Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device.

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L×L lattices with L≤32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.

Identification of genetic markers with synergistic survival effect in cancer.

BACKGROUND: Cancers are complex diseases arising from accumulated genetic mutations that disrupt intracellular signaling networks. While several predisposing genetic mutations have been found, these individual mutations account only for a small fraction of cancer incidence and mortality. With large-scale measurement technologies, such as single nucleotide polymorphism (SNP) microarrays, it is now possible to identify combinatorial effects that have significant impact on cancer patient survival. RESULTS: The identification of synergetic functioning SNPs on genome-scale is a computationally daunting task and requires advanced algorithms. We introduce a novel algorithm, Geninter, to identify SNPs that have synergetic effect on survival of cancer patients. Using a large breast cancer cohort we generate a simulator that allows assessing reliability and accuracy of Geninter and logrank test, which is a standard statistical method to integrate genetic and survival data. CONCLUSIONS: Our results show that Geninter outperforms the logrank test and is able to identify SNP-pairs with synergetic impact on survival.

Contraction of completeness-optimized basis sets: application to ground-state electron momentum densities.

Completeness-optimization is a novel method for the formation of one-electron basis sets. Contrary to conventional methods of basis set generation that optimize the basis set with respect to ground-state energy, completeness-optimization is a completely general, black-box method that can be used to form cost-effective basis sets for any wanted property at any level of theory. In our recent work [J. Lehtola, P. Manninen, M. Hakala, and K. Hämäläinen, J. Chem. Phys. 137, 104105 (2012)] we applied the completeness-optimization approach to forming primitive basis sets tuned for calculations of the electron momentum density at the Hartree-Fock (HF) level of theory. The current work extends the discussion to contracted basis sets and to the post-HF level of theory. Contractions are found to yield significant reductions in the amount of functions without compromising the accuracy. We suggest polarization-consistent and correlation-consistent basis sets for the first three rows of the periodic table, which are completeness-optimized for electron momentum density calculations.

Completeness-optimized basis sets: application to ground-state electron momentum densities.

In the current work we apply the completeness-optimization paradigm [P. Manninen and J. Vaara, J. Comput. Chem. 27, 434 (2006)] to investigate the basis set convergence of the moments of the ground-state electron momentum density at the self-consistent field level of theory. We present a black-box completeness-optimization algorithm that can be used to generate computationally efficient basis sets for computing any property at any level of theory. We show that the complete basis set (CBS) limit of the moments of the electron momentum density can be reached more cost effectively using completeness-optimized basis sets than using conventional, energy-optimized Gaussian basis sets. By using the established CBS limits, we generate a series of smaller basis sets which can be used to systematically approach the CBS and to perform calculations on larger, experimentally interesting systems.

NMR tensors in planar hydrocarbons of increasing size.

(13)C nuclear shielding and (13)C-(13)C spin-spin coupling tensors were calculated using density functional theory linear response methods for a series of planar hydrocarbons. As calculation of the spin-spin coupling is computationally demanding for large molecules due to demands placed on basis-set quality, novel, compact completeness-optimized (co) basis sets of high quality were employed. To maximize the predictive value of the data, the convergence of the co basis sets was compared to well-known basis-set families. The selection of the exchange-correlation functional was performed based on the available experimental data and coupled-cluster calculations for ethene and benzene. The series of hydrocarbons, benzene, coronene, circumcoronene and circumcircumcoronene, was chosen to simulate increasingly large fragments of carbon nanosheets. It was found that the nuclear shielding and the one-, two-, and three-bond spin-spin coupling constants, as well as the corresponding anisotropies with respect to the direction normal to the plane, approach convergence as the number of carbon atoms in the fragment is increased. Predictions of the investigated properties can then be done for the limit of large planar hydrocarbons or carbon nanosheets. From the results obtained with a judicious choice of the functional, PBE, and co basis close to convergence, limiting values are estimated as follows: sigma = 54 +/- 1 ppm [corresponding to the chemical shift of 134 ppm with methane (CH(4)) as a reference], Deltasigma = 207 +/- 4 ppm, (1)J = 59.0 +/- 0.5 Hz, Delta(1)J = -1.5 +/- 0.5 Hz, (2)J = 0.2 +/- 0.4 Hz, Delta(2)J = -4.6 +/- 0.2 Hz, (3)J = 6 +/- 1 Hz, and Delta(3)J = 3 +/- 1 Hz.

Laser-induced nuclear magnetic resonance splitting in hydrocarbons.

Irradiation of matter with circularly polarized light (CPL) shifts all nuclear magnetic resonance (NMR) lines. The phenomenon arises from the second-order interaction of the electron cloud with the optical field, combined with the orbital hyperfine interaction. The shift occurs in opposite directions for right and left CPL, and rapid switching between them will split the resonance lines into two. We present ab initio and density functional theory predictions of laser-induced NMR splittings for hydrocarbon systems with different sizes: ethene, benzene, coronene, fullerene, and circumcoronene. Due to the computationally challenging nature of the effect, traditional basis sets could not be used for the larger systems. A novel method for generating basis sets, mathematical completeness optimization, was employed. As expected, the magnitude of the spectral splitting increases with the laser beam frequency and polarizability of the system. Massive amplification of the effect is also observed close to the optical excitation energies. A much larger laser-induced splitting is found for the largest of the present molecules than for the previously investigated noble gas atoms or small molecules. The laser intensity required for experimental detection of the effect is discussed.

General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory.

With low-order scaling correlated wave function theories in mind, we present second quantization formalism as well as biorthonormalization procedures for general--singular or nonsingular--bases. Of particular interest are the so-called projected atomic orbital bases, which are obtained from a set of atom-centered functions and feature a separation of occupied and virtual spaces. We demonstrate the formalism by deriving and implementing second-order Møller-Plesset perturbation theory in it, and discuss the convergence and preconditioning of the iterative amplitude equations in detail.

Methodological aspects in the calculation of parity-violating effects in nuclear magnetic resonance parameters.

We examine the quantum chemical calculation of parity-violating (PV) electroweak contributions to the spectral parameters of nuclear magnetic resonance (NMR) from a methodological point of view. Nuclear magnetic shielding and indirect spin-spin coupling constants are considered and evaluated for three chiral molecules, H2O2, H2S2, and H2Se2. The effects of the choice of a one-particle basis set and the treatment of electron correlation, as well as the effects of special relativity, are studied. All of them are found to be relevant. The basis-set dependence is very pronounced, especially at the electron correlated ab initio levels of theory. Coupled-cluster and density-functional theory (DFT) results for PV contributions differ significantly from the Hartree-Fock data. DFT overestimates the PV effects, particularly with nonhybrid exchange-correlation functionals. Beginning from third-row elements, special relativity is of importance for the PV NMR properties, shown here by comparing perturbational one-component and various four-component calculations. In contrast to what is found for nuclear magnetic shielding, the choice of the model for nuclear charge distribution--point charge or extended (Gaussian)--has a significant impact on the PV contribution to the spin-spin coupling constants.

Linear-scaling implementation of molecular electronic self-consistent field theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.

Coupled-cluster theory in a projected atomic orbital basis.

We present a biorthogonal formulation of coupled-cluster (CC) theory using a redundant projected atomic orbital (PAO) basis. The biorthogonal formulation provides simple equations, where the projectors involved in the definition of the PAO basis are absorbed in the integrals. Explicit expressions for the coupled-cluster singles and doubles equations are derived in the PAO basis. The PAO CC equations can be written in a form identical to the standard molecular orbital CC equations, only with integrals that are related to the atomic orbital integrals through different transformation matrices. The dependence of cluster amplitudes, integrals, and correlation energy contributions on the distance between the participating atomic centers and on the number of involved atomic centers is illustrated in numerical case studies. It is also discussed how the present reformulation of the CC equations opens new possibilities for reducing the number of involved parameters and thereby the computational cost.

Systematic Gaussian basis-set limit using completeness-optimized primitive sets. A case for magnetic properties.

We discuss the connection between the completeness of a basis set, measured by the completeness profiles introduced by Chong (Can J Chem 1995, 73, 79) at a certain exponent interval, and the possibility of reproducing molecular properties that arise either in the region close to the atomic nuclei or in the valence region. We present a scheme for generating completeness-optimized Gaussian basis sets, in which a preselected range of exponents is covered to an arbitrary accuracy. This is done by requiring Gaussian functions, the exponents of which are selected without reference to the atomic structure, to span the range with completeness profile as close to unity as wanted with as few functions as possible. The initial exponent range can be chosen suitable for calculations of molecular energetics or other valence-like properties. By extending the exponent range, properties requiring augmentation of the basis at a given angular momentum value and/or in a given distance range from the nucleus may be straightforwardly and systematically treated. In this scheme a universal, element-independent exponent set is generated in an automated way. The relation of basis-set completeness and performance in the calculation of magnetizability, nuclear magnetic shielding, and spin-spin coupling is tested with the completeness-optimized primitive sets and literature basis sets.

Perturbational calculations of parity-violating effects in nuclear-magnetic-resonance parameters.

We investigate the effects of the parity-violating electroweak interaction in the spectral parameters of nuclear magnetic resonance. Perturbational theory of parity-violating effects in the nuclear magnetic shielding is presented to the order of G(F)alpha, and in the indirect spin-spin coupling, to the order of G(F)alpha3. These leading-order parity-violating corrections are evaluated using analytical linear-response theory methods based on Hartree-Fock and density-functional theory reference states. Parity-violating contributions to spin-spin couplings are evaluated for the first time at the first-principles level. Calculations are carried out for two chiral halomethanes, bromochlorofluoromethane and bromofluoroiodomethane.

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors.

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

Perturbational relativistic theory of electron spin resonance g-tensor.

We carry out a complete treatment of the leading-order relativistic one-electron contributions, arising from the Breit-Pauli Hamiltonian, to the g-tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the F2(-), Cl2(-), Br2(-), and I2(-) series, using analytical response theory calculations with a multiconfigurational self-consistent field reference state. The results are compared to available experimental data. (c) 2004 American Institute of Physics

Determination of semivolatile compounds in Baltic herring (Clupea harengus membras) by supercritical fluid extraction-supercritical fluid chromatography-gas chromatography-mass spectrometry.

The on-line supercritical fluid extraction-supercritical fluid chromatography-gas chromatography method was applied to the determination of volatile compounds of raw and baked Baltic herring (Clupea harengus membras). The analytes were extracted with supercritical carbon dioxide at 45 degrees C and 10 MPa pressure. After extraction, the volatiles and coeluted lipids were separated on-line using supercritical fluid chromatography and the volatile fraction was introduced directly into a gas chromatograph. In all, 30 compounds were identified from fish samples with mass spectrometry. The most abundant compounds in the fresh Baltic herrings were heptadecane and 1-heptadecene. When the fish were stored for 3-6 days at 6 degrees C, the total peak area of the volatiles began to increase and the proportions of short chain acids (acetic, propanoic, 2-methylpropanoic, and 3-methylbutanoic) also increased. After 8-9 days of storage, 3-methylbutanoic acid comprised about 36 and 40% of all volatiles in raw and baked herring, respectively.