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Magnetic molecules and magnetic logic
Published in Guo-ping Zhang, Georg Lefkidis, Mitsuko Murakami, Wolfgang Hübner, Tomas F. George, Introduction to Ultrafast Phenomena from Femtosecond Magnetism to high-harmonic Generation, 2020
Guo-ping Zhang, Georg Lefkidis, Mitsuko Murakami, Wolfgang Hübner, Tomas F. George
This means that one must compute the force matrix of the system (which is the Hessian matrixh of the total energy with respect to the atomic dislocations). Although there are some techniques with which one can derive the matrix analytically for a Hartree-Fock calculation, this is unfortunately not the case for most post-Hartree-Fock methods. Since in a molecule with N atoms there are 3N atomic coordinates, this is also the number of single-point energy calculations that must be performed. In reality, quite often even more calculations are needed due to numerical instabilities. And of course all the calculations refer typically only to the electronic ground state. If electron-phonon coupling constants are desired, then one must also recalculate the Hessian matrix for several electronic levels.
The SMART Cyberinfrastructure: Spa ce-Time Multiscale Approaches for Research and Technology
Published in Tanmoy Chakraborty, Prabhat Ranjan, Anand Pandey, Computational Chemistry Methodology in Structural Biology and Materials Sciences, 2017
Daniele Licari, Giordano Mancini, Andrea Brogni, Andrea Salvadori, Vincenzo Barone
Electronic structure methods are based on the law of quantum mechanics rather than classical physics and they instead of depends on a number of empirical parameters (the force field). They are based, in principle, on limited number of fundamental physical constants such as the electronic and nuclear masses and charges and Planck’s constant. Quantum mechanics states that all the properties of a molecule may be obtained by solving Schrödinger equation and obtaining the system’s energy and wave function. However, the Schrödinger equation can be solved exactly in a very limited number of scenarios. Thus approximations are used; the less serious these are, the “higher” the level of the ab initio calculation is said to be. There are two major classes of electronic structure methods: semiempirical methods, which solve an approximate form of the Schrödinger equation that depends on having appropriate parameters available for the type of chemical system under investigation (from which the definition of semiempirical) and ab initio methods, are based solely on the laws of quantum mechanics. Electronic structure methods, in particular, highly correlated methods, are able to deliver a whole lot of information about chemical reactivity, spectroscopic properties and other effects that are completely beyond the scope of MM. However this comes at high computational cost, as shown in Table 5.2: the basic electronic structure approach, the Hartree Fock method (which is seldom an appropriate choice to describe e.g., organic molecules or reactions), scales as N4 and the cost of post Hartree Fock methods grows steadily.
Complex ground-state and excitation energies in coupled-cluster theory
Published in Molecular Physics, 2021
Simon Thomas, Florian Hampe, Stella Stopkowicz, Jürgen Gauss
Coupled-cluster (CC) theory [1] is one of the most widely used quantum-chemical methods for high-accuracy computations of energies and properties. As a post-Hartree–Fock method, CC theory focuses on an adequate, i.e. size-extensive, treatment of electron correlation and ensures this by applying the exponential of an excitation operator, i.e. the so-called cluster operator, to a reference determinant, most often chosen as the Hartree–Fock (HF) wave function. The equation-of-motion CC (EOM-CC) ansatz [1–5] extends ground-state CC theory to excited states. The key step lies in the similarity transformation of the electronic Hamiltonian with the exponential of the cluster operator followed by a diagonalisation of the resulting effective Hamiltonian. However, as this transformation is not unitary, Hermiticity is lost and as a consequence complex excitation energies can in principle be obtained in an EOM-CC calculation.
Energy correction and analytic energy gradients due to triples in CCSD(T) with spin–orbit coupling on graphic processing units using single-precision data
Published in Molecular Physics, 2021
Minggang Guo, Zhifan Wang, Yanzhao Lu, Fan Wang
As a post-Hartree–Fock (post-HF) method, the coupled-cluster (CC) theory [1] is widely applied in quantum chemistry calculations. The CC approach at the singles and doubles level (CCSD) [2] augmented by a perturbative treatment of triple excitations (CCSD(T)) [3,4] can treat dynamic correlation with high accuracy and provide size-extensive energies for states with a dominant single reference character. In CCSD(T) calculations, the computational scaling of the CCSD step is iteratively N6 and that of the triple correction ((T)) is non-iteratively N7, where N represents the system size. In most cases, the calculation of (T) is more expensive than that of CCSD, even though it needs to be calculated only once. Improving the computational efficiency of the (T) step is thus the key to the application of the CCSD(T) method to larger molecules.