π-Conjugation in <i>trans</i>-1,3-Butadiene: Static and Dynamical Electronic Correlations Described through Quantum Monte Carlo

Barborini, Matteo; Guidoni, Leonardo

doi:10.1021/ct501157f

Cited by 16 publications

(46 citation statements)

References 57 publications

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“… 35 , 38 − 40 In the present work, we study the convergence of the structural properties of PA chains through VMC methods with the JAGP wave function. With a relatively small basis set we are able to give converged structural parameters, verified also at the Diffusion Monte Carlo (DMC) level, 41 and an extrapolated value of the BLA for infinite chains which is compatible with the experimental measurements. 7 − 9 We will also address the question of how electronic correlation affects the convergence of the degree of conjugation as the length of the PA chains grows, distinguishing between the contributions given by the various elements of our JAGP wave function.…”

Section: Introductionsupporting

confidence: 61%

“…For example, the coefficients associated with the p z atomic orbitals, orthogonal to the molecular plane, modulate the π coupling in the PA chains. 41 This ansatz is a multi-determinantal expansion, that includes a constraint set of molecular excitations. 41 , 48 , 49 This can be seen by diagonalizing the Geminal expansion ( eq 1 ), projecting it on a set of orthogonalized molecular orbitals built as the linear combination of the primitive orbitals that appear in eq 1 : …”

Section: Computational Approachmentioning

confidence: 99%

“…Still, by studying the modulation of the λ̃ in the expansion, it can be possible to extract informations able to help the characterization of the chemical electronic state of the molecule, as done, for example, for the diradical species in refs ( 36 and 48 ). The particularity of the JAGP ansatz is that it contains in its variational space three chemical states of the PA chains 41 summarized in Figure 1 : the highly dimerized ground state, which is typical of the HF solution; the resonating electronic state 50 in the limit of null BLA and characteristic of the metallic phase for infinite chains; and the diradical state, 48 which inverts the single and double carbon bonds in finite chains, localizing two unpaired electrons on each CH 2 ending group. As discussed in ref ( 41 ), the presence of these possible chemical states guarantees that the JAGP is able to contain all the static correlation necessary for the description of the π conjugation on PA chains, and in particular, it is able to connect the state with finite BLA (observed experimentally) to that of zero BLA in the limit of conductive chains, with degenerate HOMO and LUMO orbitals.…”

Section: Computational Approachmentioning

confidence: 99%

“…The particularity of the JAGP ansatz is that it contains in its variational space three chemical states of the PA chains 41 summarized in Figure 1 : the highly dimerized ground state, which is typical of the HF solution; the resonating electronic state 50 in the limit of null BLA and characteristic of the metallic phase for infinite chains; and the diradical state, 48 which inverts the single and double carbon bonds in finite chains, localizing two unpaired electrons on each CH 2 ending group. As discussed in ref ( 41 ), the presence of these possible chemical states guarantees that the JAGP is able to contain all the static correlation necessary for the description of the π conjugation on PA chains, and in particular, it is able to connect the state with finite BLA (observed experimentally) to that of zero BLA in the limit of conductive chains, with degenerate HOMO and LUMO orbitals. Even though it was demonstrated in ref ( 41 ) that the dominant contribution to the description of the conjugation of trans -1,3-butadiene is due to the dynamical electronic correlation , it is still unclear how the inclusion of higher order molecular orbitals in the multi-determinantal expansion contributes to the description of the conjugation for larger PA chains in which the BLA gradually decreases.…”

Section: Computational Approachmentioning

confidence: 99%

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Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Barborini

Guidoni

2015

J. Chem. Theory Comput.

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Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H–(C2H2)N–H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508–517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.

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Section: Introductionsupporting

confidence: 61%

Section: Computational Approachmentioning

confidence: 99%

Section: Computational Approachmentioning

confidence: 99%

Section: Computational Approachmentioning

confidence: 99%

See 2 more Smart Citations

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Barborini

Guidoni

2015

J. Chem. Theory Comput.

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“…To elucidate the origin of this difference, we consider here various expansions correlating the π and σ electrons: a) a single determinant; b) the complete-active-space CAS(4,4), CAS (4,16), and CAS(4,20) expansions (20, 7232, and 18100 determinants, respectively) of the four π electrons in the bonding and antibonding π orbitals constructed from the 2p z , 3p z , 3d xz , 3d yz , and 4p z atomic orbitals; c) a CAS(10,10) correlating the six σ and four π electrons of the carbon atoms in the corresponding bonding and antibonding π and σ orbitals (15912 determinants); d) the same CAS ( 1 det / JAGP [19] BLA (Å) basis set truncated with a threshold of 2×10 −4 on the coefficients of the spin-adapted configuration state functions. This last choice results in a total of 45644 determinants and is denoted as a restricted-active-space RAS(10,22) expansion.…”

Section: Numerical Resultsmentioning

confidence: 99%

Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions

Assaraf

Moroni

Filippi

2017

J. Chem. Theory Comput.

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We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g., the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number N of Slater determinants, the numerical scaling of O(N) per derivative we have recently reported is here lowered to O(N) for the entire set of derivatives. As a function of the number of electrons N, the scaling to optimize the wave function and the geometry of a molecular system is lowered to O(N) + O(NN), the same as computing the energy alone in the sampling process. The scaling is demonstrated on linear polyenes up to CH and the efficiency of the method is illustrated with the structural optimization of butadiene and octatetraene with Jastrow-Slater wave functions comprising as many as 200 000 determinants and 60 000 parameters.

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DFT studies on the structural and vibrational properties of polyenes

et al. 2016

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Detailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C = C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae. BLYP/6-311++G** calculated ν(C = C) and ν(C–C) frequencies for all-trans and all-cis polyenes containing up to 14 carbon–carbon double bonds were used to estimate these values for very long chains. Correction of raw, unscaled vibrational data was performed by comparing theoretical and experimental wavenumbers for polyenes chains containing 3 to 12 conjugated C = C units with both ends substituted by tert-butyl groups. The corrected ν(C = C) and ν(C–C) wavenumbers for all-trans molecules were used to estimate the presence of 9 – 12 C = C units in all-trans polyene pigment in red coral.Graphical abstractDetailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C=C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae.Electronic supplementary materialThe online version of this article (doi:10.1007/s00894-016-2969-1) contains supplementary material, which is available to authorized users.

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π-Conjugation in trans-1,3-Butadiene: Static and Dynamical Electronic Correlations Described through Quantum Monte Carlo

Cited by 16 publications

References 57 publications

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions

DFT studies on the structural and vibrational properties of polyenes

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