Ireneusz W. Bulik

Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence.

We present a global hybrid meta-generalized gradient approximation (meta-GGA) with three empirical parameters, as well as its underlying semilocal meta-GGA and a meta-GGA with only one empirical parameter. All of them are based on the new meta-GGA resulting from the understanding of kinetic-energy-density dependence [J. Sun, B. Xiao, and A. Ruzsinszky, J. Chem. Phys. 137, 051101 (2012)]. The obtained functionals show robust performances on the considered molecular systems for the properties of heats of formation, barrier heights, and noncovalent interactions. The pair-wise additive dispersion corrections to the functionals are also presented.

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Seniority-based coupled cluster theory

Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N(3), disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene.

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptor-substituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.

Can Single-Reference Coupled Cluster Theory Describe Static Correlation?

While restricted single-reference coupled cluster theory truncated to singles and doubles (CCSD) provides very accurate results for weakly correlated systems, it usually fails in the presence of static or strong correlation. This failure is generally attributed to the qualitative breakdown of the reference, and can accordingly be corrected by using a multideterminant reference, including higher-body cluster operators in the ansatz, or allowing symmetry breaking in the reference. None of these solutions are ideal; multireference coupled cluster is not black box, including higher-body cluster operators is computationally demanding, and allowing symmetry breaking leads to the loss of good quantum numbers. It has long been recognized that quasidegeneracies can instead be treated by modifying the coupled cluster ansatz. The recently introduced pair coupled cluster doubles (pCCD) approach is one such example which avoids catastrophic failures and accurately models strong correlations in a symmetry-adapted framework. Here, we generalize pCCD to a singlet-paired coupled cluster model (CCD0) intermediate between coupled cluster doubles and pCCD, yielding a method that possesses the invariances of the former and much of the stability of the latter. Moreover, CCD0 retains the full structure of coupled cluster theory, including a fermionic wave function, antisymmetric cluster amplitudes, and well-defined response equations and density matrices.

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.

Density matrix embedding from broken symmetry lattice mean fields

lattice mean-field allows precise control of the lattice and fragment filling while providing very good agreement between predicted properties and exact results. We present a rigorous proof that at convergence this method is guaranteed to preserve lattice and fragment filling. Differences arising from fitting the fragment one-particle density matrix alone versus fitting fragment plus bath are scrutinized. We argue that it is important to restrict the density matrix fitting to solely the fragment. Furthermore, in the proposed broken symmetry formalism, it is possible to substantially simplify the embedding procedure without sacrificing its accuracy by resorting to density instead of density matrix fitting. This simplified density embedding theory (DET) greatly improves the convergence properties of the algorithm.

Blind test of density-functional-based methods on intermolecular interaction energies

In the past decade, a number of approaches have been developed to fix the failure of (semi)local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods.

Electron correlation in solids via density embedding theory

Density matrix embedding theory [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] and density embedding theory [I. W. Bulik, G. E. Scuseria, and J. Dukelsky, Phys. Rev. B 89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to the ab initio description of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, using coupled cluster theory as the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable to coupled cluster calculations of infinite systems even when using a single unit cell as the fragment. The theory is formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.

Time-resolved photoluminescence spectroscopy for the detection of cysteine and other thiol containing amino acids in complex strongly autofluorescent media

A thiol probe based on an iridium complex with long-lived photoluminescence was synthesized, which can be used for the detection of thiols even in the presence of strong background fluorescence. This system provides an easy and fast methodology for detecting thiol containing amino acids, which has potential applications in clinical diagnostics.