Coupled cluster-inspired geminal wavefunctions.

Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.

Richardson-Gaudin mean-field for strong correlation in quantum chemistry.

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

Computational Study of the Molecular Structure and Hydrogen Bonding in the Hamilton Wedge/Cyanuric Acid Binding Motif.

Intermolecular binding between a Hamilton wedge and cyanuric acid, a frequently employed binding motif to achieve self-assembly of single-chain polymer nanoparticles, is studied by means of ab initio quantum-chemical and DFT calculations. A conformational analysis of the isolated compounds and the hydrogen-bonded complex reveals several low-energy structures, which are characterized based on their nonplanarity and binding energy. New hypothetical binding motifs are proposed and proven to possess a superior binding energy, upon becoming planar. Comparison to experimentally measured NMR spectroscopy data is made and cases of disagreement are traced back to solvent effects for isolated substituents or to thermally stretched intermolecular bonds for hydrogen-bonded species. Strong linear correlations between NMR chemical shifts and hydrogen-bond lengths are established for all compounds investigated.

Finite Field Method for Nonlinear Optical Property Prediction Using Rational Function Approximants.

The finite field (FF) method is a quick, easy-to-implement tool for the prediction of nonlinear optical properties. Here, we present and explore a novel variant of the FF method, which uses a rational function to fit a molecule's energy with respect to an electric field. Similarly to previous FF methods, factors crucial for the method's accuracy were tuned. These factors include the number of terms in the function, the distribution of fields used to construct the approximation, and the initial field in the approximation. It was found that the approximant form that best fits the energy has four numerator terms and three denominator terms. To determine a reasonable field distribution, the common ratio of a geometric progression was optimized to √2. Finally, an algorithm for determining a good initial field guess was devised. The optimized FF method was used to compute the polarizability and second hyperpolarizability for a set of 121 molecules and the first hyperpolarizability for a set of 91 molecules. The results from this were compared to a previous polynomial-based FF method. It was found that using a rational function gives higher errors compared to the polynomial model. However, unlike the polynomial model, no subsequent refinement steps were needed to obtain usable results. An overall comparison of the behavior of the two methods also shows that the rational function is less sensitive to the chosen initial field, making it a good choice for new quantum chemistry codes.

A new wavefunction hierarchy for interacting geminals.

A new truncation scheme for non-orthogonal antisymmetrized products of interacting geminals (APIG) is introduced based on antisymmetrized products of strongly orthogonal geminals (APSG). This wavefunction hierarchy of interacting geminals (IG) allows us to gradually increase the accuracy at which the ground state of a seniority-zero Hamiltonian can be estimated, ranging from APSG up to approximation-free APIG. Mathematical expressions for the lowest four orders (IG0, IG1, IG2, and IG3) are given explicitly and the computational cost to evaluate their transition density matrix is verified to scale only cubically with system size. Exemplary numerical calculations indicate that already a very early truncation level leads to results virtually identical to APIG.

Orbital Energies for Seniority-Zero Wave Functions.

A new single-pair operator for seniority-zero wave functions is introduced closely related to the single-particle Fock operator from conventional Hartree-Fock theory. This allows one to ascribe orbital energies in the context of model Hamiltonians, for which no single-particle operators exist. Several applications demonstrate the usefulness of these orbital energies. In analogy to Koopmans' theorem, atomic double ionization potentials are successfully predicted. A computationally efficient second-order perturbation scheme for seniority-zero wave functions scaling quadratically with system size is defined and applied to the dissociation of nitrogen and to strongly correlated two-dimensional Heisenberg lattices. An extension of the method for full seniority is presented leading to an intruder-free single reference perturbation theory with improved asymptotic convergence.

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal.

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

Assessing the accuracy of new geminal-based approaches.

We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansätze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals.

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surján et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2.

Impact of donor-acceptor functionalization on the properties of linearly π-conjugated oligomers: establishing quantitative relationships for the substituent and substituent cooperative effect based on quantum chemical calculations.

To understand better the impact of donor-acceptor substitution on the properties of linearly π-conjugated compounds, we performed a computational study on a series of variably substituted trans-polyacetylenes, polyynes, and polythiophenes. The focus of this work is on how rapidly the impact of a given substituent or a given combination of substituents vanishes along the π-conjugated chain. The response of the structural (bond-length alternation, rotational barrier) and molecular properties ((hyper)polarizability, chemical shift) to substitution is analyzed using different protocols, including a superposition model for the evaluation of the cooperative effect of substituents in homo- and heterosubstituted oligomers. With the exception of the (hyper)polarizability, the impact of donor-acceptor substitution is found to vanish following an exponential. The rate of decay of the substituent impact is found to be characteristic for each backbone, whereas the choice of substituent determines the absolute value of the respective property. The combination of substituents is shown to determine whether the substituent cooperative effect on a property is of an enhancing or damping nature. The rate of decay of the cooperative effect on most properties, including the (hyper)polarizability, is also found to follow an exponential law.

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities.

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude.

A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals.

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations.

We have implemented the sweep algorithm for the variational optimization of SU(2) U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.

On the effect of electron correlation on the static second hyperpolarizability of π conjugated oligomer chains.

In this article, we report on the ab initio calculation of the static longitudinal second hyperpolarizability (γ) of π conjugated unsaturated oligomer chains using polyacetylene and polyyne as model compounds. The common observation is that the electron correlation enhances γ in these systems. The present study reveals that for extended chain lengths the opposite appears to be true: Electron correlation may have a damping effect on this property. For double-zeta basis sets, a negative contribution from electron correlation to γ is found within the range of chain lengths investigated. For triple-zeta basis sets, the same behavior must be anticipated at larger chain lengths based on extrapolation schemes. The analysis of the excitation energies and transition moments shows that transition moments between excited states as predicted by the Hartree-Fock and coupled cluster methods have a different response to chain length extension. There also are indications that higher order correlation effects will enhance γ.

Chemical information media in the chemistry lecture hall: a comparative assessment of two online encyclopedias.

The chemistry encyclopedia Römpp Online and the German universal encyclopedia Wikipedia were assessed by first-year university students on the basis of a set of 30 articles about chemical thermodynamics. Criteria with regard to both content and form were applied in the comparison; 619 ratings (48% participation rate) were returned. While both encyclopedias obtained very good marks and performed nearly equally with regard to their accuracy, the average overall mark for Wikipedia was better than for Römpp Online, which obtained lower marks with regard to completeness and length. Analysis of the results and participants' comments shows that students attach importance to completeness, length and comprehensibility rather than accuracy, and also attribute less value to the availability of sources which validate an encyclopedia article. Both encyclopedias can be promoted as a starting reference to access a topic in chemistry. However, it is recommended that instructors should insist that students do not rely solely on encyclopedia texts, but use and cite primary literature in their reports.

Structural features analysis and nonlinearity of end-cap-substituted polyacetylenes.

As part of a systematic study of the impact of donor-acceptor substitution on the structure and properties of pi-conjugated compounds, we present a theoretical investigation of the all-trans polyacetylene backbone, end-capped with moieties of different donor or acceptor natures and different strengths, focusing on the effects induced by these substituents on bond lengths and shape of the conjugated chain. Optimized geometries for polyacetylene containing 15 and 20 double bonds have been computed by means of density functional theory with the Coulomb-attenuating B3LYP (CAM-B3LYP) functional. We show that the simultaneous presence of two substituents has a cooperative effect on the lengths of single and double bonds. We also show that, depending on the substitution pattern, distortion toward bow- or S-shaped structures occurs. Two new geometric parameters are defined in order to evaluate the mode and intensity of this distortion. Cubic Bezier curves have been used as simple geometric models for the chain bending behavior.

A systematic analysis of the structure and (hyper)polarizability of donor-acceptor substituted polyacetylenes using a Coulomb-attenuating density functional.

In this paper we perform a systematic investigation on all-trans polyacetylene chains of different lengths, end-capped with moieties of different donor or acceptor natures and different strengths, to infer useful structure/property relationship rules and behavioral patterns. The values for bond length alternation (BLA), longitudinal polarizability, and first and second hyperpolarizabilities have been computed with the Coulomb-attenuating density function (CAM-B3LYP), using response theory. A comparison of the relative effect that each end-capping combination contributes to BLA, linear, and nonlinear optical coefficients has been performed. This results in useful insights and general rules to ad hoc tailoring the molecular response for a specific characteristic.

On the accurate calculation of polarizabilities and second hyperpolarizabilities of polyacetylene oligomer chains using the CAM-B3LYP density functional.

The polarizability and second hyperpolarizability of polyacetylene oligomer chains of increasing size up to C(24)H(26) were investigated by means of the Coulomb-attenuating method (CAM-B3LYP) using response theory. It was found that this long-range corrected density functional removes to large parts the overestimation observed for standard methods and in many cases provides results close to those of coupled cluster calculations. A direct comparison to experimentally observed dynamic hyperpolarizabilities is made to estimate the accuracy of the method. A basis set study revealed a noticeable contribution of diffuse orbitals to the hyperpolarizability also for larger oligomers. Furthermore, CAM-B3LYP is also confirmed to provide molecular geometries close to experimentally observed structures, especially for longer chain lengths.

A Scheme for the Evaluation of Electron Delocalization and Conjugation Efficiency in Linearly π-Conjugated Systems.

In this study, we present a scheme for the evaluation of electron delocalization and conjugation efficiency in lineraly π-conjugated systems. The scheme, based on the natural bond orbital theory, allows monitoring the evolution of electron delocalization along an extended conjugation path as well as its response to chemical modification. The scheme presented is evaluated and illustrated by means of a computational investigation of π-conjugation in all-trans polyacetylene [PA; H(-CH═CH)n-H], polydiacetylene [PDA, H(-C≡C-CH═CH)n-H], and polytriacetylene [PTA, H(-C≡C-CH═CH-C≡C)n-H] with up to 180 carbon atoms, all related by the number of ethynyl units incorporated in the chain. We are able to show that for short oligomers the incorporation of ethynyl spacers into the PA chain increases the π-delocalization energy, but, on the other hand, reduces the efficiency with which π-electron delocalization is promoted along the backbone. This explains the generally shorter effective conjugation lengths observed for the properties of the polyeneynes (PDA and PTA) relative to the polyenes (PA). It will also be shown that the reduced conjugation efficiency, within the NBO-based model presented in this work, can be related to the orbital interaction pattern along the π-conjugated chain. We will show that the orbital interaction energy pattern is characteristic for the type and the length of the backbone and may therefore serve as a descriptor for linearly π-conjugated chains.

2,3-Diphenylbutadiene and donor-acceptor functionalized derivatives: exploring the competition between conjugation paths in branched pi-systems.

2,3-Diphenylbutadiene and its donor-acceptor functionalized derivatives represent branched pi systems consisting of three overlapping linearly conjugated units, namely a 1,3-butadiene and two phenylethene subsystems. The evaluation of pi conjugation using a scheme based on the natural bond orbital analysis shows that the details of the structure of these compounds is governed by electron delocalization. The potential energy surface of 2,3-diphenylbutadiene shows two minima, each one representing a distinct combination of conjugation patterns. These minima are shown to be connected by a low-energy path with transition structures that have one conjugation path fully activated, while conjugation is completely disrupted along the other path. We will show that, in response to donor-accptor functionalization, the 2,3-diphenylbutadiene backbone will switch to other conformations, which come along with substantial changes in the electronic structure.