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  • 1
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    Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states (2015)
    American Institute of Physics (AIP)
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    Publication Date: 2015-08-25
    Description: We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 2
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    A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer (2015)
    American Institute of Physics (AIP)
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    Publication Date: 2015-01-10
    Description: We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136 , 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C 2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10 12 many-body states. While our calculated energy lies within the 0.3 mE h error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE h , much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies ( T e ) of eight lowest lying excited states: a 3 Π u , b 3 Σ g − , A 1 Π u , c 3 Σ u + , B 1 Δ g , B ′ 1 Σ g + , d 3 Π g , and C 1 Π g are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σ g + , 1 Σ u + , 1 Σ g − , and 1 Σ u − , to an estimated accuracy of 0.1 mE h of the exact result in this basis.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 3
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    Quasi-degenerate perturbation theory using matrix product states (2016)
    American Institute of Physics (AIP)
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    Publication Date: 2016-01-20
    Description: In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2 n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 4
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    High-fat diet transition reduces brain DHA levels associated with altered brain plasticity and behaviour (2012)
    Springer Nature
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    Publication Date: 2012-07-09
    Description: High-fat diet transition reduces brain DHA levels associated with altered brain plasticity and behaviour Scientific Reports 2, 30052012 doi: 10.1038/srep00431 Sandeep Sharma Yumei Zhuang Fernando Gomez-Pinilla To assess how the shift from a healthy diet rich in omega-3 fatty acids to a diet rich in saturated fatty acid affects the substrates for brain plasticity and function, we used pregnant rats fed with omega-3 supplemented diet from their 2nd day of gestation period as well as their male pups for 12 weeks. Afterwards, the animals were randomly assigned to either a group fed on the same diet or a group fed on a high-fat diet (HFD) rich in saturated fats for 3 weeks. We found that the HFD increased vulnerability for anxiety-like behavior, and that these modifications harmonized with changes in the anxiety-related NPY1 receptor and the reduced levels of BDNF, and its signalling receptor pTrkB, as well as the CREB protein. Brain DHA contents were significantly associated with the levels of anxiety-like behavior in these rats.
    Electronic ISSN: 2045-2322
    Topics: Natural Sciences in General
    Published by Springer Nature
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  • 5
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    Diet transition to a high-fat diet for 3 weeks reduces brain omega-3-fatty acid levels, alters BDNF signaling and induces anxiety & depression-like behavior in adult rats (2012)
    Springer Nature
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    Publication Date: 2012-03-05
    Description: Background: The consumption of diets high in calories and low in nutrient value is becoming increasingly common in modern society, which can lead to metabolic disorders like diabetes and obesity, and potentially to psychiatric disorders. We have performed studies to assess how the shift from a healthy diet rich in omega-3 fatty acids to a diet rich in saturated fatty acid affects the substrates for brain plasticity and function, and anxiety and depression-like behavior. Methods: Pregnant rats were fed with omega-3 supplemented diet from their 2nd day of gestation period as well as their male pups for 12 weeks. Afterwards, the animals were randomly assigned to either a group fed on the same diet or a group fed on a high-fat diet (HFD) rich in saturated fats for 3 weeks. Anxiety and depression-like behaviors were assessed by using open field (OF) and elevated plus maze (EPM). Molecular assessments were performed in the frontal cortex and hippocampus as dysfunctions in these brain regions are main contributors towards depression, anxiety-like behavior and stress. Results: We found that the HFD increased vulnerability for anxiety and depression-like behavior, and that these modifications harmonized with changes in the anxiety-related neuropeptide Y (NPY)-1 receptor. The HFD reduced levels of brain-derived neurotrophic factor (BDNF), and the BDNF signaling receptor pTrkB, as well as the cyclic AMP response element binding protein (CREB), in these brain regions. Brain DHA contents were significantly associated with the levels of anxiety and depression-like behavior in these rats. Conclusions: These results suggest that the change in dietary lifestyle leading to alteration of dietary n3/n-6 fatty acids levels imposes a risk factor for anxiety-like behaviors. Dietary DHA might help for building cognitive reserve that can resist psychiatric disorders.
    Electronic ISSN: 1756-0357
    Topics: Natural Sciences in General , Geosciences , Physics , Chemistry and Pharmacology , Biology , Medicine
    Published by Springer Nature
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  • 6
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    Tillage and residue management practices affect soil biological indicators in a rice‐wheat cropping system in north‐western India (2019)
    Wiley
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    Publication Date: 2019
    Description: Abstract Agricultural productivity relies on a wide range of ecosystem services provided by the soil biota. Sustainable management practices, such as tillage and residue management, can influence structure and function of the soil microbiota, with direct consequences for the associated ecosystem services. Although there is increasing evidence that different tillage regimes alter the soil biological indices, we only have a limited understanding of their temporal changes in a rice (Oryza sativa L.) ‐ wheat (Triticum aestivum L.) cropping system. We evaluated the effects of combinations of tillage, crop residue management and green manuring on soil biological indicators after five years of the practicing rice‐wheat system (RWS). Four main plot treatments in rice included: (1) PTRW0, puddled transplanted rice with no wheat straw retained, (2) PTRW25, puddled transplanted rice with 25% anchored wheat stubbles retained, (3) PTRW0 + Sesbania aculeate L. green manure (GM), and (4) PTRW25+GM, puddled transplanted rice with 25% anchored wheat stubbles retained+ GM. There were three sub‐plot treatments in the subsequent wheat crop: (1) CTWR0, conventional tillage wheat with rice residue removed, (2) ZTWR0, zero tillage wheat with rice residue removed and (3) ZTWR100, ZTW with 100% rice residue retained as mulch. The PTRW25+GM treatment, followed by ZTWR100, significantly increased soil microbial biomass carbon, basal soil respiration, microbial quotient and mineralization quotient measured during wheat‐growing season. These biological indicators were higher at vigorous vegetative wheat growth stage than at flowering stage and decreased at maturity. The principal component analysis of the assayed variables showed that all the variables significantly contributed to the variability in parameters examined and were more related to maximum tillering stage of wheat growth than to maturity or at sowing of wheat. Three highly effective biological indicators were microbial biomass carbon, microbial quotient and mineralization quotient, which responded significantly to changes in tillage and residue management practices in the RWS. We conclude that crop residues and green manure have significant to improve soil biochemical processes by improving soil organic carbon and soil biological indicators in rice‐wheat cropping system. This article is protected by copyright. All rights reserved.
    Print ISSN: 0266-0032
    Electronic ISSN: 1475-2743
    Topics: Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Published by Wiley
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  • 7
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    Sustainability, Vol. 11, Pages 3908: Potential Indicators of Soil Health Degradation in Different Land Use-Based Ecosystems in the Shiwaliks of Northwestern India (2019)
    MDPI
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    Publication Date: 2019
    Description: Identifying the importance of soil biology in different land use systems is critical to assess the present conditions of declining soil (C) and global land degradation while regulating soil health and biogeochemical nutrient cycling. A study was undertaken in a mixed watershed comprising of different land use systems (agricultural, grassland, agroforestry, and eroded); situated in the Shiwalik region in the foot hills of the lower Himalayas in India, a fragile ecosystem susceptible to land degradation. Soil samples from 0–15 and 15–30 cm depths were collected from these land use systems and analyzed for a suite of different soil health indicators, including physio-chemical soil properties, aggregate stability, soil microflora, and the enzymatic activities that are critical for nutrient cycling. Principal component analysis was used to group different land uses and understand their association with soil microflora, enzyme activities, and soil physio-chemical properties. We found that a greater number of soil microflora and enzymatic activities were associated with grassland and agroforestry land use systems. Aggregate-associated soil C correlated well with the soil microflora under different land use systems studied. The biplots revealed that the fungal:bacterial ratio (2 × 103–0.1 × 103) was a robust indicator of C accumulation and soil health, and was in greater association with the agroforestry land use system. Random forest, a non-parametric statistical test, on average explained that 68% to 92% of the variability in soil microbial population was due to land use and other soil health properties. Overall, the biological soil health indicators used in this study demonstrated the fact that land use management systems that employ constant crop cover with minimal disturbance have the potential to improve soil sustainability and ecological functioning.
    Electronic ISSN: 2071-1050
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Published by MDPI
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  • 8
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    Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model (2014)
    American Physical Society (APS)
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    Publication Date: 2014-04-29
    Description: Author(s): Qiaoni Chen, George H. Booth, Sandeep Sharma, Gerald Knizia, and Garnet Kin-Lic Chan We obtain the phase diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2–12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible he... [Phys. Rev. B 89, 165134] Published Mon Apr 28, 2014
    Keywords: Electronic structure and strongly correlated systems
    Print ISSN: 1098-0121
    Electronic ISSN: 1095-3795
    Topics: Physics
    Published by American Physical Society (APS)
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  • 9
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    Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states (2014)
    American Institute of Physics (AIP)
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    Publication Date: 2014-09-20
    Description: We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order wavefunctions so obtained can also be used to compute the third order energy with little overhead. Our formulation has several advantages including (i) flexibility with respect to the choice of zeroth order Hamiltonian, (ii) recovery of the exact uncontracted multi-reference perturbation theory energies in the limit of large MPS bond dimension, (iii) no requirement to compute high body density matrices, (iv) an embarrassingly parallel algorithm (scaling up to the number of virtual orbitals, squared, processors). Preliminary numerical examples show that the MPS bond dimension required for accurate first order wavefunctions scales sub-linearly with the size of the basis.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 10
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    The ab-initio density matrix renormalization group in practice (2015)
    American Institute of Physics (AIP)
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    Publication Date: 2015-01-16
    Description: The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π -electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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