We compute vibrational energy levels using Gaussian basis functions whose centers are in slabs that include the lower-dimensional hyperplanes on which the Multimode approximation to the potential is based. We use more potential points than basis functions to increase the accuracy. The number of Gaussian basis functions is smaller than the number required using the best existing methods. For formaldehyde, the first 50/100 levels we compute, using 30,000 Gaussians and 120,000 points, in 4D-like slabs, differ from numerically exact levels by 0.3/0.6 cm⁻¹ (mean absolute error). With 3D-like slabs, the mae for the first 50/100 levels is 0.17/0.47 cm⁻¹ with 30,000 basis functions and 0.95/2.06 cm⁻¹ with 20,000 basis functions. Although we use a multimode-like idea to select Gaussian centers, we use a single point set and there is no need to write the potential in multimode form and no need to neglect high-order terms.

我们使用高斯基函数来计算振动能级，高斯基函数的中心在包含低维超平面的平板中，该平面是势能的多模近似所基于的。我们使用比基函数更多的潜在点来提高准确性。高斯基函数的数量小于使用最佳现有方法所需的数量。对于甲醛，在4D样板中，我们使用30,000高斯和120,000点计算的前50/100水平与精确数值水平相差0.3 / 0.6 cm ^-1（平均绝对误差）。对于类似3D的平板，前50/100级的mae为0.17 / 0.47 cm ^-1（具有30,000基函数）和0.95 / 2.06 cm ^-1具有20,000个基本功能。尽管我们使用类似多模的思想来选择高斯中心，但是我们使用单点集，因此无需以多模形式书写电势，也无需忽略高阶项。