Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon

The band structure of silicon is calculated at the Gamma, X, and L wave vectors using diffusion quantum Monte Carlo methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low lying excitations in solids.Comment: 5 pages, 1 figur

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.Comment: 15 pages, 6 figures. To appear in Phys. Rev.

Quantum Monte Carlo calculation of Compton profiles of solid lithium

Recent high resolution Compton scattering experiments in lithium have shown significant discrepancies with conventional band theoretical results. We present a pseudopotential quantum Monte Carlo study of electron-electron and electron-ion correlation effects on the momentum distribution of lithium. We compute the correlation correction to the valence Compton profiles obtained within Kohn-Sham density functional theory in the local density approximation and determine that electronic correlation does not account for the discrepancy with the experimental results. Our calculations lead do different conclusions than recent GW studies and indicate that other effects (thermal disorder, core-valence separation etc.) must be invoked to explain the discrepancy with experiments.Comment: submitted to Phys. Rev.

Variational quantum Monte Carlo calculations for solid surfaces

Quantum Monte Carlo methods have proven to predict atomic and bulk properties of light and non-light elements with high accuracy. Here we report on the first variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking the boundary condition for the simulation from a finite layer geometry, the Hamiltonian, including a nonlocal pseudopotential, is cast in a layer resolved form and evaluated with a two-dimensional Ewald summation technique. The exact cancellation of all Jellium contributions to the Hamiltonian is ensured. The many-body trial wave function consists of a Slater determinant with parameterized localized orbitals and a Jastrow factor with a common two-body term plus a new confinement term representing further variational freedom to take into account the existence of the surface. We present results for the ideal (110) surface of Galliumarsenide for different system sizes. With the optimized trial wave function, we determine some properties related to a solid surface to illustrate that VMC techniques provide standard results under full inclusion of many-body effects at solid surfaces.Comment: 9 pages with 2 figures (eps) included, Latex 2.09, uses REVTEX style, submitted to Phys. Rev.

Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.Comment: 13 pages, 4 figures. To appear in Phys. Rev.

Objectively-assessed neighbourhood destination accessibility and physical activity in adults from 10 countries : an analysis of moderators and perceptions as mediators

Rationale: Residents of neighbourhoods with high destination accessibility (higher population density, more interconnected streets, and better access to services, public transport and parks) are more physically active. Evidence on the factors that underlie these associations is sparse and inconsistent. Objective: We examined (1) five socio-demographic and four non-destination perceived neighbourhood attributes as moderators of the relationship between objectively-assessed destination accessibility and moderate-to vigorous physical activity (MVPA); (2) perceived indicators of destination accessibility as mediators of those relationships; and, (3) the generalizability of findings across 14 cities. Methods: Data were from the International Physical Activity and Environment Network (IPEN) Adult study (N = 6822), which provided comparable objective and perceived environmental variables and accelerometer based MVPA from 14 cities across 10 countries. Mediation and mediation moderation analyses were performed. Results: Objective net residential density, public transport density, and number of parks in the neighbourhood were consistently associated with MVPA across all examined socio-demographic groups and non-destination perceived neighbourhood characteristics. However, only the association between number of parks and MVPA was mediated by its conceptually-comparable perceived indicator. While the associations of objective intersection density and land use mix with MVPA were moderated by both gender and perceived pedestrian infrastructure/safety, only the latter moderating effects were mediated by the conceptually-comparable perceived indicators. Perceived neighbourhood safety and/or aesthetics moderated the associations of objective ratio of retail/civic land to total area and distance to nearest transport stop with MVPA. These associations were not mediated by the conceptually-comparable perceived indicators. Conclusion: Densely populated neighbourhoods with access to public transport and parks have the potential to significantly and equitably contribute to adults' MVPA on a global scale. Perceived neighbourhood aesthetics, pedestrian-friendliness and safety can magnify the positive effects of mixed-use neighbourhoods on residents' MVPA by interacting with the perceived ease of access to a variety of destinations

Do associations of sex, age and education with transport and leisure-time physical activity differ across 17 cities in 12 countries?

Background: Leisure-time and transport activity domains are studied most often because they are considered more amenable to intervention, but to date evidence on these domains is limited. The aim of the present study was to examine patterns of socio-demographic correlates of adults’ leisure-time and transport physical activity and how these associations varied across 17 cities in 12 countries. Methods: Participants (N = 13,745) aged 18–66 years in the IPEN Adult study and with complete data on sociodemographic and self-reported physical activity characteristics were included. Participants reported frequency and duration of leisure-time and transport activities in the last 7 days using the self-administered International Physical Activity Questionnaire-Long Form. Six physical activity outcomes were examined in relation with age, education, and sex, and analyses explored variations by city and curvilinear associations. Results: Sex had the most consistent results, with five of six physical activity outcomes showing females were less active than males. Age had the most complex associations with self-report transport and leisure-time physical activity. Compared to older people, younger adults were less likely to engage in transport physical activity, but among those who did, younger people were likely to engage in more active minutes. Curvilinear associations were found between age and all three leisure-time physical activity outcomes, with the youngest and the oldest being more active. Positive associations with education were found for leisure-time physical activity only. There were significant interactions of city with sex and education for multiple physical activity outcomes. Conclusions: Although socio-demographic correlates of physical activity are widely studied, the present results provide new information. City-specific findings suggest there will be value in conducting more detailed case studies. The curvilinear associations of age with leisure-time physical activity as well as significant interactions of leisure-time activity with sex and education should be further investigated. The findings of lower leisure-time physical activity among females as well as people with low education suggest that greater and continued efforts in physical activity policies and programs tailored to these high-risk groups are needed internationally

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Physical activity in relation to urban environments in 14 cities worldwide: a cross-sectional study

Background Physical inactivity is a global pandemic responsible for over 5 million deaths annually through its effects on multiple non-communicable diseases. We aimed to document how objectively measured attributes of the urban environment are related to objectively measured physical activity, in an international sample of adults. Methods We based our analyses on the International Physical activity and Environment Network (IPEN) adult study, which was a coordinated, international, cross-sectional study. Participants were sampled from neighbourhoods with varied levels of walkability and socioeconomic status. The present analyses of data from the IPEN adult study included 6822 adults aged 18–66 years from 14 cities in ten countries on five continents. Indicators of walkability, public transport access, and park access were assessed in 1·0 km and 0·5 km street network buffers around each participant's residential address with geographic information systems. Mean daily minutes of moderate-to-vigorous-intensity physical activity were measured with 4–7 days of accelerometer monitoring. Associations between environmental attributes and physical activity were estimated using generalised additive mixed models with gamma variance and logarithmic link functions. Results Four of six environmental attributes were significantly, positively, and linearly related to physical activity in the single variable models: net residential density (exp[b] 1·006 [95% CI 1·003–1·009]; p=0·001), intersection density (1·069 [1·011–1·130]; p=0·019), public transport density (1·037 [1·018–1·056]; p=0·0007), and number of parks (1·146 [1·033–1·272]; p=0·010). Mixed land use and distance to nearest public transport point were not related to physical activity. The difference in physical activity between participants living in the most and least activity-friendly neighbourhoods ranged from 68 min/week to 89 min/week, which represents 45–59% of the 150 min/week recommended by guidelines. Interpretation Design of urban environments has the potential to contribute substantially to physical activity. Similarity of findings across cities suggests the promise of engaging urban planning, transportation, and parks sectors in efforts to reduce the health burden of the global physical inactivity pandemic. Funding Funding for coordination of the IPEN adult study, including the present analysis, was provided by the National Cancer Institute of National Institutes of Health (CA127296) with studies in each country funded by different sources

Associations of built environment and proximity of food outlets with weight status:Analysis from 14 cities in 10 countries

The study aimed to examine associations of neighborhood built environments and proximity of food outlets (BE measures) with body weight status using pooled data from an international study (IPEN Adult). Objective BE measures were calculated using geographic information systems for 10,008 participants (4463 male, 45%) aged 16-66 years in 14 cities. Participants self-reported proximity to three types of food outlets. Outcomes were body mass index (BMI) and overweight/obesity status. Male and female weight status associations with BE measures were estimated by generalized additive mixed models. Proportion (95% CI) of overweight (BMI 25 to = 30) from 2.9% (1.3, 4.4) to 31.3% (27.7, 34.7), with Hong Kong being the lowest and Cuernavaca, Mexico highest for both proportions. Results differed by sex. Greater street intersection density, public transport density and perceived proximity to restaurants (males) were associated with lower odds of overweight/obesity (BMI >= 25). Proximity to public transport stops (females) was associated with higher odds of overweight/obesity. Composite BE measures were more strongly related to BMI and overweight/obesity status than single variables among men but not women. One standard deviation improvement in the composite measures of BE was associated with small reductions of 0.1-0.5% in BMI but meaningful reductions of 2.5-5.3% in the odds of overweight/obesity. Effects were linear and generalizable across cities. Neighborhoods designed to support public transport, with food outlets within walking distance, may contribute to global obesity control