International Journal of Quantum Chemistry

A new method is proposed for the analysis of components of molecular interaction energy within the Hartree‐Fock approximation. The Hartree‐Fock molecular orbitals of the isolated molecules are used as the basis for the construction of Fock matrix of the supermolecule. Then certain blocks of this matrix are set to zero subject to specify boundary conditions of the supermolecule molecular orbitals, and the resultant matrix is diagonalized iteratively to obtain the desired energy components. This method can be considered as an extension of our previous method, but has an advantage in the explicit definition of the charge transfer energy, placing it on an equal footing with the exchange and polarization terms. The new method is compared with existing perturbation methods, and is also applied to the energy and electron density decomposition of (H₂O)₂.

Many‐body (diagrammatic) perturbation theory (MBPT), coupled‐pair many‐electron theory (CPMET), and configuration interaction (CI) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO₂, HCN, N₂, CO, BH₃, and NH₃. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth‐order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the ¹∑ potential curve of Be₂. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET.

An approximate fourth‐order expression for the electron correlation energy in the Møller–Plesset perturbation scheme is proposed. It takes into account all the contributions to the fourthorder energy neglecting only those of the triple‐substituted determinants. It is size consistent and correct to fourth order for an assembly of isolated two‐electron systems. Illustrative calculations are reported for a series of small molecules.

The capabilities of the Crystal14program are presented, and the improvements made with respect to the previous Crystal09version discussed. Crystal14is anab initiocode that uses a Gaussian‐type basis set: both pseudopotential and all‐electron strategies are permitted; the latter is not much more expensive than the former up to the first‐second transition metal rows of the periodic table. A variety of density functionals is available, including as an extreme case Hartree–Fock; hybrids of various nature (global, range‐separated, double) can be used. In particular, a very efficient implementation of global hybrids, such as popular B3LYP and PBE0 prescriptions, allows for such calculations to be performed at relatively low computational cost. The program can treat on the same grounds zero‐dimensional (molecules), one‐dimensional (polymers), two‐dimensional (slabs), as well as three‐dimensional (3D; crystals) systems. No spurious 3D periodicity is required for low‐dimensional systems as happens when plane‐waves are used as a basis set. Symmetry is fully exploited at all steps of the calculation; this permits, for example, to investigate nanotubes of increasing radius at a nearly constant cost (better than linear scaling!) or to perform self‐consistent‐field (SCF) calculations on fullerenes as large as (10,10), with 6000 atoms, 84,000 atomic orbitals, and 20 SCF cycles, on a single core in one day. Three versions of the code exist, serial, parallel, and massive‐parallel. In the second one, the most relevant matrices are duplicated, whereas in the third one the matrices in reciprocal space are distributed for diagonalization. All the relevant vectors are now dynamically allocated and deallocated after use, making Crystal14much more agile than the previous version, in which they were statically allocated. The program now fits more easily in low‐memory machines (as many supercomputers nowadays are). Crystal14can be used on parallel machines up to a high number of cores (benchmarks up to 10,240 cores are documented) with good scalability, the main limitation remaining the diagonalization step. Many tensorial properties can be evaluated in a fully automated way by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, as well as first and second hyperpolarizabilies, electric field gradients, Born tensors and so forth. Many tools permit a complete analysis of the vibrational properties of crystalline compounds. The infrared and Raman intensities are now computed analytically and related spectra can be generated. Isotopic shifts are easily evaluated, frequencies of only a fragment of a large system computed and nuclear contribution to the dielectric tensor determined. New algorithms have been devised for the investigation of solid solutions and disordered systems. The topological analysis of the electron charge density, according to the Quantum Theory of Atoms in Molecules, is now incorporated in the code via the integrated merge of theTopondpackage. Electron correlation can be evaluated at the Möller–Plesset second‐order level (namely MP2) and a set of double‐hybrids are presently available via the integrated merge with the Cryscorprogram. © 2014 Wiley Periodicals, Inc.

Two three‐dimensional numerical schemes are presented for molecular integrands such as matrix alements of one‐electron operators occuring in the Fock operator and expectation values of one‐electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product‐Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.

The potential energy surface of curcumin [1,7‐bis(4‐hydroxy‐3‐methoxyphenyl)‐1,6‐heptadiene‐3,5‐dione] was explored with the DFT correlation functional B3LYP method using 6‐311G* basis. The single‐point calculations were performed at levels up to B3LYP/6‐311++G**//B3LYP/6‐311G*. All isomers were located and relative energies determined. According to the calculation the planar enol form is more stable than the nonplanar diketo form. The results of the optimized molecular structure are presented and compared with the experimental X‐ray diffraction. In addition, harmonic vibrational frequencies of the molecule were evaluated theoretically using B3LYP density functional methods. The computed vibrational frequencies were used to determine the types of molecular motions associated with each of the experimental bands observed. Our vibrational data show that in both the solid state and in all studied solutions curcumin exists in the enol form. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005