Symmetric Substitution Research Articles

Quantum chemical framework for designing high-performance ladder-shape NLO molecules and study of implicit vs explicit solvent effects on their NLO properties

Researchers in materials science are greatly fascinated by helicene chemistry due to its excellent optical and structural properties. In this work, we introduced symmetrical substitution of donor and acceptor groups on the [7]helicene ([7]HC-1 to [7]HC-5). DFT analysis is used to explore nonlinear optical (NLO) response for designed compounds. For [7]HC-5, the linear isotropic (αiso) and anisotropic polarizability (αaniso) are 31.59 × 10−24 esu and 59.86 × 10−24 esu, respectively. [7]HC-5 has the highest average third-order NLO polarizability (<γ>) of 47.24 × 10−36 esu which is approximately six times greater than that of para-nitroaniline, a well-known prototype NLO molecule. The effect of implicit and explicit solvents on <γ> and αiso of three selected compounds ([7]HC-1, [7]HC-3, and [7]HC-5) is also evaluated. As compared to explicit and gas phase methods, PCM model predicts an overestimation by an increment of ∼ 4-5 times for selected compounds. TD-DFT calculations show a higher transition dipole moment (4.24) and a lower transition energy (3.414 eV) for [7]HC-5. The higher NLO response is explained based on frontier molecular orbitals (FMOs), electron density difference (EDD), and molecular electrostatic potentials (MEPs). There is a red shift for studied compounds based on UV-visible results. The C-N stretching at 1372 cm-1 for [7]HC-5 indicates the presence of -N(CH3)2. Additionally, we studied photovoltaic parameters and found that [7]HC-5 has the maximum open circuit voltage and the lowest dye regeneration of 2.71 eV and 0.06 eV, respectively.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions.

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Maximum likelihood estimation and natural pairwise estimating equations are identical for three sequences and a symmetric 2-state substitution model

Consider the problem of estimating the branch lengths in a symmetric 2-state substitution model with a known topology and a general, clock-like or star-shaped tree with three leaves. We show that the maximum likelihood estimates are analytically tractable and can be obtained from pairwise sequence comparisons. Furthermore, we demonstrate that this property does not generalize to larger state spaces, more complex models or larger trees. Our arguments are based on an enumeration of the free parameters of the model and the dimension of the minimal sufficient data vector. Our interest in this problem arose from discussions with our former colleague Freddy Bugge Christiansen.

Symmetry versus asymmetry game in vaporization enthalpies of imidazolium-based ionic liquids

The vaporization enthalpy as a function of alkyl chain length was studied using both experimental techniques and molecular dynamics simulations for imidazolium based ionic liquids (ILs) with symmetric and asymmetric imidazolium substitution. It was found that the vaporization enthalpy increases with increasing alkyl chain length due to the increased van der Waals (vdW) interaction. In addition, the vaporization enthalpies of the symmetric ILs ([CnCnIm][X], X = NTf2-, Cl-, Br-, I-) series were found to be systematically lower (by 5–10 kJ mol−1) in comparison with the corresponding asymmetric imidazolium-based ILs ([CmC1Im][X]). This energetic difference was attributed to the intramolecular dispersion interactions between the two alkyl side chains existing in the symmetric cation series.

Single Benzene Yellow Fluorophore: Anodic Synthesis of Tetrahydrobenzodifuran

Fluorophores have proven to be indispensable tools in fields ranging from physics, chemistry, and biology. Organic fluorophores have high degrees of freedom in their molecular designs, which is essential for fundamental applications such as imaging probes. The strategies to produce organic fluorophores with improved physicochemical properties are two-fold, including an extension of aryl systems and a construction of push-pull motifs, where electron-donating and -withdrawing groups are conjugated. When used in bio-related research fields, the construction of push-pull motifs is preferred in terms of water solubility and molecular size, since the extension of aryl systems produces relatively large hydrophobic, planar, and thus highly crystalline, structures.The early work by Shimizu in 2009 triggered explosive growth in the development of new single-benzene fluorophores. From the viewpoints of synthetic practicality and unique and tunable photophysical properties, installing diagonally symmetrical substitution patterns with the same electron-donating and -withdrawing groups is the simplest strategy to create new single-benzene fluorophores.During the course of our studies focusing on electrochemical cycloadditions, we found that dihydrobenzofuran derivatives armed with electron-donating and -withdrawing groups exhibited bright fluorescence. In order to suppress molecular motions that cause non-radiative transitions, formation of a furan ring is effective in restricting bond rotation. Furthermore, we found that symmetrically substituted dialkoxy-dicarbonylbenzenes exhibited unique bright fluorescence. In this study, we successfully demonstrate that constructing symmetrical push-pull motifs in combination with restricting bond rotations is the key to creating small yet brightly emitting fluorophores. The anodically constructed tetrahydrobenzodifuran moiety has proven to be an effective core architecture to realize unique and powerful single-benzene fluorophores with high quantum yields and large Stokes shifts.

Solvatochromic and Proton-Responsive characteristics of Bi-1,3,4-Oxadiazole derivatives with symmetric dimethylamino substitution

D-A molecules find extensive use in intelligent stimulus–response systems due to their exceptional attributes, including high sensitivity, rapid response, wide compatibility, and structural adaptability. The strength of Intramolecular Charge Transfer (ICT) plays a pivotal role in determining the performance of these devices. To enhance the ICT strength and explore new applications for D-A molecules, we meticulously designed a pair of symmetric dimethylamino-substituted bi-1,3,4-oxadiazole derivatives (DMAOXD and DMAOXDBEN). These symmetric D-A-A-D molecules, with strong electron donor terminals, displayed a modest redshift of less than 25 nm in the UV–vis absorption spectra. However, there was a significant redshift in the emission spectra (140 nm for DMAOXD and 170 nm for DMAOXDBEN) when transitioning from cyclohexane to dimethyl sulfoxide, indicating a pronounced ICT characteristic. Theoretical calculations support the idea that the dimethylaminophenyl unit serves as an electron donor in both DMAOXD and DMAOXDBEN, while the 1,3,4-oxadiazole and central benzene ring act as acceptors. The pronounced ICT characteristic observed in DMAOXD and DMAOXDBEN can be attributed to long-distance electron transfer. Additionally, it's noteworthy that the emission of DMAOXD and DMAOXDBEN solution samples can be quenched by adding trifluoroacetic acid (TFA) and restored by the addition of triethylamine (TEA). Inspired by this, a pattern created with ink samples containing DMAOXD and DMAOXDBEN can be concealed through fumigation with TFA and subsequently revealed by treating them with TEA, suggesting their potential use in data encryption.

Understanding the Impact of Symmetrical Substitution on the Photodynamics of Sinapate Esters Using Gas-Phase Ultrafast Spectroscopy.

Two model biomimetic systems, ethyl sinapate (ES) and its symmetrical analogue, diethyl 2-(4-hydroxy-3,5-dimethoxybenzylidene)malonate (or diethyl sinapate, DES), are stripped to their core fundamentals through gas-phase spectroscopy to understand the underlying photophysics of photothermal materials. Following photoexcitation to the optically bright S1(ππ*) state, DES is found to repopulate the electronic ground state over 3 orders of magnitude quicker than its nonsymmetrical counterpart, ES. Our XMS-CASPT2 calculations shed light on the experimental results, revealing crucial differences in the potential energy surfaces and conical intersection topography between ES and DES. From this work, a peaked conical intersection, seen for DES, shows vital importance for the nonradiative ground-state recovery of photothermal materials. This fundamental comparative study highlights the potential impact that symmetrical substitution can have on the photodynamics of sinapate esters, providing a blueprint for future advancement in photothermal technology.

Manipulation of the spacing between the donor and acceptor by gradual side-chain modification to reduce energy loss of the organic solar cells

As one of the simple but effective molecular modify strategies, the side chain engineering based on siloxane-terminated alkyl side chain has been proved to be a promising design strategy for facilitating the formation of optimal film morphology, and further improving the photovoltaic performance of organic solar cells (OSCs). Herein, two polymer donors named 2FP-1EH-1Si and 2FP-2Si with symmetrical and asymmetrical siloxane-terminated alkyl side chain substitution were designed and synthesized. The results demonstrate that compared with the alkyl side chain substituted polymer 2FP-2EH, the introduction of siloxane-terminated alkyl side chain not only regulates the miscibility between the polymer donor and small molecular acceptor (SMA), but also affects the spacing between the donor (D) and the acceptor (A) molecules. As a result, the asymmetrical and symmetrical siloxane-terminated alkyl side chain substituted polymer 2FP-1EH-1Si and 2FP-2Si exhibit lower surface energy, stronger self-aggregation ability and higher hole mobility. More importantly, the OSCs based on 2FP-1EH-1Si:IT-4F and 2FP-2Si:IT-4F exhibited gradually decreased energy loss, which is suppressed by controlling the D-A spacing, along with the increased open-circuit voltage (VOC) from 0.77 V to 0.80 V and then to 0.86 V. This work further reveals the regulation mechanism of siloxane-terminated alkyl chain on the photovoltaic performance of active layer materials for efficient OSCs with enhanced stability.

СТРУКТУРА И ВНУТРИМОЛЕКУЛЯРНАЯ ПОДВИЖНОСТЬ НЕКОТОРЫХ ПРОИЗВОДНЫХ БИС(ТИО)ФОСФОРИЛИРОВАННЫХ АМИДОВ В РАСТВОРАХ CCl4, CD2Cl2 И CD3CN

The structure and intramolecular mobility of some derivatives of bis(thio)phosphorylated amides in CCl4, CD2Cl2, and CD3CN solutions were examined by 1H and 31P NMR spectroscopy. A comparative analysis of the temperature-dependent 1H and 31P NMR spectra of the studied compounds with symmetric and asymmetric substitution at phosphorus atoms was carried out. Various intramolecular processes were identified – rotation around C-N bonds, conformational transformations of molecules, tautomerism, and phosphorylotropic rearrangement with the formation of various conformational forms. It was shown that a dynamic equilibrium of several forms is reached, with the amide (phosphazo-) form having a clear advantage.

1,8‐Diarylnaphthalenes: Synthesis, Properties, and Applications

Abstract1,8‐Diarylnaphthalenes are a fascinating example of strained organic molecules that have found many practical applications due to unusual parallel face‐to‐face arrangement of two peri‐aryl rings in close proximity almost perpendicular to the central naphthalene backbone. 1,8‐Diarylnaphthalenes show notable potential as photoluminescent and chiral sensors, stereodynamic switches, nonlinear optic chromophores, blue‐transparent frequency doublers, materials for creating high‐performance blue and green OLEDs, chiral ligands and so on. Molecules of this type have also been used as convenient models for studying π‐π, dipole‐π and cation‐π interactions. 1,8‐Diarylnaphthalenes are also interesting as objects to study atropisomeric transformations: if the peri‐aryl rings have ortho‐ or meta‐substituents, then the anti‐conformer becomes C2‐symmetrical (hence chiral), and the syn‐isomer upon symmetrical substitution is achiral. In this review, data on synthetic methods, applications, atropisomerism and structural characteristics of 1,8‐diaryl‐ and 1,8‐dihetarylnaphthalenes are summarized.

Copper(I)–Thiazol-2-ylidenes: Highly Reactive N-Heterocyclic Carbenes for the Hydroboration of Terminal and Internal Alkynes. Ligand Development, Synthetic Utility, and Mechanistic Studies

In the last 15 years, copper-catalyzed borylative transformations utilizing boryl–copper have been established as a powerful activation mode in organic synthesis and catalysis, enabling direct transformations of various π-systems. Although many of these transformations use NHC (N-heterocyclic carbene) ligands, these studies have been almost exclusively limited to the derivatives of imidazol-2-ylidenes. However, the molecular properties of N-aryl-imidazol-2-ylidenes, such as IPr (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene), are limited by (1) the high degree of heteroatom stabilization and (2) symmetrical substitution of the nitrogen atoms. Herein, we report a study on Cu(I)–thiazol-2-ylidenes, thiazole analogues of imidazol-2-ylidenes, which (1) feature a distinct half-umbrella shape of the coordinating ligand and (2) exhibit lower heteroatom stabilization of the ancillary ligand through reduced π-donation from sulfur. We present the development of a family of stable Cu(I)–thiazol-2-ylidenes, where the combined sterics of thiazol-2-ylidenes lead to monomers [Cu(NHC)X] or bridged-halo dimers [Cu(NHC) (μ-X)]2, their crystallographic characteristics, and application to the hydroboration of alkynes to afford trisubstituted vinylboronates by β-hydroboration of internal alkynes or terminal vinylboronates by β-hydroboration of terminal alkynes. Application to the late-stage modification and detailed mechanistic studies on the catalyst structure and activation are presented. Most crucially, Cu(I)–thiazol-2-ylidenes show a much higher β-selectivity in the hydroboration of alkynes than that of classical imidazol-2-ylidenes, affording vinylborons in excellent yields at ambient conditions. The unique “half-umbrella” shape of thiazol-2-ylidenes reverses the α/β regioselectivity observed with imidazol-2-ylidenes in the hydroboration of terminal alkynes. Kinetic studies demonstrate that Cu(I)–thiazol-2-ylidenes supersede imidazol-2-ylidenes. Considering the significant utility of borylative transformations of π-systems, we anticipate that Cu(I)–thiazol-2-ylidenes will advance the synthetic transformations of boryl–copper in organic synthesis and catalysis.

15.51 % efficiency all-small-molecule organic solar cells achieved by symmetric thiazolyl substitution

Two new small molecule donors of SW1 and SW2 are designed and synthesized by employing thiophene and thiazole substituents as the side groups of benzo[1,2-b:4,5-b′]dithiophene central unit, respectively. Due to the more electron-withdrawing feature and enhanced intermolecular stacking of SW2 with respect to that of SW1, the all-small-molecule (ASM) organic solar cells (OSCs) based on SW2 afford a much better power conversion efficiency up to 15.51 %, along with both enlarged open-circuit voltage and fill factor. Further systematic investigation demonstrates that thiazole could act as an excellent building block to optimize the energy levels, molecular stacking as well as microscopic morphologies in ASM systems, leading to the highly efficient ASM-OSCs.

A crystalline radical cation derived from Thiele\u2019s hydrocarbon with redox range beyond 1\u2009V

Thiele’s hydrocarbon occupies a central role as an open-shell platform for new organic materials, however little is known about its redox behaviour. While recent synthetic approaches involving symmetrical carbene substitution of the CPh2 termini yield isolable neutral/dicationic analogues, the intervening radical cations are much more difficult to isolate, due to narrow compatible redox ranges (typically < 0.25 V). Here we show that a hybrid BN/carbene approach allows access to an unsymmetrical analogue of Thiele’s hydrocarbon 1, and that this strategy confers markedly enhanced stability on the radical cation. 1•+ is stable across an exceptionally wide redox range (> 1 V), permitting its isolation in crystalline form. Further single-electron oxidation affords borenium dication 12+, thereby establishing an organoboron redox system fully characterized in all three redox states. We perceive that this strategy can be extended to other transient organic radicals to widen their redox stability window and facilitate their isolation.

Crystal Engineering of Supramolecular 1,4-Benzene Bisamides by Side-Chain Modification - Towards Tuneable Anisotropic Morphologies and Surfaces.

Benzene bisamides are promising building blocks for supramolecular nano‐objects. Their functionality depends on morphology and surface properties. However, a direct link between surface properties and molecular structure itself is missing for this material class. Here, we investigate this interplay for two series of 1,4‐benzene bisamides with symmetric and asymmetric peripheral substitution. We elucidated the crystal structures, determined the nano‐object morphologies and derived the wetting behaviour of the preferentially exposed surfaces. The crystal structures were solved by combining single‐crystal and powder X‐ray diffraction, solid‐state NMR spectroscopy and computational modelling. Bulky side groups, here t‐butyl groups, serve as a structure‐directing motif into a packing pattern, which favours the formation of thin platelets. The use of slim peripheral groups on both sides, in our case linear perfluorinated, alkyl chains, self‐assemble the benzene bisamides into a second packing pattern which leads to ribbon‐like nano‐objects. For both packing types, the preferentially exposed surfaces consist of the ends of the peripheral groups. Asymmetric substitution with bulky and slim groups leads to an ordered alternating arrangement of the groups exposed to the surface. This allows the hydrophobicity of the surfaces to be gradually altered. We thus identified two leitmotifs for molecular packings of benzene bisamides providing the missing link between the molecular structure, the anisotropic morphologies and adjustable surface properties of the supramolecular nano‐objects.

Wet process feasible novel fluorene-based molecular hole transporting layer for phosphorescent organic light emitting diodes

Solution processable hole transporting materials (HTMs) are indispensable component for the cost-effective and large-area roll-to-roll fabrication of organic light emitting diodes (OLEDs). Hole transport layers should display high triplet energy, good hole injection properties along with potential electron blocking capability. In this paper, we report a series of novel fluorene-based HTMs, 9,9-diethyl-2,7-bis(2-(trifluoromethyl)phenyl)-9H-fluorene (3), 9,9-diethyl-2,7-bis(3-(trifluoromethyl)phenyl)-9H-fluorene (4) and 9,9- diethyl-2,7-bis(4-(trifluoromethyl)phenyl)-9H-fluorene (5) containing symmetrical and asymmetrical substitution of trifluoromethyl pendants at different positions. The synthesized HTMs have an exceptional solubility in common organic solvents such as THF (tetrahydrofuran), o-Xylene, etc. and possess good thermal stability to form morphologically stable films. The suitable molecular energy level alignment (HOMO-LUMO) for barrier free injection, adequate ionization potential (6.12, 6.20, and 6.23 eV) and high triplet energies (3.12,3.17, and 3.13 eV) for compound 3, 4, and 5, these suitable characteristics promote materials performance as a good hole transporting layer (HTL). Solution-processed yellow phosphorescent OLEDs fabricated by utilizing these HTMs with a conventional yellow emitter Iridium (III)bis (4-phenylthieno [3,2-c]pyridinato-N,C2′)acetylacetonate (PO-01) doped in 4,4′-bis(N-carbazolyl)-1,1′-biphenyl (CBP) host. The best device with molecule 4 showed an improvement of 54 % in current efficiency (CE) from 23.3 to 35.8 cd/A and 14 % in external quantum efficiency (EQE) from 11.3 to 12.9 %, compared to reference device containing N, N′-Bis(naphthalen-1-yl)-N,N′-bis(phenyl)benzidine (NPB) as HTL. Compounds 3 and 5 based devices also showed a competitive performance with the reference device. The effect of solvent was also studied. These outcomes recommend that this type of solution processable HTMs will be promising contender for high-efficiency OLED devices.

ECCENTRIC DISTANCE SUM OF SUBSTITUTION TREE NETWORKS

In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance generalizes the result of [T. Li, K. Jiang and L. Xi, Average distance of self-similar fractal trees, Fractals 26(1) (2018) 1850016.] from symmetric case to asymmetric case. To derive formulas, we investigate the corresponding integrals on self-similar measure and use the self-similarity of distance and measure. For simplicity, we introduce some systematic symbolic assignments and make some assumptions on the graph. We verify that our formulas are correct using the numerical calculation results.

Correction to: Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model

Correction to: Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model

Two-photon absorption of perylene-3,4,9,10-tetracarboxylic acid diimides: Effect of substituents in the bay

Improving the efficiency of photon upconversion in small organic molecules is a challenge where the molecular framework of perylene-3,4,9,10-tetracarboxylic acid diimides (PDIs) can provide meaningful achievements. To disentangle the different factors that can affect the n6onlinear optical response of such framework we present a systematic study of the two-photon absorption (TPA) properties of substituted PDIs addressing effects such as distortion from planarity, inductive vs. conjugative substituents, symmetric vs. asymmetric substitution of the bay positions and electron donor (D) vs. acceptor (A) nature of the bay substituents. The best performance in terms of nonlinear absorption was found in tetra-phenoxy bay-substituted PDIs with an A-PDI-A architecture that shows a TPA cross-section one order of magnitude higher than that of planar unsubstituted PDI, despite its distortion from planarity. This study constitutes a paradigmatic example of twisted core PDIs with enhanced optical properties.

Effects of Substitution Position of Carbazole-Dibenzofuran Based High Triplet Energy Hosts to Device Stability of Blue Phosphorescent Organic Light-Emitting Diodes.

High triplet energy hosts were developed through the modification of the substitution position of carbazole units. Two carbazole-dibenzofuran-derived compounds, 9,9′-(dibenzo[b,d]furan-2,6-diyl)bis(9H-carbazole) (26CzDBF) and 4,6-di(9H-carbazol-9-yl)dibenzo[b,d]furan (46CzDBF), were synthesized for achieving high triplet energy hosts. In comparison with the reported hole transport type host, 2,8-di(9H-carbazol-9-yl)dibenzo[b,d]furan (28CzDBF), 26CzDBF and 46CzDBF maintained high triplet energy over 2.95 eV. The device performances of the hosts were evaluated with electron transport type host, 2-phenyl-4, 6-bis(3-(triphenylsilyl)phenyl)-1,3,5-triazine (mSiTrz), to comprise a mixed host system. The deep blue phosphorescent device of 26CzDBF:mSiTrz with [[5-(1,1-dimethylethyl)-3-phenyl-1H-imidazo[4,5-b]pyrazin-1-yl-2(3H)-ylidene]-1,2-phenylene]bis[[6-(1,1-dimethylethyl)-3-phenyl-1H-imidazo[4,5-b]pyrazin-1-yl-2(3H)-ylidene]-1,2-phenylene]iridium (Ir(cb)3) dopant exhibited high external quantum efficiency of 22.9% with a color coordinate of (0.14, 0.16) and device lifetime of 1400 h at 100 cd m−2. The device lifetime was extended by 75% compared to the device lifetime of 28CzDBF:mSiTrz (800 h). These results demonstrated that the asymmetric and symmetric substitution of carbazole can make differences in the device performance of the carbazole- and dibenzofuran- derived hosts.

Information geometry for phylogenetic trees

We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than existing spaces: in wald space, trees are close if they induce similar distributions on genetic sequence data. As a point set, wald space contains the previously developed Billera–Holmes–Vogtmann (BHV) tree space; it also contains disconnected forests, like the edge-product (EP) space but without certain singularities of the EP space. We investigate two related geometries on wald space. The first is the geometry of the Fisher information metric of character distributions induced by the two-state symmetric Markov substitution process on each tree. Infinitesimally, the metric is proportional to the Kullback–Leibler divergence, or equivalently, as we show, to any f-divergence. The second geometry is obtained analogously but using a related continuous-valued Gaussian process on each tree, and it can be viewed as the trace metric of the affine-invariant metric for covariance matrices. We derive a gradient descent algorithm to project from the ambient space of covariance matrices to wald space. For both geometries we derive computational methods to compute geodesics in polynomial time and show numerically that the two information geometries (discrete and continuous) are very similar. In particular, geodesics are approximated extrinsically. Comparison with the BHV geometry shows that our canonical and biologically motivated space is substantially different.