ERKALE—A flexible program package for X‐ray properties of atoms and molecules

ERKALE is a novel software program for computing X‐ray properties, such as ground‐state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree–Fock or density‐functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange‐correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes. © 2012 Wiley Periodicals, Inc.     

New basis sets for the evaluation of interaction‐induced electric properties in hydrogen‐bonded complexes

Interaction‐induced static electric properties, that is, dipole moment, polarizability, and first hyperpolarizability, of the CO? (HF)_n and N₂? (HF)_n, n = 1–9 hydrogen‐bonded complexes are evaluated within the finite field approach using the Hartree–Fock, density functional theory, Møller–Plesset second‐order perturbation theory, and coupled cluster methods, and the LPol‐n (n = ds, dl, fs, fl) basis sets. To compare the performance of the different methods with respect to the increase of the complex size, we consider as model systems linear chains of the complexes. We analyze the results in terms of the many‐body and cooperative effects. © 2012 Wiley Periodicals, Inc.     

PSI3: an open-source Ab Initio electronic structure package

PSI3 is a program system and development platform for ab initio molecular electronic structure computations. The package includes mature programming interfaces for parsing user input, accessing commonly used data such as basis‐set information or molecular orbital coefficients, and retrieving and storing binary data (with no software limitations on file sizes or file‐system‐sizes), especially multi‐index quantities such as electron repulsion integrals. This platform is useful for the rapid implementation of both standard quantum chemical methods, as well as the development of new models. Features that have already been implemented include Hartree‐Fock, multiconfigurational self‐consistent‐field, second‐order Møller‐Plesset perturbation theory, coupled cluster, and configuration interaction wave functions. Distinctive capabilities include the ability to employ Gaussian basis functions with arbitrary angular momentum levels; linear R12 second‐order perturbation theory; coupled cluster frequency‐dependent response properties, including dipole polarizabilities and optical rotation; and diagonal Born‐Oppenheimer corrections with correlated wave functions. This article describes the programming infrastructure and main features of the package. PSI3 is available free of charge through the open‐source, GNU General Public License. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

Comparative studies on the structures,infrared spectrum,and thermodynamic properties of phthalocyanine using ab initio Hartree–Fock and density functional theory methods

The molecular structure, vibrational spectrum, standard thermodynamic functions, and enthalpy of formation of free base phthalocyanine (Pc) have been studied using the density functional theory B3LYP procedure, as well as the ab initio Hartree–Fock method. Various basis sets 3‐21G, 6‐31G*, and LANL2DZ have been employed. The results obtained at various levels are discussed and compared with each other and with the available experimental data. It is shown that calculations performed at the Hartree–Fock level cannot produce a reliable geometry and related properties such as the dipole moment of Pc and similar porphyrin‐based systems. Electron correlation must be included in the calculations. The basis set has comparatively less effect on the calculated results. The results derived at the B3LYP level using the smaller 3‐21G and LANL2DZ basis sets are very close to those produced using the medium 6‐31G* basis set. The geometry of Pc obtained at the B3LYP level has D_2h symmetry and the diameter of the central macrocycle is about 4 Å. The enthalpy of formation of Pc in the gas phase has been predicted to be 1518.50 kJ/mol at the B3LYP/6‐311G(2d,2p)//B3LYP/6‐31G* level via an isodesmic reaction. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Frequency dependent nonlinear optical properties of molecules: Formulation and implementation in the HONDO program

This article summarizes the detailed equations for the time-dependent Hartree–Fock treatment of nonlinear properties for perturbations made up of a static electric field and an oscillating field. Explicit expressions for all nonlinear processes up to third order are obtained in terms of the density matrices at the same order. For processes at second and third order in perturbation, expressions in terms of lower order quantities are also obtained by applying the (2n + 1) theorem of perturbation theory. The corresponding computer implementation in the HONDO program is described.     

Complexes of C60 fullerene with simple donor molecules: Theoretical study

The complex formation between fullerene C60 and simple donor molecules such as dimethyl ether, dimethylamine, dimethylsulfide, furan, pyrrole, and thiophene has been studied applying the hybrid MP2/6‐31G(d′):PM3 ONIOM approach for geometry optimization. Local implementation of Møller–Plesset perturbation theory in combination with 6‐31G(d) and 6‐311G(d,p) basis sets was used for binding energies estimation of fullerene complexes. Two factors were found to contribute most to the complex stability: the polarizability and molecular volume of donor molecule. As follows from positive stabilization energies at the Hartree–Fock level, the stabilization of fullerene complexes is entirely due to dispersion interactions in accordance with available experimental data. The calculations show that for donors of similar molecular volume the binding energy of molecular complex increases with polarizability of donor molecules. Similarly, for such complexes the partial charges on molecules increase with decreasing of ionization potentials of donor molecules. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Parallelization of four‐component calculations. I. Integral generation,SCF, and four‐index transformation in the Dirac–Fock package MOLFDIR

The treatment of relativity and electron correlation on an equal footing is essential for the computation of systems containing heavy elements. Correlation treatments that are based on four‐component Dirac–Hartree–Fock calculations presently provide the most accurate, albeit costly, way of taking relativity into account. The requirement of having two expansion basis sets for the molecular wave function puts a high demand on computer resources. The treatment of larger systems is thereby often prohibited by the very large run times and files that arise in a conventional Dirac–Hartree–Fock approach. A possible solution for this bottleneck is a parallel approach that not only reduces the turnaround time but also spreads out the large files over a number of local disks. Here, we present a distributed‐memory parallelization of the program package MOLFDIR for the integral generation, Dirac–Hartree–Fock and four‐index MS transformation steps. This implementation scales best for large AO spaces and moderately sized active spaces. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1176–1186, 2000     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Examination of several density functionals in numerical Kohn–Sham calculations for atoms

We studied several exchange‐only and exchange–correlation energy density functionals in numerical, i.e., basis‐set‐free, nonrelativistic Kohn–Sham calculations for closed‐shell ¹S states of atoms and atomic ions with N electrons, where 2≤N≤120. Accurate total energies are presented to serve as reference data for algebraic approaches, as do the numerical Hartree–Fock results, which are also provided. Gradient‐corrected exchange‐only functionals considerably improve the total energies obtained from the usual local density approximation, when compared to the Hartree–Fock results. Such an improvement due to gradient corrections is not seen in general for highest orbital energies, neither for exchange‐only results (to be compared with Hartree–Fock results), nor for exchange–correlation results (to be compared with experimental ionization energies). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 227–241, 2001     

Comparative study on formamide–water complex

The hydrogen bonding of 1:1 complexes formed between formamide and water molecule have been investigated systematically using Hartree–Fock (HF), hybrid density functional theory (B3LYP), and post‐Hartree–Fock (MP2 and CCSD(T)) methods with range of basis sets 6‐31G(d), cc‐pVXZ (X = D, T, Q) and aug‐cc‐pVYZ (Y = D, T). Three stable structures are considered on the potential energy surface of formamide and water system. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The IR frequencies, intensities, and frequency shifts are reported. This study shows that B3LYP/aug‐cc‐pVDZ method gives better performance for formamide‐water complexes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010.     

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin‐orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree–Fock (CAHF) algorithm for the determination of 4f quasi‐atomic active orbitals common to all multi‐electron spin manifolds contributing to the ground spin‐orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi‐Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem‐specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state–of–the–art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres , represents a more time‐efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non‐perturbative spin‐orbit coupling effects. © 2017 Wiley Periodicals, Inc.     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

HF and MP2 calculations on CN−, N2, AlF,SiO, PN,SC, ClB,and P2 using correlated molecular wave functions

Contracted basis sets of double zeta valence quality plus polarization functions (DZP) and augmented DZP basis sets, which were recently constructed for the first‐ and second‐row atoms, are applied to study the electronic ground states of the diatomic molecules CN^?, N₂, AlF, SiO, PN, SC, ClB, and P₂. At the Hartree–Fock (HF) and/or Møller–Plesset second‐order (MP2) levels, total and molecular orbital energies, dissociation energies, bond lengths, harmonic vibrational frequencies, and dipole moments are calculated and compared with available experimental data and with the results obtained from correlation consistent polarized valence basis sets of Dunning's group. For N₂, calculations of polarizabilities at the HF and MP2 levels with the sets presented above are also done and compared with results reported in the literature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Implementation of dynamical nucleation theory with quantum potentials

A method is implemented within the context of dynamical nucleation theory in order to efficiently determine the ab initio water dimer evaporation rate constant. The drive for increased efficiency in a Monte Carlo methodology is established by the need to use relatively expensive quantum mechanical interaction potentials. A discussion is presented illustrating the theory, algorithm, and implementation of this method to the water dimer. Hartree–Fock and second order Møller–Plesset perturbation theories along with the Dang–Chang polarizable classical potential are utilized to determine the ab initio water dimer evaporation rate constant. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Structural,Electronic and Optical Properties of Multifunctional Iridium(III) and Platinum(II) Metallophosphors for Organic Light‐Emitting Diodes

An elaborated theoretical investigation on the optical and electronic properties of three fluorene‐based platinum(II) and iridium(III) cyclometalated complexes Pt‐a , Ir‐a and Ir‐b is reported. The geometric and electronic structures of the complexes in the ground state are studied with density functional theory and Hartree Fock approaches, while the lowest triplet excited states are optimized by singles configuration interaction (CIS) methods. At the time‐dependent density functional theory (TD‐DFT) level, molecular absorption and emission properties were calculated on the basis of optimized ground‐ and excited‐state geometries, respectively. The computational results show that the appearance of triphenylamino (TPA) moiety at the 9‐position of fluorene ring favors the hole‐creation and leads to red‐shifts of absorption and emission spectra. Moreover, Pt‐a and Ir‐b are nice hole‐transporting materials whereas Ir‐a has good charge‐transfer balance, which render them useful for the realization of efficient OLEDs (Organic Light‐Emitting Diodes).