Alejandro J. Garza

Predicting Band Gaps with Hybrid Density Functionals

We compare the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical difference in their overall performance, although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large band gap materials-without affecting that of semiconductors-by including a larger portion of Hartree-Fock exchange in its short-range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option for the black box prediction of band gaps.

Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds?

The hyperpolarizabilities of five prototypical and four recently synthesized long-range charge-transfer (CT) organic compounds are calculated using short- and middle-range (SR and MR) hybrid functionals. These results are compared with data from MP2 and other DFT methods including GGAs, global hybrids, long-range corrected functionals (LC-DFT), and optimally tuned LC-DFT. Although it is commonly believed that the overestimation of hyperpolarizabilities associated with CT excitations by GGA and global hybrid functionals is the result of their wrong asymptotic exchange potential, and that LC-DFT heals this issue, we show here that SR and MR functionals yield results similar to those from LC-DFT. Hence, the long-range correction per se does not appear to be the key element in the well-known improved description of hyperpolarizabilities by LC-DFT. Rather, we argue that the inclusion of substantial amounts of Hartree-Fock exchange, which reduces the many-electron self-interaction error, is responsible for the relatively good results afforded by range separated hybrids. Additionally, we evaluate the effects of solvent and frequency on hyperpolarizabilities computed by SR and MR hybrids and compare these predictions with other DFT methods and available experimental data.

Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories.

This paper explores the possibility of combining projected Hartree-Fock and density functional theories for treating static and dynamic correlations in molecular systems with mean-field computational cost. The combination of spin-projected unrestricted Hartree-Fock (SUHF) with the TPSS correlation functional (SUHF+TPSS) yields excellent results for non-metallic molecular dissociations and singlet-triplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve shape for Cr2 can be obtained; unfortunately, such a combination is found to lead to overcorrelation in the general case.

A computational study of the nonlinear optical properties of carbazole derivatives: theory refines experiment

Abstract The nonlinear optical (NLO) properties of N-ethyl dicyanocarbazole (1), N-ethyl cyanoethylacetatecarbazole (2), and N-ethyl dimethylacetatecarbazole (3) are studied with traditional hybrid and long-range corrected (LC) density functional theory (DFT) methods. The carbazoles are predicted to have planar structures with a high degree of π-conjugation and charge transfer, resulting in measurable NLO responses. The DFT data here calculated allow us to refine and correct previously reported experimental hyperpolarizabilities for these compounds. Experimental UV–vis absorption bands (related to hyperpolarizabilities estimated via solvatochromism) are also accurately reproduced by LC-DFT when using gap fitting schemes. The effects of different functionals on the HOMO–LUMO energy gaps and eventually on the total hyperpolarizabilities are discussed.

Nonlinear optical properties of DPO and DMPO: a theoretical and computational study

The gas phase properties of the Z- and E-isomers of 4-(p-N,N-dimethyl-aminophenylmethylene)-2-phenyl-5-oxazolone (DPO) and 4-(2,5-dimethoxyphenylmethylene)-2-phenyl-5-oxazolone (DMPO) are studied using traditional hybrid and long-range-corrected density functional theories (LC-DFT). Excellent agreement is found between the optimized molecular geometries and the experimental crystal structures. Our calculations predict both DPO and DMPO to have significant nonlinear optical (NLO) susceptibilities. These results are compared with data for the prototypical NLO chromophore p-nitroaniline, and the effect of the range separation parameter on LC-DFT hyperpolarizabilities is also analyzed.

Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories.

Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+fcDFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+fcDFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+fcDFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+fcDFT scheme are discussed in light of these results.

Comparison of self-consistent field convergence acceleration techniques

The recently proposed ADIIS and LIST methods for accelerating self-consistent field (SCF) convergence are compared to the previously proposed energy-DIIS (EDIIS) + DIIS technique. We here show mathematically that the ADIIS functional is identical to EDIIS for Hartree-Fock wavefunctions. Convergence failures of EDIIS + DIIS reported in the literature are not reproduced with our codes. We also show that when correctly implemented, the EDIIS + DIIS method is generally better than the LIST methods, at least for the cases previously examined in the literature. We conclude that, among the family of DIIS methods, EDIIS + DIIS remains the method of choice for SCF convergence acceleration.

Synergy between pair coupled cluster doubles and pair density functional theory

Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn-Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that-as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix-pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.

Conformational Preferences of trans-1,2- and cis-1,3-Cyclohexanedicarboxylic Acids in Water and Dimethyl Sulfoxide as a Function of the Ionization State As Determined from NMR Spectroscopy and Density Functional Theory Quantum Mechanical Calculations

The populations of diaxial (aa) and diequatorial (ee) conformers of trans-1,2- and cis-1,3-cyclohexanedicarboxylic acids (CDCAs; 1 and 2, respectively) and their salts were determined in water and dimethyl sulfoxide (DMSO) solutions from vicinal proton-proton NMR J couplings ((3)J(HH)). Optimized geometries and free energies for these compounds were obtained at the M06-2X/cc-pVTZ(-f)++ level. Although carboxylic acid groups in cyclohexane rings are generally believed to be far more stable (~2 kcal/mol) in equatorial than axial positions, this investigation demonstrated that an aa conformation (normally assumed to be completely insignificant for these compounds) can be favored depending on the medium and ionization state: strong ee preferences (>90%) were observed in water and DMSO for both diacids and their salts, except for the dianion of 1 in DMSO, which was found to be substantially aa (~57%). The possibility of intramolecular hydrogen bonding (H-bonding) was also investigated; the ratios of the ionization constants (K(1)/K(2)) indicated an absence of intramolecular H-bonding because K(1)/K(2) ≪ 10(4) (a standard criterion for non-H-bonding in dicarboxylic acids) for both 1 and 2 in water and also for 2 in DMSO. For 1, K(1)/K(2) increased drastically in DMSO (K(1)/K(2) = 4 × 10(6)), where (3)J(HH) and the ratio K(1)/K(E) = 10, K(E) being the acidity constant of the monomethyl ester of 1, indicated the formation of an intramolecular H-bond for the monoanion in this solvent. An explanation for the observation of compact dianions in solution in terms of the generalized Born equation is also provided.

Electronic Structure and Properties of Berkelium Iodates

The reaction of 249Bk(OH)4 with iodate under hydrothermal conditions results in the formation of Bk(IO3)3 as the major product with trace amounts of Bk(IO3)4 also crystallizing from the reaction mixture. The structure of Bk(IO3)3 consists of nine-coordinate BkIII cations that are bridged by iodate anions to yield layers that are isomorphous with those found for AmIII, CfIII, and with lanthanides that possess similar ionic radii. Bk(IO3)4 was expected to adopt the same structure as M(IO3)4 (M = Ce, Np, Pu), but instead parallels the structural chemistry of the smaller ZrIV cation. BkIII-O and BkIV-O bond lengths are shorter than anticipated and provide further support for a postcurium break in the actinide series. Photoluminescence and absorption spectra collected from single crystals of Bk(IO3)4 show evidence for doping with BkIII in these crystals. In addition to luminescence from BkIII in the Bk(IO3)4 crystals, a broad-band absorption feature is initially present that is similar to features observed in systems with intervalence charge transfer. However, the high-specific activity of 249Bk (t1/2 = 320 d) causes oxidation of BkIII and only BkIV is present after a few days with concomitant loss of both the BkIII luminescence and the broadband feature. The electronic structure of Bk(IO3)3 and Bk(IO3)4 were examined using a range of computational methods that include density functional theory both on clusters and on periodic structures, relativistic ab initio wave function calculations that incorporate spin-orbit coupling (CASSCF), and by a full-model Hamiltonian with spin-orbit coupling and Slater-Condon parameters (CONDON). Some of these methods provide evidence for an asymmetric ground state present in BkIV that does not strictly adhere to Russel-Saunders coupling and Hunds Rule even though it possesses a half-filled 5f 7 shell. Multiple factors contribute to the asymmetry that include 5f electrons being present in microstates that are not solely spin up, spin-orbit coupling induced mixing of low-lying excited states with the ground state, and covalency in the BkIV-O bonds that distributes the 5f electrons onto the ligands. These factors are absent or diminished in other f7 ions such as GdIII or CmIII.