QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:  B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic−aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid)...

Density functionals with broad applicability in chemistry.

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry--calculating the ground-state molecular energy for He-H(+). The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.

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A variational eigenvalue solver on a photonic quantum processor

A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations GGAs for exchange by Becke B and for correlation by Lee, Yang, and Parr LYP with Hartree-Fock HF exchange and a perturbative second-order correlation part PT2 that is obtained from the Kohn-Sham GGA orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange ax and of the PT2 and GGA correlation c, respectively. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large 53% with c=27% which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult including transition-metal compounds, weakly bonded complexes, and reaction barriers and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, respectively, for the best other density functionals. Very importantly, also the maximum and minium errors outliers are strongly reduced by about 10‐20 kcal/mol. Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of virtual orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose. © 2006 American Institute of Physics. DOI: 10.1063/1.2148954

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Semiempirical hybrid density functional with perturbative second-order correlation

The torsional potential function for butane was probed theoretically using increasingly complete basis sets (up to 840 functions) and treatments of electron correlation [up to the CCSD(T) method] until it was shown that the sequence of relative energies approached convergence. The Schrodinger limit in the Born–Oppenheimer approximation was thus estimated. The equilibrium energies relative to the anti conformation (ΔEe) as obtained by this focal-point extrapolation were 0.62, 3.31, and 5.51 kcal mol−1 for the geometrically optimized stationary points having carbon backbone torsion angles of 64.8°, 119.6°, and 0°, respectively. The final prediction of the anti–syn difference is 5.40±0.15 kcal mol−1. Some consequences of this result are discussed.

The torsional conformations of butane: Definitive energetics from ab initio methods

This paper reports a comprehensive theoretical examination of the re and r0 geometrical structures, harmonic and anharmonic vibrational frequencies, and infrared intensities ofX2Π SiH, X 1A1, a 3B1, and A1B1 SiH2, X2A1 SiH3, and X1A1 SiH4. Both self-consistent-field (SCF) and configuration interaction singles and doubles (CISD) methods have been employed with two basis sets (B1 and B2) of double-zeta plus polarization (DZ +P) and triple-zeta plus double polarization (TZ+2P) quality. For SiH the B2 CISD parameters re = 1.5214 A, r0 = 1.5326 A, ωe = 2062 cm−1, and v0 = 1985 cm−1 are in excellent agreement with the experimental values re = 1.5201 A, r0 = 1.5313 A, ωe = 2042 cm−1, and v0 = 1971 cm−1. The B2 CISD αi rovibrational constants for SiH2D2, SiH4, SiD4, and SiHD3 when utilized to correct experimental A0, B0, and C0 rotational constants give re = 1.4735 A for SiH4. With the same procedure, re(SiH) = 1.5141 A and θe (HSiH) = 92.0° are found for X 1A1 SiH2, and re(SiH) = 1.4871 A and θe(HSiH) = 121.8° are found for A1B1 SiH2. All of these experimentally derived re parameters are in excellent agreement with the B2 CISD re structures for X 1A1 SiH4, X1A1 SiH2, and A1B1 SiH2. For a3B1 SiH2, re = 1.4768 A, θe = 118.3°, and Te = 19.6 kcal/mol are predicted. The B2 CISD harmonic vibrational frequencies for the SiH stretches of SiH4 are only 1–2% too large, and the corresponding theoretical anharmonicities are in error by less than 7 cm−1. Using the SiH4 data to separately scale the B2 CISD ω3 and x3 values for X1A1 SiH2, ν3 = 1981 cm−1 is obtained, which confirms the recent experimental frequencies of Fredin, Hauge, Kafafi, and Margrave. In a similar fashion ν1 = 2117 cm−1, ν2 = 892 cm−1, and ν3 = 2180 cm−1 are predicted for a3B1 SiH2 and ν1 = 2016 cm−1 and ν3 = 2115 cm−1 for A1B1 SiH2. The B2 CISD geometrical parameters for X2A1 SiH3 are re(SiH) = 1.4768 A and θe(HSiH) = 111.1°, and the final (scaled) B2 CISD fundamental frequencies are ν1 = 2150 cm−1, ν2 = 773 cm−1, ν3 = 2180 cm−1, and ν4 = 933 cm−1. These frequencies definitely show that the 1999, 1955, and 996 cm−1 IR absorptions of Milligan and Jacox are not attributable to SiH3. Finally, at the highest level of theory used here, a classical inversion barrier of 5.8 kcal/mol is obtained for SiH3.

Geometrical structures, force constants, and vibrational spectra of SiH, SiH2, SiH3, and SiH4

The geometries, energies, and vibrational frequencies of the reactants, transition states, intermediates, and products of the reaction of ethyl radical with the oxygen molecule have been examined using density functional theory (DFT). Rather different theoretical predictions are obtained from the BLYP, B3LYP, and BHLYP methods. Comparisons with experimental deductions and high-level coupled cluster results suggest that the B3LYP method is superior for the C2H5+O2 problem. Using the B3LYP method with a triple-zeta plus double-polarization plus f function (TZ2Pf) basis set, a transition state between the ethylperoxy radical and products is discovered which lies 3.3 kcal mol−1 below reactants. This transition-state energy is consistent with the observed high yields of ethylene in the high-temperature reaction and is in good agreement with the height of the barrier estimated via modeling of the experimental kinetic data. However, this transition state (TS1) corresponds not to the internal proton transfer lead...

Mechanism of the C2H5+O2 reaction

The effects of Hartree–Fock orbital instabilities on force constant predictions at both Hartree–Fock and correlated levels of theory are investigated. Due to the quadratic dependence of the second derivative of correlated energies on the orbital rotation parameters, anomalous force constant singularities enveloped by “instability volcanoes” are given by the single-reference correlation methods examined here. Infinite-order coupled-cluster methods are indeed affected by the reference instability, but over a rather small region of the potential surface, whereas perturbative triples corrections tend to widen the coupled-cluster volcano. Finite-order many-body perturbation theory yields very wide volcanoes, and corresponding predictions of vibrational spectra may be seriously compromised if the geometry of interest lies at all in the vicinity of an instability in the reference determinant.

Hartree-Fock orbital instability envelopes in highly correlated single-reference wave functions

Structures, accurate relative energies, equilibrium and vibrationally averaged rotational constants, quartic and sextic centrifugal distortion constants, dipole moments, (14)N nuclear quadrupole coupling constants, anharmonic vibrational frequencies, and double-harmonic infrared intensities have been determined from ab initio electronic structure computations for conformers of the neutral form of the natural amino acid l-cysteine (Cys). A systematic scan located 71 unique conformers of Cys using the MP2(FC)/cc-pVTZ method. The large number of structurally diverse low-energy conformers of Cys necessitates the highest possible levels of electronic structure theory to determine their relative energies with some certainty. For this reason, we determined the relative energies of the lowest-energy eleven conformers, accurate within a standard error (1σ) of about 0.3 kJ mol(-1), through first-principles composite focal-point analyses (FPA), which employed extrapolations using basis sets as large as aug-cc-pV(5+d)Z and correlation treatments as extensive as CCSD(T). Three and eleven conformers of l-cysteine fall within a relative energy of 6 and 10 kJ mol(-1), respectively. The vibrationally averaged rotational constants computed in this study agree well with Fourier-transform microwave spectroscopy results. The effects determining the relative energies of the low-energy conformers of cysteine are analyzed in detail on the basis of hydrogen bond additivity schemes and natural bond orbital analysis.

Wesley D. Allen

Papers

The torsional conformations of butane: Definitive energetics from ab initio methods

Geometrical structures, force constants, and vibrational spectra of SiH, SiH2, SiH3, and SiH4

Mechanism of the C2H5+O2 reaction

Hartree-Fock orbital instability envelopes in highly correlated single-reference wave functions

Conformers of Gaseous Cysteine.