Investigation of challenging spin systems using Monte Carlo configuration interaction and the density matrix renormalization group

We investigate if a range of challenging spin systems can be described sufficiently well using Monte Carlo configuration interaction (MCCI) and the density matrix renormalization group (DMRG) in a way that heads toward a more “black box” approach. Experimental results and other computational methods are used for comparison. The gap between the lowest doublet and quartet state of methylidyne (CH) is first considered. We then look at a range of first‐row transition metal monocarbonyls: MCO when M is titanium, vanadium, chromium, or manganese. For these MCO systems we also employ partially spin restricted open‐shell coupled‐cluster (RCCSD). We finally investigate the high‐spin low‐lying states of the iron dimer, its cation and its anion. The multireference character of these molecules is also considered. We find that these systems can be computationally challenging with close low‐lying states and often multireference character. For this more straightforward application and for the basis sets considered, we generally find qualitative agreement between DMRG and MCCI. © 2017 Wiley Periodicals, Inc.     

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).     

Matrix element factorization in the unitary group approach for configuration interaction calculations

Techniques of diagrammatic spin algebra are employed to derive segment factorization formulas for spin-adapted matrix elements of one- and two-electron excitation operators. The spin-adapted basis is formed by the Yamanouchi–;Kotani geneological coupling method, and therefore constitutes an irreducible basis of the unitary group U(N), as prescribed by Gel'fand and Tsetlin. Several features distinguish this paper from similar work that has recently been published. First, intermediate steps in the derivation of each segment factor are fully documented. Comprehensive tables list the spin diagrams and phases that contribute to the possible segment factors. Second, a special effort has been made to distinguish between those parts of a segment factor that can be ascribed to a spin diagram and those parts which arise from the orbitals. The results of this paper should thus be useful for those who wish to extend diagrammatic spin algebra to evaluation of matrix elements for states built from nonorthogonal orbitals. Third, a novel graphical method has been introduced to keep track of phase changes that are induced by line up permutations of creation and annihilation operators. This technique may be useful for extension of our analysis to higher excitations. The necessary concepts of second quantization and diagrammatic spin algebra are developed in situ, so the present derivation should be accessible to those who have little prior knowledge of such methods.     

Computation of determinant expansion coefficients within the graphically contracted function method

Most electronic structure methods express the wavefunction as an expansion of N‐electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

A method to fast determine the coupling coefficients in CI calculation

A new algorithm for evaluating the coupling coefficients and the addresses of molecular integrals in configuration interaction (CI) calculations is presented, which leads to an improved CI calculation program CGUGA. The validity and efficiency of the new code are compared with other programs, such as MELD and GAUSSIAN-94.     

Analytical formulas for the magnetic field produced by a spin or a paramagnetic current density in the case of Gaussian basis functions

We present a derivation of simple formulas for the evaluation at any point of space of the magnetic field produced by a spin or a paramagnetic orbital current when Cartesian Gaussian basis functions are used, as is often the case in quantum chemistry. These formulas can be useful to plot the magnetic field vector density obtained from ab initio calculations or from a density operator fitted on experimental data. The magnetic field density is the observable probed in polarized neutron diffraction (PND) experiment, for it is, in fact, with this quantity that the neutron spins interact and not with the spin or magnetization density. The formulas make extensive use of the confluent hypergeometric function. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 11–15, 2001     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001     

On the zeroth‐order hamiltonian for CASPT2 calculations of spin crossover compounds

Complete active space self‐consistent field theory (CASSCF) calculations and subsequent second‐order perturbation theory treatment (CASPT2) are discussed in the evaluation of the spin‐states energy difference (ΔH_elec) of a series of seven spin crossover (SCO) compounds. The reference values have been extracted from a combination of experimental measurements and DFT + U calculations, as discussed in a recent article (Vela et al., Phys Chem Chem Phys 2015, 17, 16306). It is definitely proven that the critical IPEA parameter used in CASPT2 calculations of ΔH_elec, a key parameter in the design of SCO compounds, should be modified with respect to its default value of 0.25 a.u. and increased up to 0.50 a.u. The satisfactory agreement observed previously in the literature might result from an error cancellation originated in the default IPEA, which overestimates the stability of the HS state, and the erroneous atomic orbital basis set contraction of carbon atoms, which stabilizes the LS states. © 2015 Wiley Periodicals, Inc.     

Reducing I/O costs for the eigenvalue procedure in large-scale configuration interaction calculations

Several aspects of the matrix diagonalization method used for CI calculations in the COLUMBUS Program System are discussed, including a linear basis-contraction algorithm and the use of a nonorthogonal expansion basis. Both of these features significantly reduce the I/O requirements during the iterations.     

The performance of nonhybrid density functionals for calculating the structures and spin states of Fe(II) and Fe(III) complexes

The local density approximation and a range of nonhybrid gradient corrected density functionals (PW91, BLYP, PBE, revPBE, RPBE) have been assessed with respect to the prediction of geometries and spin-state energy preferences for a range of homoleptic Fe(II)L6 and Fe(III)L6 complexes, where L = Cl-, CN-, NH3, pyridine, imidazole, H2O, O=CH2 and tetrahydrofuran. While the qualitative spin-state energies from in vacuo structure optimizations are reasonable the geometries are relatively poorly treated, especially for [FeCl6]3-/4-. Structural results for all the complexes are significantly improved by including environmental effects. The best compromise between structural and spin-state predictive accuracy was obtained for the RPBE functional in combination with the COSMO solvation approach. This approach systematically overestimates the energetic preference for a low spin state, which is partly due to the well-known effect of the lack of exact exchange in nonhybrid functionals and partly due to the larger solvation stabilization of low-spin complexes that have shorter bond lengths and thus smaller molecular volumes than their high-spin partners. Calculations on low spin [Fe(bipy)3]2+ and [Fe(phen)3]2+ and their ortho methyl substituted analogs, which are high spin at room temperature but cross over to low spin at low temperature, suggest the RPBE/COSMO combination generates low spin states which are too stable by approximately 13 kcal mol(-1).     

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.     

Ion interaction approach to calculations of volumetric properties of aqueous multiple-solute electrolyte solutions

The ion interaction approach developed by Pitzer was used for the prediction of volumetric properties of mixed electrolyte solutions at 25°C based on parameters calculated from experimental data for single-solute electrolyte solutions. Such an approach was shown to be especially effective for application to the calculation of volumetric properties of natural hypersaline brines and of industrial electrolyte solutions of large complexity. The use of the latest recommended sets of volumetric ion interaction parameters for single electrolyte solutions and symmetrical mixing parameters for Na–K–Cl ion combinations considerably improved the precision of the density calculations of highly concentrated mixed electrolyte solutions and of various natural waters.     

The devil in the details: A tutorial review on some undervalued aspects of density functional theory calculations

Density functional theory (DFT) has become ubiquitous for chemical applications in research and in education. The exact functional at the foundation of DFT is unfortunately unknown, and issues arise when choosing an approximation for a specific application. With this tutorial review, we tackle the selection problem and many related ones, such as the choices of a basis set and of an integration grid, that are often overlooked by occasional practitioners and by more experienced users as well. We offer a practical approach in the form of a commented notebook containing 12 experiences that can be run on a simple computer in just a few hours. We propose this review as a primary source for those who are willing to include DFT in their everyday research or teaching activities in a way that reflects the research advances of the field in the last couple of decades.     

A graphical symmetric group approach for a spin adapted full configuration interaction: partitioning of a configuration graph into sets of closed-shell and open-shell graphs

We developed a spin adapted full configuration interaction (FCI) method which was expected to be effective for parallel processing. The graphical symmetric group approach (GSGA) was employed, where a configuration graph was partitioned into several sets of closed-shell and open-shell graphs. The configuration state functions (CSFs) bearing the same number of closed-shells and open-shells were assembled in a configuration group. The graphical approach provided a number to identify each CSF in a sequential order within the group. Combination of this partitioning and an intermediate configuration-driven algorithm in calculating the so-called σ vectors allowed us to use symbolic coupling constants. Furthermore, this combination made it easy to implement an efficient algorithm suitable to task-distributed parallel procedure for evaluating σ vectors. A program was written and some test calculations were carried out with high parallel efficiency. The largest size of FCI used 10 million CSFs (20 million determinants).     

Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity,chirality, and aromaticity

Quantum information theory is applied to formulate a new technique for dealing with molecular similarity problems. In this technique, the so‐called quantum fidelity appears to be a counterpart of the conventional similarity measure due to Carbo (Carbo, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980, 17, 1185). We define many‐body spin‐free density matrices for atoms and fragments in molecule, and compute corresponding fidelity measures for molecular subsystems. It allows us to treat the problem from the beginning within a many‐electron setting. The approach is employed for analyzing similarity between free atoms and atoms in molecule. A new chirality index, as based on the fidelity between molecule and its mirror image, is suggested to be an approximately additive nonnegative quantity. We also examine a local aromaticity by computing the fidelity measures for benzenoid fragments in polyaromatic hydrocarbons. A detailed study of the proposed indices is reported at the ab initio or semiempirical levels. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

M(CO)4~(2+)(M=Ni,Pd,Pt)的几何结构与自旋态的理论研究

对标题化合物的几何结构和可能的自旋态在密度泛函DFT-BP86和从头算的水平上进行了研究.计算结果表明:作为16电子配合物阳离子,Pd(CO)_4~(2+)和Pt(CO)~(2+)都以低自旋态平面四边形构型存在,这与实验事实相符,计算得到的键长Pd-C和Pt-C相对趋势也与实验数据一致.而对于Ni(CO)_4~(2+)阳离子计算,在低自旋态平面四边形构型和高自旋态的(扭曲)四面体之间无法给出明确的答案,因为CCSD(T)//BP86和CCSD(T)//MP2水平下得到的两种结构之间的能量差几乎可以忽略.     

Molecular electronegativity in density functional theory (II) --Direct calculation of group electronegativity and the atomic charges in a group

On the basis of a more precise expression of the atomic effective electronegativity deduced from the density functional theory and electronegativity equalization principle, a new scheme for calculating the group electronegativity and the atomic charges in a group is proposed and programed, and various parameters of electronegativity and hardness are given for some common atoms. Through calculation, analysis and comparison of more than one hundred groups, it is shown that the results from this scheme are reasonable and may be extended.     

Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations

Atomic shell approximation (ASA) constitutes a way to fit first‐order density functions to a linear combination of spherical functions. The ASA fitting method makes use of positive definite expansion coefficients to ensure appropriate probability distribution features. The ASA electron density is sufficiently accurate for the practical implementation of quantum similarity measures, as was proved in previous published work. Here, a new application of the ASA density formalism is analyzed, and employed to obtain an initial guess of the density matrix for SCF procedures. The number of cycles needed to assess the convergence criterion in electronic energy calculations appears comparable to or less than those obtained by other means. Several molecular structures of different classes, including organic systems and metal complexes, were chosen as representative test cases. In addition, an ASA basis set for atoms Sc‐Kr fitted to an ab initio 6‐311G basis set is also presented. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Two-hole-one-particle configuration interaction approach for the ionization of open-shell molecules: Application to NO2

A special configuration interaction approach for the ionic states of open-shell molecules with a spatially nondegenerate ground state is presented. This approach takes into account all genuine one-hole and two-hole-one-particle excitations with respect to the ground state and allows for the determination of ionic energies and relative intensities for the whole energy range. A numerical application for NO₂ is reported providing in particular theoretical access to the inner-valence region where the interpretation of experimental data hitherto has been open to question.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999