Role of trans-Planckian modes in cosmology

Motivated by the old trans-Planckian (TP) problem of inflationary cosmology, it has been conjectured that any consistent effective field theory should keep TP modes `hidden' behind the Hubble horizon, so as to prevent them from turning classical and thereby affecting macroscopic observations. In this paper we present two arguments against the Hubble horizon being a scale of singular significance as has been put forward in the TP Censorship Conjecture (TCC). First, refinements of TCC are presented that allow for the TP modes to grow beyond the horizon while still keeping the de-Sitter conjecture valid. Second, we show that TP modes can turn classical even well within the Hubble horizon, which, as such, negates this rationale behind keeping them from crossing it. The role of TP modes is known to be less of a problem in warm inflation, because fluctuations start out usually as classical. This allows warm inflation to be more resilient to the TP problem compared to cold inflation. To understand how robust this is, we identity limits where quantum modes can affect the primordial power spectrum in one specific case.Comment: 33 pages, comments welcome; v2: References updated, matches published versio

Synthesis, Structure, and Properties of a Series of Chiral Tweezer–Diamine Complexes Consisting of an Achiral Zinc(II) Bisporphyrin Host and Chiral Diamine Guest: Induction and Rationalization of Supramolecular Chirality

We report here the synthesis, structure, and spectroscopic properties of a series of supramolecular chiral 1:1 tweezer–diamine complexes consisting of an achiral Zn­(II) bisporphyrin (Zn₂DPO) host and five different chiral diamine guests, namely, (<i>R</i>)-diaminopropane (DAP), (1<i>S</i>,2<i>S</i>)-diaminocyclohexane (CHDA), (<i>S</i>)-phenylpropane diamine (PPDA), (<i>S</i>)-phenyl ethylenediamine (PEDA), and (1<i>R</i>,2<i>R</i>)-diphenylethylene diamine (DPEA). The solid-state structures are preserved in solution, as reflected in their ¹H NMR spectra, which also revealed the remarkably large upfield shifts of the N<i>H</i>₂ guest protons with the order Zn₂DPO·DAP > Zn₂DPO·CHDA > Zn₂DPO·PPDA> Zn₂DPO·PEDA ≫ Zn₂DPO·DPEA, which happens to be the order of binding constants of the respective diamines with Zn₂DPO. As the bulk of the substituent at the chiral center of the guest ligand increases, the Zn–N_ax distance of the tweezer–diamine complex also increases, which eventually lowers the binding of the guest ligand toward the host. Also, the angle between the two porphyrin rings gradually increases with increasing bulk of the guest in order to accommodate the guest within the bisporphyrin cavity with minimal steric clash. The notably high amplitude bisignate CD signal response by Zn₂DPO·DAP, Zn₂DPO·CHDA, and Zn₂DPO·PPDA can be ascribed to the complex’s high stability and the formation of a unidirectional screw as observed in the X-ray structures of the complexes. A relatively lower value of CD amplitude shown by Zn₂DPO·PEDA is due to the lower stability of the complex. The projection of the diamine binding sites of the chiral guest would make the two porphyrin macrocycles oriented in either a clockwise or anticlockwise direction in order to minimize host–guest steric clash. In sharp contrast, Zn₂DPO·DPEA shows a very low amplitude bisignate CD signal due to the presence of both left- (dictated by the pre-existing chirality of (1<i>R</i>,2<i>R</i>)-DPEA) and right-handed screws (dictated by the steric differentiation at the chiral center) of the molecule, as evident from X-ray crystallography. The present work demonstrates a full and unambiguous rationalization of the observed chirality transfer processes from the chiral guest to the achiral host

Building-up Remarkably Stable Magnesium Porphyrin Polymers Self-Assembled via Bidentate Axial Ligands: Synthesis, Structure, Surface Morphology, and Effect of Bridging Ligands

A series of supramolecular architectures of magnesium tetranitrooctaethylporphyrins mediated by several bidentate axial ligands have been synthesized in excellent yields and structurally characterized. Six conjugated axial ligand with increasing chain lengths have been utilized in the present investigations in which the Mg···Mg nonbonding distance between successive ions also increases from 0.73 to 2.70 nm in the series. To the best of our knowledge, this is the first report where stable metallo-porphyrin polymers with such long spacers have been synthesized in one pot so easily. Linear one-dimensional (1D) polymeric chains were observed in the X-ray structure of the six-coordinated complexes in which porphyrin units are aligned parallel to each other to have so-called “shish kebab” like architectures to maintain offset-stacked overlap. However, after an optimum Mg···Mg nonbonding distance, these 1D chain do not continue, rather they form five-coordinated porphyrin dimers with “wheel-and-axle” like architectures which are then self-aggregated by π–π interactions in a perpendicular manner to fill space created by large bridging ligands more effectively which consequently results in spherical structures. The structures of the molecules in solution and their surface patterns on highly ordered pyrolytic graphite (HOPG) have also been investigated

Highly Enhanced Bisignate Circular Dichroism of Ferrocene-Bridged Zn(II) Bisporphyrin <i>Tweezer</i> with Extended Chiral Substrates due to Well-Matched Host–Guest System

Four new chiral <i>tweezer-</i>diamine complexes, consisting of an achiral ferrocene-bridged Zn­(II)­bisporhyrin host (<b>1</b>) and two small diamines (1<i>R</i>,2<i>R</i>)-1,2-diphenylethylene diamine {(1<i>R</i>,2<i>R</i>)-DPEA} and (1<i>S</i>,2<i>S</i>)-1,2-cyclohexane diamine {(1<i>S</i>,2<i>S</i>)-CHDA} and two extended diamines (1<i>R</i>,2<i>R</i>)-<i>N</i>,<i>N</i>′-bis-(isonicotinoyl)-1,2-diphenylethylene diamine {(1<i>R</i>,2<i>R</i>)-DPEApy} and (1<i>S</i>,2<i>S</i>)-<i>N</i>,<i>N</i>′-bis-(isonicotinoyl)-1,2-cyclohexane diamine {(1<i>S</i>,2<i>S</i>)-CHDApy} chiral guests, are reported. Additions of (1<i>R</i>,2<i>R</i>)-DPEA and (1<i>S</i>,2<i>S</i>)-CHDA separately to <b>1</b> in dichloromethane result in the formation of 1:1 sandwich complexes <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)}, respectively, at low guest concentration and 1:2 anti complexes <b>1·</b>(DPEA_{(<i>R</i>,<i>R</i>)})₂ and <b>1·</b>(CHDA_{(<i>S</i>,<i>S</i>)})₂, respectively, at higher guest concentration. In contrast, separate additions of (1<i>R</i>,2<i>R</i>)-DPEApy and (1<i>S</i>,2<i>S</i>)-CHDApy to <b>1</b> produce only 1:1 sandwich complexes of <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)}, respectively. The binding constants at 295 K between <b>1</b> and (1<i>R</i>,2<i>R</i>)-DPEA are observed to be (4.7 ± 0.2) × 10⁴ M^–1 and (4.3 ± 0.3) × 10³ M^–1 for 1:1 sandwich and 1:2 anti form, respectively, while the respective values with (1<i>S</i>,2<i>S</i>)-CHDA are (1.5 ± 0.2) × 10⁵ M^–1 and (5.9 ± 0.3) × 10³ M^–1. However, much larger values of (2.5 ± 0.3) × 10⁵ M^–1 and (1.3 ± 0.3) × 10⁶ M^–1 have been observed with DPEApy_{(<i>R</i>,<i>R</i>)} and CHDApy_{(<i>S</i>,<i>S</i>)}, respectively, to produce the corresponding 1:1 sandwich complexes. <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} (<i>A</i>_cal, −1759 cm^–1 M^–1) (<i>A</i>_cal = Δε₁ – Δε₂, representing the total amplitude of the calculated circular dichroism (CD) couplets) shows ∼10-fold increase in CD amplitude compared to the values observed for <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} (<i>A</i>_cal, +187 cm^–1 M^–1), while <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)} (<i>A</i>_cal, +1886 cm^–1 M^–1) shows nearly 3-fold increase of the CD amplitude compared to the value observed for <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)} (<i>A</i>_cal, −785 cm^–1 M^–1) at 295 K. The <i>A</i>_cal values of −1759 cm^–1 M^–1 and +1886 cm^–1 M^–1 observed for the <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)}, respectively, are extremely high. To the best of our knowledge, these are some of the largest values reported for a chirality induction process involving bisporphyrin <i>tweezer</i> receptors. The large enhancement in the CD signal intensity is due to the well complementarity size between Zn­(II)­bisporphyrin host and the extended chiral diamines guest, which results large unidirectional twisting of two porphyrin units to accommodate the guests having preorganized binding sites with minimum host–guest steric interactions. It is interesting to note that <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} and <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} show CD signal opposite in sign to each other, which happens to be the case between <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)} also

Highly Enhanced Bisignate Circular Dichroism of Ferrocene-Bridged Zn(II) Bisporphyrin <i>Tweezer</i> with Extended Chiral Substrates due to Well-Matched Host–Guest System

Four new chiral <i>tweezer-</i>diamine complexes, consisting of an achiral ferrocene-bridged Zn­(II)­bisporhyrin host (<b>1</b>) and two small diamines (1<i>R</i>,2<i>R</i>)-1,2-diphenylethylene diamine {(1<i>R</i>,2<i>R</i>)-DPEA} and (1<i>S</i>,2<i>S</i>)-1,2-cyclohexane diamine {(1<i>S</i>,2<i>S</i>)-CHDA} and two extended diamines (1<i>R</i>,2<i>R</i>)-<i>N</i>,<i>N</i>′-bis-(isonicotinoyl)-1,2-diphenylethylene diamine {(1<i>R</i>,2<i>R</i>)-DPEApy} and (1<i>S</i>,2<i>S</i>)-<i>N</i>,<i>N</i>′-bis-(isonicotinoyl)-1,2-cyclohexane diamine {(1<i>S</i>,2<i>S</i>)-CHDApy} chiral guests, are reported. Additions of (1<i>R</i>,2<i>R</i>)-DPEA and (1<i>S</i>,2<i>S</i>)-CHDA separately to <b>1</b> in dichloromethane result in the formation of 1:1 sandwich complexes <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)}, respectively, at low guest concentration and 1:2 anti complexes <b>1·</b>(DPEA_{(<i>R</i>,<i>R</i>)})₂ and <b>1·</b>(CHDA_{(<i>S</i>,<i>S</i>)})₂, respectively, at higher guest concentration. In contrast, separate additions of (1<i>R</i>,2<i>R</i>)-DPEApy and (1<i>S</i>,2<i>S</i>)-CHDApy to <b>1</b> produce only 1:1 sandwich complexes of <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)}, respectively. The binding constants at 295 K between <b>1</b> and (1<i>R</i>,2<i>R</i>)-DPEA are observed to be (4.7 ± 0.2) × 10⁴ M^–1 and (4.3 ± 0.3) × 10³ M^–1 for 1:1 sandwich and 1:2 anti form, respectively, while the respective values with (1<i>S</i>,2<i>S</i>)-CHDA are (1.5 ± 0.2) × 10⁵ M^–1 and (5.9 ± 0.3) × 10³ M^–1. However, much larger values of (2.5 ± 0.3) × 10⁵ M^–1 and (1.3 ± 0.3) × 10⁶ M^–1 have been observed with DPEApy_{(<i>R</i>,<i>R</i>)} and CHDApy_{(<i>S</i>,<i>S</i>)}, respectively, to produce the corresponding 1:1 sandwich complexes. <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} (<i>A</i>_cal, −1759 cm^–1 M^–1) (<i>A</i>_cal = Δε₁ – Δε₂, representing the total amplitude of the calculated circular dichroism (CD) couplets) shows ∼10-fold increase in CD amplitude compared to the values observed for <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} (<i>A</i>_cal, +187 cm^–1 M^–1), while <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)} (<i>A</i>_cal, +1886 cm^–1 M^–1) shows nearly 3-fold increase of the CD amplitude compared to the value observed for <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)} (<i>A</i>_cal, −785 cm^–1 M^–1) at 295 K. The <i>A</i>_cal values of −1759 cm^–1 M^–1 and +1886 cm^–1 M^–1 observed for the <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)}, respectively, are extremely high. To the best of our knowledge, these are some of the largest values reported for a chirality induction process involving bisporphyrin <i>tweezer</i> receptors. The large enhancement in the CD signal intensity is due to the well complementarity size between Zn­(II)­bisporphyrin host and the extended chiral diamines guest, which results large unidirectional twisting of two porphyrin units to accommodate the guests having preorganized binding sites with minimum host–guest steric interactions. It is interesting to note that <b>1·</b>DPEA_{(<i>R</i>,<i>R</i>)} and <b>1·</b>DPEApy_{(<i>R</i>,<i>R</i>)} show CD signal opposite in sign to each other, which happens to be the case between <b>1·</b>CHDA_{(<i>S</i>,<i>S</i>)} and <b>1·</b>CHDApy_{(<i>S</i>,<i>S</i>)} also

A Nonempirical Approach for Direct Determination of the Absolute Configuration of 1,2-Diols and Amino Alcohols Using Mg(II)bisporphyrin

We report here a simple, facile, and direct nonempirical protocol for determining the absolute stereochemistry of a variety of chiral 1,2-diols and amino alcohols at room temperature with no chemical derivatization using Mg­(II)­bisporphyrin as a host. Addition of excess substrates resulted in the formation of a 1:2 host–guest complex in which two substrates bind in an unusual <i>endo-endo</i> fashion because of interligand H-bonding within the bisporphyrin cavity leading to the formation of a unidirectional screw in the bisporphyrin moiety that allowed us an accurate absolute stereochemical determination of the chiral substrate via exciton-coupled circular dichroism (ECCD). The sign of the CD couplet has also been found to be inverted when the stereogenic center is moved by one C atom simply from the bound to an unbound functionality and thus able to discriminate between them successfully. Strong complexation of the alcoholic oxygen with Mg­(II)­bisporphyrin rigidifies the host–guest complex, which eventually enhances its ability to stereochemically differentiate the asymmetric center. The ECCD sign of a large number of substrates has followed consistent and predictable trends; thus, the system is widely applicable. Moreover, computational calculations clearly support the experimental observations along with the absolute stereochemistry of the chiral substrate

A Nonempirical Approach for Direct Determination of the Absolute Configuration of 1,2-Diols and Amino Alcohols Using Mg(II)bisporphyrin

We report here a simple, facile, and direct nonempirical protocol for determining the absolute stereochemistry of a variety of chiral 1,2-diols and amino alcohols at room temperature with no chemical derivatization using Mg­(II)­bisporphyrin as a host. Addition of excess substrates resulted in the formation of a 1:2 host–guest complex in which two substrates bind in an unusual <i>endo-endo</i> fashion because of interligand H-bonding within the bisporphyrin cavity leading to the formation of a unidirectional screw in the bisporphyrin moiety that allowed us an accurate absolute stereochemical determination of the chiral substrate via exciton-coupled circular dichroism (ECCD). The sign of the CD couplet has also been found to be inverted when the stereogenic center is moved by one C atom simply from the bound to an unbound functionality and thus able to discriminate between them successfully. Strong complexation of the alcoholic oxygen with Mg­(II)­bisporphyrin rigidifies the host–guest complex, which eventually enhances its ability to stereochemically differentiate the asymmetric center. The ECCD sign of a large number of substrates has followed consistent and predictable trends; thus, the system is widely applicable. Moreover, computational calculations clearly support the experimental observations along with the absolute stereochemistry of the chiral substrate

A Nonempirical Approach for Direct Determination of the Absolute Configuration of 1,2-Diols and Amino Alcohols Using Mg(II)bisporphyrin

We report here a simple, facile, and direct nonempirical protocol for determining the absolute stereochemistry of a variety of chiral 1,2-diols and amino alcohols at room temperature with no chemical derivatization using Mg­(II)­bisporphyrin as a host. Addition of excess substrates resulted in the formation of a 1:2 host–guest complex in which two substrates bind in an unusual <i>endo-endo</i> fashion because of interligand H-bonding within the bisporphyrin cavity leading to the formation of a unidirectional screw in the bisporphyrin moiety that allowed us an accurate absolute stereochemical determination of the chiral substrate via exciton-coupled circular dichroism (ECCD). The sign of the CD couplet has also been found to be inverted when the stereogenic center is moved by one C atom simply from the bound to an unbound functionality and thus able to discriminate between them successfully. Strong complexation of the alcoholic oxygen with Mg­(II)­bisporphyrin rigidifies the host–guest complex, which eventually enhances its ability to stereochemically differentiate the asymmetric center. The ECCD sign of a large number of substrates has followed consistent and predictable trends; thus, the system is widely applicable. Moreover, computational calculations clearly support the experimental observations along with the absolute stereochemistry of the chiral substrate