Reconfigurable and real-time high-bandwidth Nyquist signal detection with low-bandwidth in silicon photonics.

We demonstrate for the first time, to the best of our knowledge, reconfigurable and real-time orthogonal time-domain detection of a high-bandwidth Nyquist signal with a low-bandwidth silicon photonics Mach-Zehnder modulator based receiver. As the Nyquist signal has a rectangular bandwidth, it can be multiplexed in the wavelength domain without any guardband as a part of a Nyquist-WDM superchannel. These superchannels can be additionally multiplexed in space and polarization. Thus, the presented demonstration can open a new possibility for the detection of multidimensional parallel data signals with silicon photonics. No external pulse source is needed for the receiver, and frequency-time coherence is used to sample the incoming Nyquist signal with orthogonal sinc-shaped Nyquist pulse sequences. All parameters are completely tunable in the electrical domain. The feasibility of the scheme is demonstrated through a proof-of-concept experiment over the entire C-band (1530 nm-1560 nm), employing a 24 Gbaud Nyquist QPSK signal due to experimental constraints on the transmitter side electronics. However, the silicon Mach-Zehnder modulator with a 3-dB bandwidth of only 16 GHz can process Nyquist signals of 90 GHz optical bandwidth, suggesting a possibility to detect symbol rates up to 90 GBd in an integrated Nyquist receiver.

Analysis of the effects of jitter, relative intensity noise, and nonlinearity on a photonic digital-to-analog converter based on optical Nyquist pulse synthesis.

An analysis of an optical Nyquist pulse synthesizer using Mach-Zehnder modulators is presented. The analysis allows to predict the upper limit of the effective number of bits of this type of photonic digital-to-analog converter. The analytical solution has been verified by means of electro-optic simulations. With this analysis the limiting factor for certain scenarios: relative intensity noise, distortions by driving the Mach-Zehnder modulator, or the signal generator phase noise can quickly be identified.

Evaluation of DFT-D3 dispersion corrections for various structural benchmark sets.

We present an evaluation of our newly developed density functional theory (DFT)-D3 dispersion correction D3(CSO) in comparison to its predecessor D3(BJ) for geometry optimizations. Therefore, various benchmark sets covering bond lengths, rotational constants, and center of mass distances of supramolecular complexes have been chosen. Overall both corrections give accurate structures and show no systematic differences. Additionally, we present an optimized algorithm for the computation of the DFT-D3 gradient, which reduces the formal scaling of the gradient calculation from O(N3) to O(N2).

Efficient determination of accurate atomic polarizabilities for polarizeable embedding calculations.

We evaluate embedding potentials, obtained via various methods, used for polarizable embedding computations of excitation energies of para-nitroaniline in water and organic solvents as well as of the green fluorescent protein. We found that isotropic polarizabilities derived from DFTD3 dispersion coefficients correlate well with those obtained via the LoProp method. We show that these polarizabilities in conjunction with appropriately derived point charges are in good agreement with calculations employing static multipole moments up to quadrupoles and anisotropic polarizabilities for both computed systems. The (partial) use of these easily-accessible parameters drastically reduces the computational effort to obtain accurate embedding potentials especially for proteins. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Correction: Analysis of computational models for an accurate study of electronic excitations in GFP.

Correction for 'Analysis of computational models for an accurate study of electronic excitations in GFP' by Tobias Schwabe et al., Phys. Chem. Chem. Phys., 2015, 17, 2582-2588.

General theory for environmental effects on (vertical) electronic excitation energies.

Almost 70 years ago, the first theoretical model for environmental effects on electronic excitation energies has been derived. Since then, several different interpretations and refined models have been proposed for the perichromic shift of a chromophore due to its surrounding medium. Some of these models are contradictory. Here, the contributing terms are derived within the framework of long-range perturbation theory with the least approximations so far. The derivation is based on a state-specific interpretation of the interaction energies and all terms can be identified with individual properties of either the chromophore or the surroundings, respectively. Further, the much debated contribution due to transition moments coupled to the environment can be verified in the form of a non-resonant excitonic coupling to the dynamic polarizabilities in the environment. These general insights should clarify discussions and interpretations of environmental effects on electronic excitations and should foster the development of new models for the computation of these effects.

Analysis of computational models for an accurate study of electronic excitations in GFP.

Using the chromophore of the green fluorescent protein (GFP), the performance of a hybrid RI-CC2/polarizable embedding (PE) model is tested against a quantum chemical cluster approach. Moreover, the effect of the rest of the protein environment is studied by systematically increasing the size of the cluster and analyzing the convergence of the excitation energies. It is found that the influence of the environment of the chromophore can accurately be described using a polarizable embedding model with only a minor error compared to a full quantum chemical description. It is also shown that the treatment of only a small region around the chromophore is only by coincidence a good approximation. Therefore, such cluster approaches should be used with care. Based on our results, we suggest that polarizable embedding models, including a large part of the environment to describe its effect on biochromophores on top of an accurate way of describing the central subsystem, are both accurate and computationally favourable in many cases.

An isomeric reaction benchmark set to test if the performance of state-of-the-art density functionals can be regarded as independent of the external potential.

Some representative density functionals are assessed for isomerization reactions in which heteroatoms are systematically substituted with heavier members of the same element group. By this, it is investigated if the functional performance depends on the elements involved, i.e. on the external potential imposed by the atomic nuclei. Special emphasis is placed on reliable theoretical reference data and the attempt to minimize basis set effects. Both issues are challenging for molecules including heavy elements. The data suggest that no general bias can be identified for the functionals under investigation except for one case - M11-L. Nevertheless, large deviations from the reference data can be found for all functional approximations in some cases. The average error range for the nine functionals in this test is 17.6 kcal mol(-1). These outliers depreciate the general reliability of density functional approximations.

Effect of chromophore encapsulation on linear and nonlinear optical properties: the case of "miniSOG", a protein-encased flavin.

Linear and nonlinear spectroscopic parameters of flavin mononucleotide, FMN, have been examined both experimentally and computationally under conditions in which FMN is (1) solvated in a buffered aqueous solution, and (2) encased in a protein that is likewise solvated in a buffered aqueous solution. The latter was achieved using "miniSOG" which is an FMN-containing protein engineered from Arabidopsis thaliana phototropin 2. Although it is reasonable to expect that the encasing protein could have an appreciable effect, certainly on the nonlinear two-photon absorption cross section, we find that replacing the dynamic aqueous environment with the more static protein environment does little to influence the spectroscopic properties of FMN. The experimental and computational studies are consistent in this regard, and this agreement indicates that comparatively high-level computational methods can indeed be used with success on large chromophores with a complicated local environment. The results of the present study facilitate the much-needed development of well-characterized and readily-controlled chromophores suitable for use as intracellular sensitizers and fluorophores.

Computational screening of one- and two-photon spectrally tuned channelrhodopsin mutants.

Optogenetics is by now a well-established field within neuroscience where neuro-response is controlled at the molecular level using the photochemical properties of channelrhodopsin (ChR). In this study the recently published X-ray structure of retinal inside the ChR binding pocket serves as the basis for conducting high-level polarizable embedding quantum mechanical/molecular mechanical (QM/MM) mutation studies with the aim of providing insight into the tuning mechanisms of this remarkable protein. The levels of theory applied are the recently developed PERI-CC2 and PE-DFT approaches. Their computational efficiency makes it possible to rapidly carry out a large number of spectral calculations. This is exploited to construct in silico mutated ChR variants which are characterized in terms of the location of the relevant excitation energy and the magnitude of the two-photon absorption cross section. In turn, this allows us to pinpoint the amino acids that have the largest electrostatic effect on the studied excited state properties. We show that a single/double site mutation strategy in ChR does not perturb the electronic properties of retinal to a degree that satisfies the experimental demand for a significant red-shift. With respect to non-linear absorption we conjecture that the recently synthesized ChETA variant possesses an even larger two-photon cross section than the C1C2 variant and it is thus an ideal candidate for further studies on the two-photon activation of ChR.

Systematic study of the basis set superposition error in core-electron correlation effects.

In a recent paper, Xu et al. [J. Phys. Chem. A 2012, 116, 11668] emphasized the importance of core-electron correlation effects to describe the Si2H6BH3 complex and related systems properly. Unexpected large energy differences between a frozen core and all electron treatment were observed. In the present study, it will be shown that these energy differences are an artifact of an insufficient choice of basis set and can be attributed to an intramolecular basis set superposition error (BSSE). Although the general problem is known, systematic studies on the effect are scarce. Therefore, the BSSE in related systems is investigated. This study shows that the problem of BSSE for core-electron correlation is quite common if inadequate basis sets are applied and that it amounts to 2 kcal mol(-1) on average in binding energies for the given test set (with a maximum of 5.8 kcal mol(-1)).

Accurate and fast treatment of large molecular systems: Assessment of CEPA and pCCSD within the local pair natural orbital approximation.

The local pair natural orbital approach, which has been combined with two post-Hartree-Fock methods, CEPA-1 and pCCSD-1a, recently, is assessed for its applicability to large real-world problems without abundant computing resources. Test cases are selected based on being representative for computational chemistry problems and availability of reliable reference data. Both methods show a good performance and can be applied easily to systems of up to 100 atoms when very accurate energies are sought after. A considerable demand for basis sets of good quality has been identified and practical guidelines to satisfy this are mapped out.

Scrutinizing the effects of polarization in QM/MM excited state calculations.

In this paper we demonstrate the importance of including polarization-especially in a fully self-consistent-field manner-when calculating excited states within linear response QM/MM methods based on correlated electronic structure methods. We perform a systematic investigation of solvent polarization effects by identifying lower order polarization reaction fields as compared to the full treatment. In the process we highlight the different nature of static and dynamic reaction fields and demonstrate-by method of example on both solvated systems as well as on biomolecules-that inclusion of both of these is mandatory for an accurate description of excited states. Ultimately, these findings reflect the importance of the change in the solvent reaction field upon electronic excitations. In light of the recent increasing interest in excited state QM/MM methods incorporating mutual polarization between subsystems as a method for treating large molecular systems, the reported investigation constitutes an important step towards dissecting the accuracy of such calculations.

The polarizable embedding coupled cluster method.

We formulate a new combined quantum mechanics/molecular mechanics (QM/MM) method based on a self-consistent polarizable embedding (PE) scheme. For the description of the QM region, we apply the popular coupled cluster (CC) method detailing the inclusion of electrostatic and polarization effects into the CC Lagrangian. Also, we consider the transformations required to obtain molecular properties from the linear and quadratic response functions and provide an implementation for the calculation of excitation energies, one- and two-photon absorption properties, polarizabilities and hyperpolarizabilities all coupled to a polarizable MM environment. In the process, we identify CC densitylike intermediates that allow for a very efficient implementation retaining a computational low cost of the QM/MM terms even when the number of MM sites increases. The strengths of the new implementation are illustrated by property calculations on different systems representing the frontier of the capabilities of the CC/MM method. We combine our method with a molecular dynamics sampling scheme such that statistical averages of different excited state solvated properties may be obtained. Especially, we systematically investigate the relative importance of multipoles and polarizabilities in the description of two-photon absorption activity for formamide in aqueous solution. Also, we demonstrate the strengths of the CC hierarchies by incorporating correlation effects both at the CC2, CCSD, and at the triples level in the so-called PE-CCSDR(3) model. Finally, we utilize the presented method in the description of a full protein by investigating the shift of the intense electronic excitation energy of the photoactive yellow protein due to the surrounding amino acids.

Noncovalent metal-metal interactions: the crucial role of london dispersion in a bimetallic indenyl system.

The nature of the "heterodox" metal-metal bond in bimetallic indenyl systems is revealed by a new high-level electronic structure analysis procedure based on perturbation theory within a localized molecular orbital basis. Surprisingly strong metal-metal interactions are found, and their origin in London dispersion effects has been uncovered. The importance of intramolecular van der Waals interactions, even for quite small organometallic systems, is highlighted.

Theoretical thermodynamics for large molecules: walking the thin line between accuracy and computational cost.

The thermodynamic properties of molecules are of fundamental interest in physics, chemistry, and biology. This Account deals with the developments that we have made in the about last five years to find quantum chemical electronic structure methods that have the prospect of being applicable to larger molecules. The typical target accuracy is about 0.5-1 kcal mol(-1) for chemical reaction and 0.1 kcal mol(-1) for conformational energies. These goals can be achieved when a few physically motivated corrections to first-principles methods are introduced to standard quantum chemical techniques. These do not lead to a significantly increased computational expense, and thus our methods have the computer hardware requirements of the corresponding standard treatments. Together with the use of density-fitting (RI) integral approximations, routine computations on systems with about 100 non-hydrogen atoms (2000-4000 basis functions) can be performed on modern PCs. Our improvements regarding accuracy are basically due to the use of modified second-order perturbation theory to account for many-particle (electron correlation) effects. Such nonlocal correlations are responsible for important parts of the interaction in and between atoms and molecules. A common example is the long-range dispersion interaction that lead to van der Waals complexes, but as shown here also the conventional thermodynamics of large molecules is significantly influenced by intramolecular dispersion effects. We first present the basic theoretical ideas behind our approaches, which are the spin-component-scaled Møller-Plesset perturbation theory (SCS-MP2) and double-hybrid density functionals (DHDF). Furthermore, the effect of the independently developed empirical dispersion correction (DFT-D) is discussed. Together with the use of large atomic orbital basis sets (of at least triple- or quadruple-zeta quality), the accuracy of the new methods is even competitive with computationally very expensive coupled-cluster methods, but they still remain routinely applicable for day-to-day chemical problems. This is demonstrated for the G3/99 benchmark set of heats of formation, 34 organic isomerization energies, and barriers for a number of pericyclic reactions. As an electronically complicated example, the relative energies of three isomeric Au(8) clusters are considered. In general, we recommend the very robust B2PLYP-D density functional approach for heat of formation calculations and for electronically complicated situations like transition metal complexes or open-shell species. With B2PLYP-D, an unprecedented low mean absolute deviation for the G3/99 test set with a DFT approach of 1.7 kcal mol(-1) has been achieved. For closed-shell main-group molecules and many relative energies, SCS-MP2 is the method of choice, because it completely avoids the self-interaction error problem that still plagues current DFT. In critical cases, it is recommended to apply SCS-MP2 and B2PLYP-D simultaneously, where also the comparison with standard MP2 and density functionals like B3LYP may lead to additional insight.

Benzenium-ethene complex: a fundamental problem for standard second-order Møller-Plesset theory.

Recently, Kolboe and Svelle pointed out that second-order Møller-Plesset perturbation theory (MP2) incorrectly predicts a barrierless reaction of the benzenium-ethene complex to the ethyl-1H-benzene cation in contrast to other considered quantum chemical methods [J. Phys. Chem. A 2008, 112, 6399]. In a subsequent Letter in this Journal, van Mourik related this behavior to the basis set superposition error [J. Phys. Chem. A 2008, 112, 11017]. Here we can show that this is not the case but that the failure is due to an intrinsic (overcorrelation) problem of MP2. Improved perturbation methods (SCS-MP2 and B2PLYP double-hybrid functionals) provide correct results.

Corrected Polarizable Embedding: Improving the Induction Contribution to Perichromism for Linear Response Theory.

An extension of the polarizable embedding (PE) approach for the computation of perichromatic shifts within linear response theory, termed corrected PE, is presented. It covers the change in induction effects in addition to contributions from electrostatics and nonresonant excitonic coupling and thereby presents a combination of the corrected linear response and the PE method. Using this method, we analyzed the individual contributions for six different excitations from four molecules in different solvents to clarify the question, which effects should be accounted for by a polarizable solvation model? The (vertical) reference excitation energies are evaluated by the means of full quantum mechanical computations of large solute-solvent clusters. Excellent agreement is achieved when both the shift due to the change in induction and nonresonant excitonic coupling in addition to the shift due to electrostatics are accounted for.

Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling.

For the first time, we combine time-dependent double-hybrid density functional approximations (TD-DHDFAs) for the calculation of electronic excitation energies with the concepts of spin-component and spin-opposite scaling (SCS/SOS) of electron-pair contributions to their nonlocal correlation components. Different flavors of this idea, ranging from standard SCS parameters to fully fitted parameter sets, are presented and tested on six different parent DHDFAs. For cross-validation, we assess those methods on three benchmark sets that cover small- to medium-sized chromophores (up to 78 atoms) and different excitation types. For this purpose, we also introduce new CC3 reference values for the popular Gordon benchmark set that we recommend using in future studies. Our results confirm that already the (unscaled) parent TD-DHDFAs are accurate and outperform some wave function methods. Further introduction of SCS/SOS eliminates extreme outliers, reduces deviation spans from reference values by up to 0.5 eV, aligns the performance of the Tamm-Dancoff approximation (TDA) to that of full TD calculations, and also enables a more balanced description of different excitation types. The best-performing TD-based methods in our cross validation have mean absolute deviations as low as 0.14 eV compared to the time- and resource-intensive CC3 approach. A very important finding is that we also obtained SOS variants with excellent performance, contrary to wave function based methods. This opens a future pathway to highly efficient methods for the optimization of excited-state geometries, particularly when paired with computing strategies such as the Laplace transform. We recommend our SCS- and SOS-based variants for further testing and subsequent applications.