Many reaction pathway finding algorithms require an initial estimate of the minimum energy path (MEP). This initial estimate is usually computed variationally and must be seeded from an even simpler path, where care must be taken to avoid atomic intersections. As an alternative, we estimate the MEP by integrating a velocity vector projected from redundant internal coordinates into the Cartesian manifold. We compare this method to the image dependent pair potential, the geodesic method, linear synchronous transit, and linear Cartesian interpolation. In our first test, rotation of a methyl group in ethane, a zero-temperature string calculation seeded with our method converged to the MEP significantly faster than from any other method. In our second test, HCN$\to$HNC tautomerization, only the geodesic method slightly outperformed ours. In the third test, HONO elimination from dimethylnitramine, our method produced an estimate for the transition state that was geometrically the closest to the true transition state and converged the fastest.

许多反应路径查找算法都需要对最小能量路径（MEP）进行初始估计。通常，该初始估计是可变计算的，并且必须从甚至更简单的路径中获得种子，在该路径中，必须注意避免原子相交。作为替代，我们通过将从冗余内部坐标投影到笛卡尔流形中的速度矢量进行积分来估计MEP。我们将该方法与图像相关对电位，测地线方法，线性同步过渡和线性笛卡尔插值进行了比较。在我们的第一个测试中，乙烷中的甲基旋转（使用我们的方法播种的零温度字符串计算）收敛到MEP的速度明显快于任何其他方法。在我们的第二次测试中，HCN$\to$HNC互变异构，只有短程线法略胜于我们的方法。在第三个测试中，从二甲基亚硝胺中消除HONO，我们的方法对过渡态进行了估算，该过渡态在几何上最接近真实过渡态，并且收敛最快。