Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions v...Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.展开更多
We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probabili...We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.展开更多
A novel organic-inorganic chromium(III) hybrid salt, triethylammonium<em> trans</em>-diaquabis(oxalato-<em>κ</em><sup>2</sup>O<sup>1</sup>,O<sup>2</sup>)chr...A novel organic-inorganic chromium(III) hybrid salt, triethylammonium<em> trans</em>-diaquabis(oxalato-<em>κ</em><sup>2</sup>O<sup>1</sup>,O<sup>2</sup>)chromate(III), (C<sub>6</sub>H<sub>16</sub>N)[Cr(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub>] (1), has been synthesized in aqueous solution and characterized by elemental and thermal analyses, FTIR and UV-Vis spectroscopies, and by single crystal X-ray structure determination. Compound 1 crystallizes in the orthorhombic system, <em>Pbcn</em> space group with the unit cell parameters <em>a</em> = 11.1776(10), <em>b </em>= 7.6105(10), <em>c</em> = 17.5654(2) <span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">Å</span>, <em>α</em> = <em>β</em> = <em>γ</em> = 90<span style="white-space:nowrap;">°</span>, <em>V</em> = 1494.24(3) <span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">Å</span>3, <em>Z</em> = 4 and <em>Z’</em> = 1/2. The structure of 1 consists of [Cr(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub>]<span style="white-space:nowrap;"><sup>−</sup></span> mononuclear anions and triethylammonium [(C<sub>2</sub>H<sub>5</sub>)<sub>3</sub>NH]<sup>+</sup> cations. In the anionic unit, the CrIII ion is six coordinated, in a distorted octahedral geometry, by four equatorial O atoms of two oxalate anions acting as chelating ligands and two O atoms from <em>trans</em>-coordinated water molecules occupying the apical positions with longer metal-oxygen distances. In the solid, O-H … O and N-H … O intra and inter molecular hydrogen bonding interactions connect the components into a 3D network. The triethylammonium cations are disordered among two possible orientations with occupancies rates around 50% for C4, N1, C1a, C1b, C4<sup>ii</sup>, N1<sup>ii</sup>, C1a<sup>ii</sup>, C1b<sup>ii</sup> (ii = <span style="white-space:nowrap;">−</span><em>x</em> + 1, <em>y</em>, <span style="white-space:nowrap;">−</span> <em>z</em> + 1/2). The IR spectrum of 1 is consistent with the presence of the various molecular building constituents. The UV-Vis spectrum shows two absorption bands around 564 and 416 nm which are compatible with an anionic chromium (III) complex in an octahedral environment. Thermal studies carried out in air between 25<span style="white-space:nowrap;">°</span>C and 700°C confirm the anhydrous character of 1 and show that it is stable up to 210<span style="white-space:nowrap;">°</span>C.展开更多
基金supported by the National Natural Science Foundation of China(No.22273005 and No.22422301)the Innovation Program for Quantum Science and Technology(No.2023ZD0300200)+1 种基金the National Security Academic Foundation(No.U2330201)the Fundamental Research Funds for the Central Universities.
文摘Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174370)
文摘We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.
文摘A novel organic-inorganic chromium(III) hybrid salt, triethylammonium<em> trans</em>-diaquabis(oxalato-<em>κ</em><sup>2</sup>O<sup>1</sup>,O<sup>2</sup>)chromate(III), (C<sub>6</sub>H<sub>16</sub>N)[Cr(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub>] (1), has been synthesized in aqueous solution and characterized by elemental and thermal analyses, FTIR and UV-Vis spectroscopies, and by single crystal X-ray structure determination. Compound 1 crystallizes in the orthorhombic system, <em>Pbcn</em> space group with the unit cell parameters <em>a</em> = 11.1776(10), <em>b </em>= 7.6105(10), <em>c</em> = 17.5654(2) <span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">Å</span>, <em>α</em> = <em>β</em> = <em>γ</em> = 90<span style="white-space:nowrap;">°</span>, <em>V</em> = 1494.24(3) <span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">Å</span>3, <em>Z</em> = 4 and <em>Z’</em> = 1/2. The structure of 1 consists of [Cr(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub>(H<sub>2</sub>O)<sub>2</sub>]<span style="white-space:nowrap;"><sup>−</sup></span> mononuclear anions and triethylammonium [(C<sub>2</sub>H<sub>5</sub>)<sub>3</sub>NH]<sup>+</sup> cations. In the anionic unit, the CrIII ion is six coordinated, in a distorted octahedral geometry, by four equatorial O atoms of two oxalate anions acting as chelating ligands and two O atoms from <em>trans</em>-coordinated water molecules occupying the apical positions with longer metal-oxygen distances. In the solid, O-H … O and N-H … O intra and inter molecular hydrogen bonding interactions connect the components into a 3D network. The triethylammonium cations are disordered among two possible orientations with occupancies rates around 50% for C4, N1, C1a, C1b, C4<sup>ii</sup>, N1<sup>ii</sup>, C1a<sup>ii</sup>, C1b<sup>ii</sup> (ii = <span style="white-space:nowrap;">−</span><em>x</em> + 1, <em>y</em>, <span style="white-space:nowrap;">−</span> <em>z</em> + 1/2). The IR spectrum of 1 is consistent with the presence of the various molecular building constituents. The UV-Vis spectrum shows two absorption bands around 564 and 416 nm which are compatible with an anionic chromium (III) complex in an octahedral environment. Thermal studies carried out in air between 25<span style="white-space:nowrap;">°</span>C and 700°C confirm the anhydrous character of 1 and show that it is stable up to 210<span style="white-space:nowrap;">°</span>C.
