Decomposition of density matrix renormalization group states into a Slater determinant basis

The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.     

Construction of environment states in quantum-chemical density-matrix renormalization group calculations

The application of the quantum-chemical density-matrix renormalization group (DMRG) algorithm is cumbersome for complex electronic structures with many active orbitals. The high computational cost is mainly due to the poor convergence of standard DMRG calculations. A factor which affects the convergence behavior of the calculations is the choice of the start-up procedure. In this start-up step matrix representations of operators have to be calculated in a guessed many-electron basis of the DMRG environment block. Different possibilities for the construction of these basis states exist, and we first compare four procedures to approximate the environment states using Slater determinants explicitly. These start-up procedures are applied to DMRG calculations on a sophisticated test system: the chromium dimer. It is found that the converged energies and the rate of convergence depend significantly on the choice of the start-up procedure. However, since already the most simple start-up procedure, which uses only the Hartree-Fock determinant, is comparatively good, Slater determinants, in general, appear not to be a good choice as approximate environment basis states for convergence acceleration. Based on extensive test calculations it is demonstrated that the computational cost can be significantly reduced if the number of total states m is successively increased. This is done in such a way that the environment states are built up stepwise from system states of previous truncated DMRG sweeps for slowly increasing m values.     

Relativistic DMRG calculations on the curve crossing of cesium hydride

Over the past few years, it has been shown in various studies on small molecules with only a few electrons that the density-matrix renormalization group (DMRG) method converges to results close to the full configuration-interaction limit for the total electronic energy. In order to test the capabilities of the method for molecules with complex electronic structures, we performed a study on the potential-energy curves of the ground state and the first excited state of 1sigma+ symmetry of the cesium hydride molecule. For cesium relativistic effects cannot be neglected, therefore we have used the generalized arbitrary-order Douglas-Kroll-Hess protocol up to tenth order, which allows for a complete decoupling of the Dirac Hamiltonian. Scalar-relativistic effects are thus fully incorporated in the calculations. The potential curves of the cesium hydride molecule feature an avoided crossing between the ground state and the first excited state, which is shown to be very well described by the DMRG method. Compared to multireference configuration-interaction results, the potential curves hardly differ in shape, for both the ground state and the excited state, but the total energies from the DMRG calculations are in general consistently lower. However, the DMRG energies are as accurate as corresponding coupled cluster energies at the equilibrium distance, but convergence to the full configuration-interaction limit is not achieved.     

autoCAS: A Program for Fully Automated Multiconfigurational Calculations

We present our implementation autoCAS for fully automated multiconfigurational calculations, which we also make available free of charge on our webpages. The graphical user interface of autoCAS connects a general electronic structure program with a density-matrix renormalization group program to carry out our recently introduced automated active space selection protocol for multiconfigurational calculations (Stein and Reiher, J. Chem. Theory Comput., 2016, 12, 1760). Next to this active space selection, autoCAS carries out several steps of multiconfigurational calculations so that only a minimal input is required to start them, comparable to that of a standard Kohn–Sham density-functional theory calculation, so that black-box multiconfigurational calculations become feasible. Furthermore, we introduce a new extension to the selection algorithm that facilitates automated selections for molecules with large valence orbital spaces consisting of several hundred orbitals. © 2019 Wiley Periodicals, Inc.     

Quadratically convergent calculation of localized molecular orbitals

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.     

猪胰岛素的活力位置的电子结构分析

本文采用负因子计数方法对猪胰岛素分子作了完整分子的量子化学计算,其中对矩阵元的计算采用EHMO方法。我们将前线轨道的概念推广为靠近Fermi能级的能量区域中的分子轨道,将局域于少数氨基酸残基上的前线轨道简称为活性轨道。计算结果表明,猪胰岛素70％的活力敏感位置上局域有活性轨道。对全部结果的分析说明猪胰岛素的活性轨道和生物活力之间存在某些内在联系,但不是一一对应关系;猪胰岛素的三级构象的变化可以引起电子结构的变化;相同种类的氨基酸残基在分子的不同位置上可以有不同的活性轨道能级和轨道分布。     

Self‐consistent field for fragmented quantum mechanical model of large molecular systems

Fragment‐based linear scaling quantum chemistry methods are a promising tool for the accurate simulation of chemical and biomolecular systems. Because of the coupled inter‐fragment electrostatic interactions, a dual‐layer iterative scheme is often employed to compute the fragment electronic structure and the total energy. In the dual‐layer scheme, the self‐consistent field (SCF) of the electronic structure of a fragment must be solved first, then followed by the updating of the inter‐fragment electrostatic interactions. The two steps are sequentially carried out and repeated; as such a significant total number of fragment SCF iterations is required to converge the total energy and becomes the computational bottleneck in many fragment quantum chemistry methods. To reduce the number of fragment SCF iterations and speed up the convergence of the total energy, we develop here a new SCF scheme in which the inter‐fragment interactions can be updated concurrently without converging the fragment electronic structure. By constructing the global, block‐wise Fock matrix and density matrix, we prove that the commutation between the two global matrices guarantees the commutation of the corresponding matrices in each fragment. Therefore, many highly efficient numerical techniques such as the direct inversion of the iterative subspace method can be employed to converge simultaneously the electronic structure of all fragments, reducing significantly the computational cost. Numerical examples for water clusters of different sizes suggest that the method shall be very useful in improving the scalability of fragment quantum chemistry methods. © 2015 Wiley Periodicals, Inc.     

面向有机光电材料的电子激发态结构与过程的计算方法

共轭聚合物与有机分子材料中的电子激发结构与过程决定了材料的光电功能：根据Kasha规则,低能级激发态的排序决定能否发光;最低激发态至基态的辐射跃迁与无辐射跃迁之间的竞争决定了发光效率,后者主要由非绝热耦合（声子作用）决定;电荷激发态载体的传输由电子分布与振动耦合或杂质和无序的散射弛豫过程决定．本文针对有机功能材料的发光性能,介绍两种理论方法的研究进展,即可用于计算共轭聚合物激发态结构的量子化学密度矩阵重整化群方法和计算发光效率的多模耦合无辐射跃迁速率方法．这些方法被应用于有机功能材料的性能预测和分子设计中．     

含时密度矩阵重正化群的理论与应用

密度矩阵重正化群(DMRG)作为计算低维强关联体系强有力的方法为人熟知, 在量子化学电子结构计算中得到广泛应用. 最近几年, 含时密度矩阵重正化群(TD-DMRG)的理论取得较快发展, TD-DMRG逐渐成为复杂体系量子动力学理论模拟的重要新兴方法之一. 本文综述了基于矩阵乘积态(MPS) 和矩阵乘积算符(MPO)的DMRG基本理论, 并重点介绍了若干最常见的TD-DMRG时间演化算法, 包括基于演化再压缩(P&C) 的算法、 基于含时变分原理(TDVP)的算法和时间步瞄准(TST)算法; 还对利用TD-DMRG模拟有限温体系的纯化(Purification)算法和最小纠缠典型量子热态(METTS)算法进行了介绍. 最后, 对近年TD-DMRG在复杂体系量子动力学中的应用进行了总结.     

频域空间密度矩阵重正化群的研究进展

密度矩阵重正化群(DMRG)作为低维强关联体系中电子结构计算的强有力方法被广泛熟知, 并被迅速地应用于量子化学, 不仅在电子结构计算中发挥重要作用, 同时也在近几年迅速地成为复杂体系量子动力学计算的重要方法. 在DMRG框架中, 衍生出了一系列计算动态响应性质的有效方法, 并得到了广泛应用. 本文简述了DMRG的基本理论, 其矩阵乘积态(MPS)表示有效地扩展了该方法的应用范围. 重点介绍了基于线性响应理论的动态DMRG, 在频率空间求解系统在零温以及有限温度下响应性质的算法, 并介绍其在电子关联问题和电子-声子关联问题中的应用, 最后展望了该领域的未来发展方向.     

Localized orbital theory and ammonia triborane

In a previous paper [J. Subotnik, Y. Shao and W. Liang, and M. Head-Gordon, J. Chem. Phys., 2004, 121, 9220], we proposed a new and efficient method for computing localized Edmiston-Ruedenberg (ER) orbitals, which are those localized orbitals that maximize self-interaction. In this paper, we improve upon our previous algorithm in two ways. First, we incorporate the resolution of the identity (RI) and atomic resolution of the identity (ARI) approximations when generating the relevant integrals, which allows for a drastic reduction in computational cost. Second, after convergence to a stationary point, we efficiently calculate the lowest mode of the Hessian matrix in order to either (i) confirm that we have found a minimum, or if not, (ii) move us away from the current saddle point. This gives our algorithm added stability. As a chemical example, in this paper, we investigate the electronic structure (including the localized orbitals) of ammonia triborane (NH(3)B(3)H(7)). Though ammonia triborane is a very electron-deficient compound, it forms a stable white powder which is now being investigated as a potential hydrogen storage material. In contrast to previous electronic structure predictions, our calculations show that ammonia triborane has one localized molecular orbital in the center of the electron-deficient triborane ring (much like the single molecular orbital in H(3)(+)), which gives the molecule added energetic stability. Furthermore, we believe that NH(3)B(3)H(7) is the smallest stable molecule supporting such a closed, three-center BBB bond.     

Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters

The accurate first-principles calculation of relative energies of transition metal complexes and clusters is still one of the great challenges for quantum chemistry. Dense lying electronic states and near degeneracies make accurate predictions difficult, and multireference methods with large active spaces are required. Often density functional theory calculations are employed for feasibility reasons, but their actual accuracy for a given system is usually difficult to assess (also because accurate ab initio reference data are lacking). In this work we study the performance of the density matrix renormalization group algorithm for the prediction of relative energies of transition metal complexes and clusters of different spin and molecular structure. In particular, the focus is on the relative energetical order of electronic states of different spin for mononuclear complexes and on the relative energy of different isomers of dinuclear oxo-bridged copper clusters.     

Optimization of molecular electronic structure calculations. 1. Local symmetry and local symmetricized orbitals

A formalism is suggested of the so-called local symmetricized orbitals to be used for the construction of a symmetricized basis in molecular electronic structure calculations. The local symmetricized orbitals are defined as additive contributions to the symmetry orbitals of a molecule that arise from symmetry operations of a corresponding atom. The local symmetricized orbitals are transformed according to the irreducible representations of the molecular symmetry group. This approach appears to be most suitable for the optimization of quantum mechanical calculations accounting for the spatial symmetry of compounds under consideration. This fact is due to the formalism of the local symmetricized orbitals that explicitly accounts for the local symmetry of basis function centers, which is essential for such optimization.     

Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.     

Quantifying the symmetry content of the electronic structure of molecules: molecular orbitals and the wave function

A scheme to quantify the symmetry content of the electronic wave function and molecular orbitals for arbitrary molecules is developed within the formalism of Continuous Symmetry Measures (CSMs). After defining the symmetry operation expectation values (SOEVs) as the key quantity to gauge the symmetry content of molecular wavefunctions, we present the working equations to be implemented in order to carry out real calculations using standard quantum chemistry software. The potentialities of a symmetry analysis using this new method are shown by means of some illustrative examples such as the changes induced in the molecular orbitals of a diatomic molecule by an electronegativity perturbation, the breaking of orbital symmetry along the dissociation path of the H(2) molecule, the changes in the molecular orbitals upon a geometrical distortion of the benzene molecule, and the inversion symmetry content in the different spin states of the [Fe(CH(3))(4)](2-) complex.     

Carbon nanotube, graphene, nanowire, and molecule-based electron and spin transport phenomena using the nonequilibrium Green's function method at the level of first principles theory

Based on density functional theory, we have developed a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals, particularly focusing on k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the nonequilibrium Green's function method enables calculation of the transmission coefficients at a given energy and voltage in a self-consistent manner as well as the corresponding current-voltage (I-V) characteristics. This scheme has advantages because it is applicable to large systems, easily transportable to different types of quantum chemistry packages, and extendable to time-dependent phenomena or inelastic scatterings. It has been applied to diverse types of practical electronic devices such as carbon nanotubes, graphene nanoribbons, metallic nanowires, and molecular electronic devices. The quantum conductance phenomena for systems involving quantum point contacts and I-V curves for a single molecule in contact with metal electrodes using the k-point sampling method are described.