Dynamic Correlation Method Research Articles

Signal synchronization methods when measuring tailpipe emissions with PEMS

This study describes the effects of using different signal synchronization methods on the tailpipe emission factors obtained by on-road tests using PEMS (Portable Emission Measurement Systems). The event-based, static correlation, and dynamics correlation methods were applied to data obtained using different PEMS. The first database included 36 cargo vehicles following the same driving cycle in various cities in Colombia. The second database involved 16 passenger transport vehicles monitored under real operating conditions in Mexico. When comparing results with the event-based synchronization method as the reference, significant differences in emission factors (>25 %) were observed. Those differences depend directly on the physical setup of the PEMS. The dynamic correlation method exhibited the best performance in all cases. When using this method, we recommend to synchronize the CO2 mass flow and fuel consumption variables first and then adjust the obtained synchronization to other species to account for differences in species diffusivities.

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals.

Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The ACn method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, ACn is more efficient than existing ab initio multireference dynamic correlation methods. ACn affords excellent results for singlet–triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.

Improving Excited-State Potential Energy Surfaces via Optimal Orbital Shapes

We demonstrate that, rather than resorting to high-cost dynamic correlation methods, qualitative failures in excited-state potential energy surface predictions can often be remedied at no additional cost by ensuring that optimal molecular orbitals are used for each individual excited state. This approach also avoids the weighting choices required by state-averaging and dynamic weighting and obviates their need for expensive wave function response calculations when relaxing excited-state geometries. Although multistate approaches are of course preferred near conical intersections, other features of excited-state potential energy surfaces can benefit significantly from our single-state approach. In three different systems, including a double bond dissociation, a biologically relevant amino hydrogen dissociation, and an amino-to-ring intramolecular charge transfer, we show that state-specific orbitals offer qualitative improvements over the state-averaged status quo.

Multi-reference Epstein–Nesbet perturbation theory with density matrix renormalization group reference wavefunction

The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein–Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H2S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H64 square lattice with an active space of (42e, 42o).

Dynamic correlation for non-orthogonal reference states: Improved perturbational and variational methods.

The use of non-orthogonal orbitals allows the construction and use of more compact wave functions than offered by standard methods using orthogonal molecular orbitals; in particular, for molecules containing partly occupied atomic orbitals as present, for example, in transition metal complexes. With the purpose of developing efficient dynamic correlation methods, we discuss several new internal correlation methods employing a reference state containing non-orthogonal active orbitals. The non-orthogonal internally contracted perturbation theory approach is improved in several directions. The major improvements are the use of the Dyall Hamiltonian including two-electron interactions within the active space as the zero-order operator, the calculation of third-order energy-corrections, and the inclusion of excitations in the space of active orbitals. The latter improvement corrects for the use of an incomplete reference state. The improvements are tested for the nitrogen molecule and the challenging chromium dimer. The combined use of the improved zero-order Hamiltonian and the inclusion of active space excitations allow us to obtain potential curves for the chromium dimer that are close to those obtained using the larger complete active space reference wave function.

Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function.

The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multireference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use an active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with an active space larger than 30 orbitals and/or a large basis set because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use reconstructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA) [ Luo et al. J. Chem. Theory Comput. 2017 , 13 , 4699 - 4710 . ] and integrate it with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation, and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, the DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of the potential energy curve of Cr2, single-triplet gaps of higher n-acene molecules, and the energy of the Eu-BTBP(NO3)3 complex.

Unveiling the multiscale teleconnection between Pacific Decadal Oscillation and global surface temperature using time-dependent intrinsic correlation analysis

Global surface temperature is significantly influenced by different climate forcings operating at specific time scales. This study investigates the association between global surface temperature and the Pacific Decadal Oscillation (PDO) in a multiscaling framework in terms of both time scale of variability and non-stationarity. First, the ensemble empirical mode decomposition (EEMD) is used for multiscale disintegration of the Global Surface Temperature Anomaly (GSTA) and PDO datasets. A close matching of the periodicity of different modes of PDO and GSTA is noticed, and the subsequent cross-correlation analysis of the modes showed that their linear association is the most perceptible at the slowly varying trend component. The correlation between the different modes is further analyzed using a multiscale dynamic correlation method namely, time-dependent intrinsic correlation (TDIC). This study found a strong long-range positive correlation between the time series pairs in decadal and inter-decadal modes exceeding 20-year periodicity. Further it is found that, the multiscale teleconnection between PDO and GSTA is not always of unique character but associated with localized reversals in the nature of correlation in the time domain. The study further observed a similar pattern of correlation for both cold phases of the 20th century (1901–1924 and 1947–1976); whereas the pattern of correlation is different for the warm phases of PDO (1925–1946 and 1977–1995) in different process scales.

A super-resolution polarimetric wavefront extraction algorithm for UWB-radar under massive interference conditions

To provide short-range super-resolution ultra-wideband (UWB) radar under multi-scattering conditions, a superior wavefront extraction algorithm is proposed in this paper. Conventional correlation-based pulse separation methods based on SAGE, CLEAN or the previously introduced superior dynamic correlation method (DCM) are revised, validated, and compared. In this paper, the DCM is improved significantly by applying the Pauli scattering matrix decomposition onto the radar data. This novel wavefront extraction algorithm is called polarimetric dynamic correlation method (PDCM) and is suitable to resolve several overlapping pulses, which consist of both strong echoes and weak echoes which are masked by the strong ones. The performance of the PDCM and the comparison with alternative algorithms is carried out by a subsequent feature extraction algorithm for visual verification. Experimental validations are performed with two complex test objects, a maximum length sequence radar device (4.5–13.5 GHz) and compact dual-polarized UWB antennas.

Density matrix renormalization group for ab initio Calculations and associated dynamic correlation methods: A review of theory and applications

The recent advent of the density matrix renormalization group (DMRG) theory has delivered a new capability to compute multireference (MR) wave function with large configuration space, which far exceeds the limitation of conventional approaches. Here, we provide an overview of our recent work on the developments of ab initio DMRG methods in the context of the active space approaches and their applications to MR chemical systems. © 2014 Wiley Periodicals, Inc.

A detailed study on the symmetry breaking and its effect on the potential surface of NO3

The tenacious symmetry breaking of the electronic wave function of the nitrate radical (NO3) and its effect on the ground-state potential energy surface is investigated in detail. The symmetry breaking of Hartree–Fock wave functions results from a dominance of the orbital localization effect over the resonance effect and leads to three different solutions, one symmetrical and two distorted ones, for the same electronic state. The respective equilibrium geometries of these solutions are points on different potential surfaces, making their comparison meaningless. The resonance effect is promoted by dynamic as well as static electron correlation. However, the dynamic correlation methods [e.g., many-body perturbation theory (MBPT) and coupled-cluster single double (CCSD)] cannot overcome the symmetry breaking of the reference function and the problem of multiple solutions persists. The symmetry breaking can be avoided by the complete active space self-consistent field (CASSCF) approach that yields unique, single-valued surfaces for all electronic states. However, a sufficiently large and appropriately selected active space has to be used to avoid unphysical distortion of the wave function. Still the orbital localization effect leads to equilibrium geometries of C2v symmetry which strongly depend on the state-averaging of the CASSCF wave function. Multireference single double configuration interaction (MR-SDCI) wave functions are also free of symmetry breaking, if the reference orbitals are and if the configuration space is invariant under the symmetry operations. MRCI geometry optimizations only result in D3h symmetric structures with bond lengths and harmonic frequencies in close agreement with experimental data.