjustable Parameters , Chem. Phys. Lett., 274, 242. 

Baker, J. Muir, M. Andzelm, J., J. Chem. Phys., 1995, 102, 2063-2079. B3LYP is called ACM (adiabatic connection model) in this paper. 

Adiabatic Connection Model (ACM), 187 172 CID, CTSD, CTSDT, CTSDTQ methods, 107 Cusp, of a wave function, 140, 214 ... 

Most of the remaining error in DFT calculations comes from the assumption that the so-called exchange holes are localized, which causes them to fail to connect adiabatically between the KS independent-electron reference system and the real molecule. As a cure, the exchange functional is modified so it incorporates a degree of the HF exchange density, which leads to hybrid HF/DFT methods, also known as adiabatic connection models. These functionals constitute the current stare of the art in the field of DFT calculations. 

Adiabatic approximation, 53, 56 Adiabatic connection formula, 409 Adiabatic Connection Model (ACM), 187 Aliasing, in pseudospectral methods, 174 Allowed reaction, Woodward-Hoffmann rules, 356... 

Adamo, C. and Barone, V. 1998. Exchange Functionals with Improved Long-range Behavior and Adiabatic Connection Methods Without Adjustable Parameters The zwPW and zwPWlPW Models , J. Chem. Phys., 108, 664. 

We use the standard model [18, 19, 20] for Fermi-liquid leads adiabatically connected to the wire. We assume that the action (3) is applicable for x < L only. At large x the interaction strength K(x—y), Eq. (1), is zero. This model can be interpreted as a quantum wire with electron interaction completely screened by the gates near its ends. Electric fields of external charges are assumed to be screened in all parts of the wire. A simple modification of this model describes electrically neutral leads [20]. All results coincide for our set-up and the model [20]. 

Adamo C. Barone V. Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters the mPW and mPW 1PW models. J. Chem. Phys. 1998, 108, 664—675. 

The quantity 2Ec(2)[n] is particularly important because it is the initial slope in the adiabatic connection method (coupling-constant formula) for Ec[n] [10,14-18]. In fact, quite good use of the evaluation of 2Ec(2)[n] has recently been made by Ernzerhof [19] and by Perdew, Burke, and Ernzerhof [20-23] in their modeling of... 

We performed adiabatic connection calculations for the inhomogeneous spin-unpolarized electron gas with average electron density n0 = 3/(4wr ) corresponding to rs = 2. In the QMC simulations we model this system by a finite... 

Lifetimes for collision complexes and specific rate coefficients for unimolecular decay of metastable states can be derived in several ways in the framework of the adiabatic channel model, resulting in similar fundamental expressions. The major differences between the various derivations of lifetimes are connected to the physical interpretation. 

The statistical adiabatic channel model was originally introduced as a simple empirical model to describe kinetic experiments with as few parameters as possible, providing nevertheless a connection to a more fundamental theory. While it was clear from the start that the model could also be used as an ab initio theory, the numerical computations necessary in this context seemed impractical at the time of the invention of the model. Indeed, even the simple empirical approach was computationally demanding by the standard of the resources available then. During the past decades the computational... 

The present paper is organized as follows In a first step, the derivation of QCMD and related models is reviewed in the framework of the semiclassical approach, 2. This approach, however, does not reveal the close connection between the QCMD and BO models. For establishing this connection, the BO model is shown to be the adiabatic limit of both, QD and QCMD, 3. Since the BO model is well-known to fail at energy level crossings, we have to discuss the influence of such crossings on QCMD-like models, too. This is done by the means of a relatively simple test system for a specific type of such a crossing where non-adiabatic excitations take place, 4. Here, all models so far discussed fail. Finally, we suggest a modification of the QCMD system to overcome this failure. 

We refer to this equation as to the time-dependent Bom-Oppenheimer (BO) model of adiabatic motion. Notice that Assumption (A) does not exclude energy level crossings along the limit solution q o- Using a density matrix formulation of QCMD and the technique of weak convergence one can prove the following theorem about the connection between the QCMD and the BO model ... 

Fig. 2. The BO model is the adiabatic limit of full QD if energy level crossings do not appear. QCMD is connected to QD by the semiclassical approach if no caustics are present. Its adiabatic limit is again the BO solution, this time if the Hamiltonian H is smoothly diagonalizable. Thus, QCMD may be justified indirectly by the adiabatic limit excluding energy level crossings and other discontinuities of the spectral decomposition.

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